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FREE 10+ Problem Solving Report Samples in PDF | DOC

10+ Problem Solving Report Samples

Whether it may be for personal or professional reasons , problem solving skills are very important to have. Being good at problem solving shows a scope of different abilities like flexibility, creativity , and logic . What’s more, it helps you figure out how to take a gander at challenges through a new viewpoint. This is why they let little children constantly practice their problem solving skills at school , and why employers value these skills just as much. So, to assist you with your career or home life, here are free examples of Problem Solving Report . Continue reading to discover more!

Problem Solving Report

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Problem solving is a psychological and methodical process that includes finding, dissecting, and taking care of issues. The Problem Solving Report helps you to understand what’s going on in your current circumstance, distinguish things you need to change and then sort out the things that should be done to make the ideal result. This way, it is easier for you to make educated decisions, which will cause your work and daily life to be much better.

Employers value problem-solving abilities because they demonstrate a variety of other qualities such as logic, creativity, resilience, imagination, lateral thinking, and determination. It’s an important talent to have in both your career and personal life. Aside from the variety of free Problem Solving Report template that is provided above, you can also make one of your own! Here are some general steps you should remember in making a Problem Solving Report:

As you identify the issue, specifically make sure that you are looking for the core problem, as the effects could be mistaken as the root cause in a very major way. Additionally, it is vital to literally look at this objectively, and to separate the facts from opinion. This really is why the needed data and information should mostly be taken into account. They are quite significant. Also, don’t forget to review how current processes work and in which the problem actually stands. Flowcharts could be incorporated to distinguish the normal strides of a process and to characterize and dissect very main drivers.

It is very helpful if you come up with various alternatives to your problem. This could be done through brainstorming, specifically with a group that includes all the people involved in the problem. In this step, the generation of ideas must be the main priority; the evaluation must be delayed until the next step. So, even when the proposed alternative doesn’t seem like it’s the best, list it down and consider it later. Just make sure that it is in line with the main objective. If you do it this way, there would be room for acquiring genuine improvement and at the same time, gaining a new lesson, which could be valuable for the future.

When choosing alternatives, choose one that will not only work the problem out but will also not bring about another unnecessary one. Of course, there should be no bias, so you must make sure that all those that are involved accept the considered alternative. This alternative must also be realistic to your given circumstance. You should assess all of the possible effects if this solution were to take place. Leave no room for confusion and doubt by being clear with everything the solution entails.

To carry out the solution properly, you must first do a test run and accumulate input from those influenced by it. If there is consensus from them, then you can proceed into setting up continuous measures. After all of that, asses the long haul results of this alternative. Notwithstanding how the solution is carried out, input channels ought to be incorporated into the execution. This takes constant observing and testing. Solutions are best if it stays and is refreshed to react to future changes.

Problems are rarely handled on one’s own, therefore possessing complicated problem-solving skills is advantageous when working with others. This keeps the team focused on actual solutions and prevents them from becoming distracted by potentially impossible ideas.

A report’s goal is to give facts about a subject in a straightforward and objective manner.

To handle the myriad difficulties that arise in the workplace, problem solving models are applied. Using a shared, collaborative, and methodical approach to problem solving, complex difficulties for teams, working groups, and boards, for example, are frequently solved more quickly.

Problem solving is the root of the progress we made as a society; therefore, to practice our skills in this area is to ensure a great future ahead of us. Download our free, editable, and printable samples of Problem Solving Reports develop better problem solvers, and in turn, an improved world.

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What is 8D? A template for efficient problem-solving

How you respond when problems arise is one of the most defining qualities of a manager. Luckily, there are tools you can use to master problem-solving. The 8D method of problem-solving combines teamwork and basic statistics to help you reach a logical solution and prevent new issues from arising.

You’ve spent months overseeing the development of your company's newest project. From initiation, planning, and execution, you’re confident this may be your best work yet.

Until the feedback starts rolling in.

There’s no sugar-coating it—things don’t always go as planned. But production or process issues are hardly a signal to throw in the towel. Instead, focus on honing your problem-solving skills to find a solution that keeps it from happening again. 

The 8D method of problem solving emphasizes the importance of teamwork to not only solve your process woes but prevent new ones from occurring. In this guide, we’ll break down what 8D is, how to use this methodology, and the benefits it can give to you and your team. Plus, get an 8D template to make solving your issue easier. 

What is 8D?

The eight disciplines (8D) method is a problem-solving approach that identifies, corrects, and eliminates recurring problems. By determining the root causes of a problem, managers can use this method to establish a permanent corrective action and prevent recurring issues. 

How do you use the 8D method?

The 8D method is a proven strategy for avoiding long-term damage from recurring problems. If you’re noticing issues in your workflow or processes, then it’s a good time to give this problem-solving method a try. 

To complete an 8D analysis, follow “the eight disciplines” to construct a statistical analysis of the problem and determine the best solution.

The eight disciplines of problem-solving

8D stands for the eight disciplines you will use to establish an 8D report. As you may notice, this outline starts with zero, which makes nine total disciplines. The “zero stage” was developed later as an initial planning stage. 

To illustrate these steps, imagine your organization experienced a decline in team innovation and productivity this past year. Your stakeholders have noticed and want to see changes implemented within the next six months. Below, we’ll use the 8D process to uncover a morale-boosting solution.

D0: Prepare and plan

Before starting the problem-solving process, evaluate the problem you want to solve. Understanding the background of the problem will help you identify the root cause in later steps. 

Collect information about how the problem has affected a process or product and what the most severe consequences may be. Planning can include:

Gathering data

Determining the prerequisites for solving the problem

Collecting feedback from others involved

If we look back at our example, you may want to figure out whether this decline in morale is organization-wide or only applies to a few departments. Consider interviewing a few employees from different departments and levels of management to gain some perspective. Next, determine what knowledge and skills you will need to solve this lapse in productivity. 

D1: Form your team

Create a cross-functional team made up of people who have knowledge of the various products and workflows involved. These team members should have the skills needed to solve the problem and put corrective actions in place. 

Steps in this discipline may include:

Appointing a team leader

Developing and implementing team guidelines

Determining team goals and priorities

Assigning individual roles

Arranging team-building activities

From our example, a solid team would consist of people with first-hand experience with the issues—like representatives from all departments and key people close to workshop-level work. You may also want to pull someone in from your HR department to help design and implement a solution. Most importantly, make sure the people you choose want to be involved and contribute to the solution.

D2: Identify the problem

You may have a good understanding of your problem by now, but this phase aims to break it down into clear and quantifiable terms by identifying the five W’s a and two H’s (5W2H):

Who first reported the problem?

What is the problem about?

When did it occur and how often?

Where did it occur (relating to the sector, supplier, machine, or production line involved)?

Why is solving the problem important?

How was the problem first detected?

How many parts/units/customers are affected?

Use your team’s insights to answer these questions. From our example, your team may conclude that: 

Employees feel overwhelmed with their current workload. 

There is no real structure or opportunity to share new ideas.

Managers have had no training for meetings or innovation settings.

Disgruntled employees know they can achieve more—and want to achieve more—even if they seem disengaged.

Once you answer these questions, record an official problem statement to describe the issue. If possible, include photos, videos, and diagrams to ensure all parties have a clear understanding of the problem. It may also help to create a flowchart of the process that includes various steps related to the problem description.

D3: Develop an interim containment plan

Much like we can expect speedy first aid after an accident, your team should take immediate actions to ensure you contain the problem—especially if the problem is related to customer safety. 

An interim containment plan will provide a temporary solution to isolate the problem from customers and clients while your team works to develop a permanent corrective action. This band-aid will help keep your customers informed and safe—and your reputation intact.

Because your findings revealed workers were overworked and managers lacked training, your team suggests scheduling a few mandatory training sessions for leaders of each department covering time and stress management and combating burnout . You may also want to have a presentation outlining the topics of this training to get key managers and stakeholders interested and primed for positive upcoming changes. 

D4: Verify root causes and escape points

Refer back to your findings and consult with your team about how the problem may have occurred. The root cause analysis involves mapping each potential root cause against the problem statement and its related test data. Make sure to test all potential causes—fuzzy brainstorming and sloppy analyses may cause you to overlook vital information. 

In our example, focus on the “why” portion of the 5W2H. You and your team identify six root causes:

Managers have never had any training

There is a lack of trust and psychological safety

Employees don’t understand the objectives and goals

Communication is poor

Time management is poor

Employees lack confidence

In addition to identifying the root causes, try to pinpoint where you first detected the problem in the process, and why it went unnoticed. This is called the escape point, and there may be more than one. 

D5: Choose permanent corrective actions

Work with your team to determine the most likely solution to remove the root cause of the problem and address the issues with the escape points. Quantitatively confirm that the selected permanent corrective action(s) (PCA) will resolve the problem for the customer. 

Steps to choosing a PCA may include:

Determining if you require further expertise

Ensuring the 5W2Hs are defined correctly

Carrying out a decision analysis and risk assessment

Considering alternative measures

Collecting evidence to prove the PCA will be effective

Your team decides to roll out the training used in the interim plan to all employees, with monthly company-wide workshops on improving well-being. You also plan to implement meetings, innovation sessions, and team-coaching training for managers. Lastly, you suggest adopting software to improve communication and collaboration. 

D6: Implement your corrective actions

Once all parties have agreed on a solution, the next step is to create an action plan to remove the root causes and escape points. Once the solution is in effect, you can remove your interim containment actions.

After seeing success with the training in the interim phase, your stakeholders approve all of your team’s proposed PCAs. Your representative from HR also plans to implement periodic employee wellness checks to track employee morale .

To ensure your corrective action was a success, monitor the results, customer, or employee feedback over a long period of time and take note of any negative effects. Setting up “controls” like employee wellness checks will help you validate whether your solution is working or more needs to be done. 

D7: Take preventive measures

One of the main benefits of using the 8D method is the improved ability to identify necessary systematic changes to prevent future issues from occurring. Look for ways to improve your management systems, operating methods, and procedures to not only eliminate your current problem, but stop similar problems from developing later on.

Based on our example, the training your team suggested is now adopted in the new manager onboarding curriculum. Every manager now has a “meeting system” that all meetings must be guided by, and workloads and projects are managed as a team within your new collaboration software . Innovation is improving, and morale is at an all-time high!

D8: Celebrate with your team

The 8D method of problem-solving is impossible to accomplish without dedicated team members and first-class collaboration. Once notes, lessons, research, and test data are documented and saved, congratulate your teammates on a job well done! Make an effort to recognize each individual for their contribution to uncovering a successful solution.

8D report template and example

Check out our 8D report template below to help you record your findings as you navigate through the eight disciplines of problem solving. This is a formal report that can be used as a means of communication within companies, which makes for transparent problem-solving that you can apply to the entire production or process chain.

Benefits of using the 8D method

The 8D method is one of the most popular problem-solving strategies for good reason. Its strength lies in teamwork and fact-based analyses to create a culture of continuous improvement —making it one of the most effective tools for quality managers. The benefits of using the 8D method include: 

Improved team-oriented problem-solving skills rather than relying on an individual to provide a solution

Increased familiarity with a problem-solving structure

A better understanding of how to use basic statistical tools for problem-solving

Open and honest communication in problem-solving discussions

Prevent future problems from occurring by identifying system weaknesses and solutions

Improved effectiveness and efficiency at problem-solving

Better collaboration = better problem solving

No matter how good a manager you are, production and process issues are inevitable. It’s how you solve them that separates the good from the great. The 8D method of problem solving allows you to not only solve the problem at hand but improve team collaboration, improve processes, and prevent future issues from arising. 

Try Asana’s project management tool to break communication barriers and keep your team on track.

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• Mechanical & Industrial Engineering Department
• Durward K. Sobek II

The A3 Report

the A3 Report goes hand-in-hand with steps 0-6 of the A3 Process. The purpose of the A3 Report is to:

• Document the learning, decisions, and planning involved with solving a problem
• Facilitate communication with people in other departments
• Provide structure to problem-solving so as to maximize learning

The report (template) is designed to be printed on 11x17 inch paper (or two pieces of 8.5x11 inch paper) as shown in the diagram below. For additional explanations of the individual parts of the report, click on the title box for that part. You can also download an A3 Report template in MS Word format; however, remember this is a flexible tool and can be adapted to specific situations-just don't short circuit the process!

• Download A3 Report Template (MS Word)
• Download A3 Report Format (PDF)

The theme of your A3 report should be a concise statement of what the A3 report is about. It should answer the question, "What are we trying to do here?"

An example of a theme might be, "Decrease patient transport time to diagnostic department."

Background:

The background section includes any contextual or background information necessary to fully understand the issue. it's also important to indicate how this problem relates to the company's goals or values.

The transportation department regularly receives complaints from diagnostic departments that patients arrive late for their appointments. This causes delays in patient treatment, idle time for diagnostic department staff members, and backups in the diagnostic areas resulting in long patient wait times.

Current Condition:

For the A3 report, the current condition needs to be an image illustrating how the current process works. It's important to label the diagram so that anyone knowledgeable about the process will be able to understand it. major problems also need to be included. Put them in storm bursts so they are set apart from the diagram. Hand-drawn diagrams (in pencil) are often the most effective because they can be done quickly and changed easily on-the-spot.

Cause Analysis:

To start your root cause analysis, make a list of the main problem(s). Next ask the appropriate "why?" questions until you reach the root cause. A good rule-of-thumb is that you haven't reached the root cause until you've asked "why?" at least five times. Record the casual chain(s) on the A3 report.

Problem: Backups in diagnostic departments

• Patients arriving late
• Transporter not called on time
• Ward secretaries are busy and often forget
• No written message
• No protocol
• Transport unable to locate patient
• Page does not include patient location (name only)
• No standard protocol for transport paging
• Patient not ready for transport
• Nurses unaware of prescribed test
• No mechanism to inform RN of scheduled procedure

Target Condition:

Comparable to the current condition, the target condition diagram should illustrate how the proposed process will work with the countermeasures in place, with appropriate labels. It's also important to note or list the specific countermeasures that will address the root cause(s). Finally, the problem-solver (or team) should predict the expected specifically and quantitatively, and note it.

Implementation Plan:

The implementation plan is the set of tasks required to develop the countermeasures, put them in place, and realize the target condition. For each task, a person responsible for that task is listed along with a deadline for task completion. It may also be helpful to list the expected outcome of each task, as shown below.

Follow-up Plan and Results:

In the left-hand side, record the plan to measure the effectiveness of the proposed change: what will be measured, when, and who will do the measuring. Leave the right-hand side blank for recording the actual results. Then, after implementation, complete the follow-up plan and record the results of implementation and dates of the actual follow-up.

Durward K. Sobek II, PhD

Office of Academic Affairs

Montana State University  P.O. Box 172560 Bozeman, MT 59717-2560

Tel: (406) 994-7140 Office: 212 Montana Hall Email: [email protected]  

An A3 Report is a Toyota-pioneered practice of getting the problem, the analysis, the corrective actions, and the action plan down on a single sheet of large (A3) paper, often with the use of graphics. At Toyota, A3 reports have evolved into a standard method for summarizing problem-solving exercises, status reports, and planning exercises like value-stream mapping.

But it is much more than a sheet a paper with facts and figures. It is a management process  learned through dialogue about concrete problems. It does this by means of a dialogue between a lean manager and a subordinate who learns lean management and leadership as she solves an important problem.

This process of solving problems while creating better employees—A3 analysis—is core to the Toyota management system. An A3 report guides the dialogue and analysis. It identifies the current situation, the nature of the issue, the range of possible counter- measures, the best countermeasure, the means (who will do what when) to put it into practice, and the evidence that the issue has actually been addressed.

The lean leader’s job is to develop people. If the worker hasn’t learned, the teacher hasn’t taught. Training Within Industry Report (Washington, DC: War Manpower Commission, Bureau of Training, 1945).

Effective use of the A3 process can facilitate the shift from a  debate  about who owns what (an authority-focused debate) to a  dialogue  around  what is the right thing to do  (a responsibility-focused conversation). This shift has a radical impact on the way decisions are made. Individuals earn the authority to take action through the manner in which they frame the issue. They form consensus and get decisions made by focusing relentlessly on indisputable facts that they and their peers derive from the gemba.

As a result, A3 management can best be understood as neither “top-down” nor “bottom-up.” The process clarifies responsibility by placing ownership squarely on the shoulders of the author-owner of the A3, the individual whose initials appear in the upper right-hand corner of the paper. This person may not have direct authority over every aspect of the proposal. Yet this owner is clearly identified as the person who has taken or accepted responsibility  to get decisions made and implemented .

Example A3s

The Many Facets of A3

• A standard paper size:  At its most fundamental, “A3” is the international term for a sheet of paper 297 millimeters wide and 420 millimeters long. The closest U.S. paper size is the 11-by-17-inch tabloid sheet. 
• A template:  Many companies and individuals use an A3-sized document pre-printed with the steps needed to conduct lean problem-solving or improvement efforts, with generous white space for “A3 owners” to record their progress. While they refer to this document as a template, an “A3” is not a template.
• A storyboard:  As users record their problem-solving or improvement project’s progress, the A3 becomes a storyboard used to facilitate communication, collaboration, and coordination with other stakeholders affected by the goal the A3 owner is working toward (e.g., solving a problem or improving a  process ). By having all the facts about the effort in one place, logically presented and summarized, the A3 owner is better able to gain buy-in from other stakeholders for recommended process changes. 
• A report:  Once the A3 problem-solving effort concludes, the A3 storyboard serves as a report of the problem-solving or improvement initiative, including the facts and data gathered, hypotheses considered, countermeasures tried, experiment results, corrective actions taken, and the overall thinking of the A3 owner and stakeholders. At Toyota and elsewhere, A3 reports have evolved into a standard method for summarizing problem-solving exercises, status reports, and planning exercises like value-stream mapping.  
• A problem-solving methodology (or process):  Most lean practitioners know “the A3” as a problem-solving process guided by specific steps or questions. The left side of the A3 focuses on various elements of the problem or current condition, and the right on the countermeasures considered, tested, and chosen that resolves the issue or creates a higher standard.
• A management discipline (or process):  At a higher level, lean leaders, managers, and supervisors use “the A3” as a means by which they oversee and guide subordinates while simultaneously helping them develop their  lean thinking and practice  — particularly lean leadership and problem-solving — capabilities. With A3 management, leaders challenge their direct reports to solve a problem. Then, with the A3 report guiding the dialogue and analysis, leaders coach them through the problem-solving process. Importantly, leaders coach by asking questions versus providing answers, ensuring responsibility remains with the subordinate to solve the problem by pursuing facts and building consensus. Through this interaction, subordinates address the issue, allowing them to make progress toward the objective and, in so doing, learn the lean approach to leadership and management and gain problem-solving capability.
• A3 thinking (or analysis):  Most A3 coaches and advanced lean practitioners refer to “the A3” as a thinking process. In this case, the term refers to a systematic approach to resolving problems or improving  work  processes. Someone can follow this systematic approach, regardless of whether they are guided by or record their findings on an A3 document.
• An alignment tool:  Advanced lean organizations that have incorporated lean thinking and practices throughout their operations use “A3s” as part of their  strategy deployment  and execution efforts. In this case, the A3 process ensures a standard approach to managing and  coaching  people, all directed toward solving problems that help achieve corporate objectives.

Additional Resources

How Do I Start My A3?

When asked “where do I start to write my A3,” David Verble responds “don’t start by writing.” His piece, the first in a series about getting started, offers lessons he has learned about the nature of thinking, and a productive way to start the A3 by recognzing it as a thinking process. 

Don’t Present Your A3: Share Your A3

When asked “where do I start to write my A3,” David Verble responds “don’t start by writing.” His piece, the first in a series about getting started, offers lessons he has learned about the nature of thinking, and a productive way to start by recognizing it as a thinking process. 

Related Books

Related Online Courses

Intro to Problem Solving

Problem-solving is critical to every position in every industry. In this course, you will learn to grasp the situation at the gemba (where the work is done) and use all of your senses to understand what is truly happening.

See: Value Stream Mapping

Privacy Overview

A Step-by-Step Guide to A3 Problem Solving Methodology

Author: Daniel Croft

Daniel Croft is an experienced continuous improvement manager with a Lean Six Sigma Black Belt and a Bachelor's degree in Business Management. With more than ten years of experience applying his skills across various industries, Daniel specializes in optimizing processes and improving efficiency. His approach combines practical experience with a deep understanding of business fundamentals to drive meaningful change.

Problem-solving is an important component of any business or organization. It entails identifying, analyzing, and resolving problems in order to improve processes, drive results, and foster a culture of continuous improvement. A3 Problem solving is one of the most effective problem-solving methodologies.

A3 Problem solving is a structured and systematic approach to problem-solving that originated with the lean manufacturing methodology. It visualizes the problem-solving process using a one-page document known as an A3 report. The A3 report provides an overview of the problem, data analysis, root causes, solutions, and results in a clear and concise manner.

A3 Problem Solving has numerous advantages, including improved communication, better decision-making, increased efficiency, and reduced waste. It is a powerful tool for businesses of all sizes and industries, and it is especially useful for solving complex and multi-faceted problems.

In this blog post, we will walk you through the A3 Problem Solving methodology step by step. Whether you are new to A3 Problem Solving or simply want to improve your skills, this guide will help you understand and apply the process in your workplace.

What is A3 Problem Solving?

A3 Problem Solving is a structured and systematic approach to problem-solving that makes use of a one-page document called an A3 report to visually represent the process. The A3 report provides an overview of the problem, data analysis, root causes, solutions, and results in a clear and concise manner. The method was created within the framework of the Lean manufacturing methodology and is based on the principles of continuous improvement and visual management.

Looking for a A3 Problem solving template? Click here

Origin and History of A3 Problem Solving

A3 Problem Solving was developed by Toyota Motor Corporation and was first used in the manufacture of automobiles. The term “A3” refers to the size of the paper used to create the report, which is an ISO standard known as “A3”. The goal of the A3 report is to provide a visual representation of the problem-solving process that all members of the organisation can easily understand and share. A3 Problem Solving has been adopted by organisations in a variety of industries over the years, and it has become a widely used and recognised method for problem-solving.

Key Principles of A3 Problem Solving

The following are the key principles of A3 Problem Solving:

• Define the problem clearly and concisely
• Gather and analyze data to gain a deep understanding of the problem
• Identify the root causes of the problem
• Develop and implement effective solutions
• Evaluate results and continuously improve

These principles serve as the foundation of the A3 Problem Solving methodology and are intended to assist organisations in continuously improving and achieving their objectives. Organizations can effectively solve problems, identify areas for improvement, and drive results by adhering to these principles.

Step 1: Define the Problem

Importance of clearly defining the problem.

The first step in the A3 Problem Solving process is critical because it lays the groundwork for the remaining steps. To define the problem clearly and accurately, you must first understand the problem and identify the underlying root cause. This step is critical because if the problem is not correctly defined, the rest of the process will be based on incorrect information, and the solution developed may not address the issue effectively.

The significance of defining the problem clearly cannot be overstated. It aids in the collection and analysis of relevant data, which is critical for developing effective solutions. When the problem is clearly defined, the data gathered is more relevant and targeted, resulting in a more comprehensive understanding of the issue. This will enable the development of solutions that are more likely to be effective because they are founded on a thorough and accurate understanding of the problem.

However, if the problem is not clearly defined, the data gathered may be irrelevant or incorrect, resulting in incorrect conclusions and ineffective solutions. Furthermore, the process of collecting and analysing data can become time-consuming and inefficient, resulting in resource waste. Furthermore, if the problem is not accurately defined, the solutions developed may fail to address the root cause of the problem, resulting in ongoing issues and a lack of improvement.

Techniques for Defining the Problem

The first step in the A3 Problem Solving process is to clearly and accurately define the problem. This is an important step because a clearly defined problem will help to ensure that the appropriate data is collected and solutions are developed. If the problem is not clearly defined, incorrect data may be collected, solutions that do not address the root cause of the problem, and time and resources may be wasted.

A problem can be defined using a variety of techniques, including brainstorming , root cause analysis , process mapping , and Ishikawa diagrams . Each of these techniques has its own advantages and disadvantages and can be used in a variety of situations depending on the nature of the problem.

Best Practice for Defining the Problem

In addition to brainstorming, root cause analysis, process mapping, and Ishikawa diagram s, best practices should be followed when defining a problem in A3 Problem Solving. Among these best practices are:

• Define the issue in a specific and quantifiable way: It is critical to be specific and concise when defining the problem, as well as to quantify the problem in terms of its impact. This will help to ensure that all stakeholders understand the problem and that data collection is focused on the right areas.
• Focus on the problem’s root cause: The A3 Problem Solving methodology is intended to assist organisations in identifying and addressing the root cause of a problem, rather than just the symptoms. Organizations can ensure that their solutions are effective and long-lasting by focusing on the root cause of the problem.
• Ascertain that all stakeholders agree on the problem’s definition: All stakeholders must agree on the definition of the problem for the A3 Problem Solving process to be effective. This ensures that everyone is working towards the same goal and that the solutions developed are relevant and appropriate.
• Consider the problem’s impact on the organisation and its stakeholders: It is critical to consider the impact of the problem on the organisation and its stakeholders when defining it. This will assist in ensuring that the appropriate data is gathered and that the solutions developed are relevant and appropriate.

Organizations can ensure that their problem is defined in a way that allows for effective data collection, analysis, and solution development by following these best practices. This will aid in the development of appropriate solutions and the effective resolution of the problem, resulting in improvements in the organization’s processes and outcomes.

Step 2: Gather Data

Gathering data in a3 problem solving.

Data collection is an important step in the A3 Problem Solving process because it allows organisations to gain a thorough understanding of the problem they are attempting to solve. This step entails gathering pertinent information about the problem, such as data on its origin, impact, and any related factors. This information is then used to help identify root causes and develop effective solutions.

One of the most important advantages of data collection in A3 Problem Solving is that it allows organisations to identify patterns and trends in data, which can be useful in determining the root cause of the problem. This information can then be used to create effective solutions that address the problem’s root cause rather than just its symptoms.

In A3 Problem Solving, data collection is a collaborative effort involving all stakeholders, including those directly impacted by the problem and those with relevant expertise or experience. Stakeholders can ensure that all relevant information is collected and that the data is accurate and complete by working together.

Overall, data collection is an important step in the A3 Problem Solving process because it serves as the foundation for effective problem-solving. Organizations can gain a deep understanding of the problem they are attempting to solve and develop effective solutions that address its root cause by collecting and analysing relevant data.

Data Collection Methods

In A3 Problem Solving, several data collection methods are available, including:

• Observations
• Process diagrams

The best data collection method will be determined by the problem being solved and the type of data required. To gain a complete understanding of the problem, it is critical to use multiple data collection methods.

Tools for Data Analysis and Visualization

Once the data has been collected, it must be analysed and visualised in order to gain insights into the problem. This process can be aided by the following tools:

• Excel Spreadsheets
• Flow diagrams
• Pareto diagrams
• Scatter Plots
• Control diagrams

These tools can assist in organising data and making it easier to understand. They can also be used to generate visual representations of data, such as graphs and charts, to communicate the findings to others.

Finally, the data collection and analysis step is an important part of the A3 Problem Solving process. Organizations can gain a better understanding of the problem and develop effective solutions by collecting and analysing relevant data.

Step 3: Identify Root Causes

Identifying the root causes of the problem is the third step in the A3 Problem Solving process. This step is critical because it assists organisations in understanding the root causes of a problem rather than just its symptoms. Once the underlying cause of the problem is identified, it can be addressed more effectively, leading to more long-term solutions.

Overview of the Root Cause Analysis Process

The process of determining the underlying causes of a problem is known as root cause analysis. This process can assist organisations in determining why a problem is occurring and what can be done to prevent it from recurring in the future. The goal of root cause analysis is to identify the underlying cause of a problem rather than just its symptoms, allowing it to be addressed more effectively.

To understand Root cause analysis in more detail check out RCA in our Lean Six Sigma Yellow Belt Course Root Cause Analysis section

Techniques for Identifying Root Causes

There are several techniques for determining the root causes of a problem, including:

• Brainstorming
• Ishikawa diagrams (also known as fishbone diagrams)
• Root Cause Tree Analysis

These methods can be used to investigate the issue in-depth and identify potential root causes. Organizations can gain a deeper understanding of the problem and identify the underlying causes that must be addressed by using these techniques.

Best Practices for Conducting Root Cause Analysis

It is critical to follow these best practices when conducting root cause analysis in A3 Problem Solving:

• Make certain that all stakeholders participate in the root cause analysis process.
• Concentrate on determining the root cause of the problem rather than just its symptoms.
• Take into account all potential root causes, not just the most obvious ones.
• To identify root causes, use a systematic approach, such as the 5 Whys or root cause tree analysis.

Organizations can ensure that root cause analysis is carried out effectively and that the root cause of the problem is identified by adhering to these best practises. This will aid in the development of appropriate solutions and the effective resolution of the problem.

Step 4: Develop Solutions

Developing solutions is the fourth step in the A3 Problem Solving process. This entails generating ideas and options for dealing with the problem, followed by selecting the best solution. The goal is to develop a solution that addresses the root cause of the problem and prevents it from recurring.

Solution Development in A3 Problem Solving

A3 solution development Problem solving is an iterative process in which options are generated and evaluated. The data gathered in the previous steps, as well as the insights and understanding gained from the root cause analysis, guide this process. The solution should be based on a thorough understanding of the problem and address the underlying cause.

Techniques for Developing Solutions

There are several techniques that can be used to develop solutions in A3 Problem Solving, including:

• Brainwriting
• Solution matrix
• Multi voting
• Force field analysis

These techniques can help to generate a range of options and to select the best solution.

Best Practice for Developing Solutions

It is critical to follow the following best practices when developing solutions in A3 Problem Solving:

• Participate in the solution development process with all stakeholders.
• Make certain that the solution addresses the underlying cause of the problem.
• Make certain that the solution is feasible and achievable.
• Consider the solution’s impact on the organisation and its stakeholders.

Organizations can ensure that the solutions they develop are effective and sustainable by adhering to these best practises. This will help to ensure that the problem is addressed effectively and that it does not reoccur.

Step 5: Implement Solutions

The final and most important step in the A3 Problem Solving methodology is solution implementation. This is the stage at which the identified and developed solutions are put into action to address the problem. This step’s goal is to ensure that the solutions are effective, efficient, and long-lasting.

The implementation Process

The implementation process entails putting the solutions developed in the previous step into action. This could include changes to processes, procedures, and systems, as well as employee training and education. To ensure that the solutions are effective, the implementation process should be well-planned and meticulously executed.

Techniques for Implementing Solutions

A3 Problem Solving solutions can be implemented using a variety of techniques, including:

• Piloting the solution on a small scale before broadening its application
• Participating in the implementation process with all relevant stakeholders
• ensuring that the solution is in line with the goals and objectives of the organisation
• Monitoring the solution to determine its effectiveness and make any necessary changes

Best Practice for Implementing Solutions

It is critical to follow these best practices when implementing solutions in A3 Problem Solving:

Make certain that all relevant stakeholders are involved and supportive of the solution. Have a clear implementation plan that outlines the steps, timeline, and resources required. Continuously monitor and evaluate the solution to determine its efficacy and make any necessary changes. Encourage all stakeholders to communicate and collaborate openly. Organizations can ensure that solutions are effectively implemented and problems are effectively addressed by adhering to these best practices. The ultimate goal is to find a long-term solution to the problem and improve the organization’s overall performance.

In conclusion, A3 Problem Solving is a comprehensive and structured methodology for problem-solving that can be applied in various industries and organisations. The A3 Problem Solving process’s five steps – Define the Problem, Gather Data, Identify Root Causes, Develop Solutions, and Implement Solutions – provide a road map for effectively addressing problems and making long-term improvements.

Organizations can improve their problem-solving skills and achieve better results by following the key principles, techniques, and best practices outlined in this guide. As a result, both the organisation and its stakeholders will benefit from increased efficiency, effectiveness, and satisfaction. So, whether you’re an experienced problem solver or just getting started, consider incorporating the A3 Problem Solving methodology into your work and start reaping the benefits right away.

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Daniel Croft

Daniel Croft is a seasoned continuous improvement manager with a Black Belt in Lean Six Sigma. With over 10 years of real-world application experience across diverse sectors, Daniel has a passion for optimizing processes and fostering a culture of efficiency. He's not just a practitioner but also an avid learner, constantly seeking to expand his knowledge. Outside of his professional life, Daniel has a keen Investing, statistics and knowledge-sharing, which led him to create the website www.learnleansigma.com, a platform dedicated to Lean Six Sigma and process improvement insights.

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How to use A3 report – example and template for free

A3 report is one page report about project progress, its background, and challenges. It is easily explanation tool for broader audience, and stakeholders interested in the project.

this article contains:

What is A3 problem solving report?

A3 report out as a option, steps to create a3 report, a3 report example – restaurant improvement, a3 report at project start, a3 report as project progress, a3 report at project end.

• A3 report template download

Hot news, folks. In order to help you as much as I can in your improvement efforts, I have launched non-binding consultation program. I would like to help you with:

• Lean culture implementation in your organization
• Six Sigma projects consultations
• Lean Six Sigma trainings and certifications support
• Project management theory turn into practical usage
• Your career planning

First 30 minutes of consultation for free, every additional 1 hour 10 USD.

On a literal level, A3 refers to a paper size 29.7 x 42.0 in cm 11×17 in inches. In the lean six sigma world, we use this report out tool to show teams thinking, when addressing project goal. Use A3 during whole project life cycle. Create A3 right after project charter creation.

Six sigma tools to use in your (not just) first project – read here

Well, I suggest to agree with stakeholders, the way they want to see project report out. There are different ways possible. And A3 is one of possibilities.

So, no need to use A3 in every project. But be consistent, once using it.

A3 creation, preparation and updating is much faster, than creating presentation for example. It is simple to use and read. It is great tool, when presenting more projects updates in one meeting. A3 helps team focusing on the project goal and its deliverables, and makes it much simpler to review progress for those interested in the project.

5 simple Green belt project ideas – read here

A3 form template, is available for download in the end of this article. For free. Use it, share it.

These are areas should be filled at project beginning, as already mentioned.

• Project name,
• Current state pains
• Project goal, and the
• Section with team information

It takes some time with working on projects following DMAIC. But it worth it. So, do not jump into the solutions however attractive and tempting it would be. Try to understand current problem, identify your ideal state, and create a plan to reach it.

Here is a link to download project charter template for your usage, with the brief description of each section. You are free to share and distribute this list.

I do videos, blog posts, and all templates for free, in my free time. I will appreciate if you can donate me a cup of cofee, for more energy in my creation. (1 dollar counts, too 😉 Click on this link: I would like to support Erik in his effort

A3 sections to be updated this way..

• Create 4 sections prior project start, as mentioned.
• Develop high level activities and their schedule in project beginning together with team. It can be DMAIC phases at beginning. You can add more details as progressing with project.
• Update the rest of A3 areas with project progress. Do the update together with your team.
• Review A3 during one on one project progress review with sponsor, prior showing to stakeholders.
• Update stakeholders regularly. Minimally after finishing each project phase.

What are Six Sigma project types? (+templates) – read here

Let me share an A3 report example with you. A3 refers to my earlier video – improving fast food restaurant, called “Eating mania”.

OK, you can argue, that there is no real stakeholder in this project, to whom to report out. It is true statement. I will show correlations between project, and reporting out progress by A3.

Restaurant owner has a problem with very slow business growth. And he would like to develop process, that would bring 15% more customers in 3 months. This is perfect project goal.

Download DMAIC tools list, I suggest allways to follow.

22 green belt certification companies prices review – read here

And this is how A3 would look like when project starts:

Team have developed high level project plan right after project kick off. There are leaders of each step, time frame where each step should be addressed. It needs teams discussions to define those steps, when there is no experienced leader.

How to select your first green belt project? – read here

As team is progressing, accomplished tasks are updated with current status. Additional information, as Analysis, and project challenges is provided to the report. Use pictures, graphs or other visualization to show used tools in the analyze section.

Follow ups and challenges are here to share with stakeholders and sponsor, what difficulties team is facing. You might ask for helping hand in the case team is stuck up.

You can update any A3 section accordingly, as project goes on. It must reflect reality.

Construction DMAIC improvement example – read here

And this is A3 after finishing whole project. Note, there are project results showed in follow up, and analyze section. It is important to share positive things, as well as those, which did not run very well, and need some more attention, or different approach.

And there you are. Filled A3 report after project finalization.

A3 report template

What you will get, by downloading this file:

• A3 form Excel template
• Restaurant example – filled A3 report (above used pictures)

To download entire A3 report template –click on the link below

Do not forget to visit and subscribe my YouTube channel . I am uploading Six Sigma, Lean and Project oriented videos regurarly. So, stay tuned.

Yours sincerely Erik.

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The A3 Problem Solving Report: A 10-Step Scientific Method to Execute Performance Improvements in an Academic Research Vivarium

James a. bassuk.

1 Department of Research Continuous Performance Improvement, Seattle Children's Research Institute, Seattle, Washington, United States of America

Ida M. Washington

2 Office of Animal Care, Seattle Children's Research Institute, Seattle, Washington, United States of America

Conceived and designed the experiments: JAB IMW. Performed the experiments: JAB IMW. Analyzed the data: JAB IMW. Contributed reagents/materials/analysis tools: JAB IMW. Wrote the paper: JAB.

Associated Data

The purpose of this study was to illustrate the application of A3 Problem Solving Reports of the Toyota Production System to our research vivarium through the methodology of Continuous Performance Improvement, a lean approach to healthcare management at Seattle Children's (Hospital, Research Institute, Foundation). The Report format is described within the perspective of a 10-step scientific method designed to realize measurable improvements of Issues identified by the Report's Author, Sponsor and Coach. The 10-step method (Issue, Background, Current Condition, Goal, Root Cause, Target Condition, Countermeasures, Implementation Plan, Test, and Follow-up) was shown to align with Shewhart's Plan-Do-Check-Act process improvement cycle in a manner that allowed for quantitative analysis of the Countermeasure's outcomes and of Testing results. During fiscal year 2012, 9 A3 Problem Solving Reports were completed in the vivarium under the teaching and coaching system implemented by the Research Institute. Two of the 9 reports are described herein. Report #1 addressed the issue of the vivarium's veterinarian not being able to provide input into sick animal cases during the work day, while report #7 tackled the lack of a standard in keeping track of weekend/holiday animal health inspections. In each Report, a measurable Goal that established the basis for improvement recognition was present. A Five Whys analysis identified the Root Cause for Report #1 as historical work patterns that existed before the veterinarian was hired on and that modern electronic communication tools had not been implemented. The same analysis identified the Root Cause for Report #7 as the vivarium had never standardized the process for weekend/holiday checks. Successful outcomes for both Reports were obtained and validated by robust audit plans. The collective data indicate that vivarium staff acquired a disciplined way of reporting on, as well as solving, problems in a manner consistent with high level A3 Thinking.

Introduction

Problem solving tools come in many shapes and sizes. From a complex, multipage research grant application designed to unravel the molecular mechanisms of human disease [1] , [2] , to the one-page A3 Report developed by the Toyota Motor Corporation [3] , [4] , problem solving tools typically have the scientific hypothesis as the one common attribute. A3 Reports exist as the following 3 types: (i) The Problem Solving A3 Report, (ii) The Proposal A3 Report, and (iii) The Status A3 Report [4] .

Originally developed on A3 paper (297×420 mm, 11.69×16.54 in), the largest size that can fit through a fax machine, the A3 Problem Solving Report fully documents a given process on one side of one sheet of paper. Based on the 13 th Principle of the Toyota Way (“Make Decisions Slowly by Consensus”) [3] , the A3 Problem Solving Report is a tool that describes how consensus on complex decisions can be efficiently reached. The key to generating a good A3 Report is nemawashi – the process of getting consensus. The purpose of A3 Reports has been described as written documents to support mentor/mentee dialogues during application of the improvement kata [5] . Excellent textbooks have been written that provide expert A3 advice and insights, especially in A3 Thinking [4] , [6] , [7] .

A3 Reports are based on the Plan-Do-Check-Act cycle, a high level problem solving algorithm pioneered by Walter Shewhart in the 1930s [8] and later adopted by W. Edwards Deming in the 1950s [9] . The PDCA cycle has evolved into the Plan-Do-Study-Act (PDSA) cycle and has recently been reviewed [10] .

Performance improvement (“lean”) initiatives in a non-profit research organization are being championed by Seattle Children's Research Institute (SCRI), a multicenter complex founded in 2006 by Seattle Children's Hospital. The early adapter of lean at the Institute was the Office of Animal Care (OAC), which oversees an accredited vivarium facility that supports dozens of laboratories through approved animal use protocols. Such accreditation has been granted by the Association for Assessment and Accreditation of Laboratory Animal Care International. Using the same tools and methods of the Toyota Production System [11] , the OAC reported that the elimination of wasteful procedural steps in the dirty cage wash area led to marked improvements in material flow, macroenvironmental quality, increased employee safety and enhanced customer service [12] . Despite being reported by Seattle Children's research leaders [13] , [14] , these improvements were not sustained when the vivarium relocated from a temporary research facility to its permanent home in downtown Seattle.

Another academic research vivarium engaged in performance improvement via lean thinking is the Center for Comparative Medicine at Massachusetts General Hospital, who introduced their management of animal facility operations using the Toyota Production System approach to the 2005 Annual Meeting of the American Association for Laboratory Animal Science [15] . Waste removal and process improvements have converted the Center from operating in a deficit to annually realizing a small profit [16] .

Two problems that the OAC chose to examine are of importance to all vivariums due to their impact on animal welfare. The first problem addressed involvement of the veterinarian during the OAC response to sick animals. The second problem focused on the potpourri of inefficient methods that OAC staff employed on weekends and holidays to keep track of animal health checks. The current publication describes how the OAC utilized A3 Thinking to drive A3 Problem Solving Reports to completion. Specific attention is drawn to the increase in the level of quality of its animal care and associated services while simultaneously removing waste from its system.

Materials and Methods

I. human subject research.

The study presented in this manuscript did not perform any research that used, created, or shared Protected Health Information. The study was therefore not subject to the State of Washington Uniform Health Information Act or the United States of America Health Insurance Portability and Accountability Act.

II. The A3 form

The blank A3 Problem Solving Tool form used at Seattle Children's Research Institute is populated on both sides of 11×17 inch paper. The front side of the form consists of a left and right side, and has 10 sections which are listed below and illustrated in Figure 1 . Sponsor approval lines are provided for signoff once the left and right sides have each been sequentially completed.

The A3 form is printed on 11×17 inch paper, is filled out with a pencil, and contains 10 sections, as illustrated above. The Goal statement is a hypothesis which is “checked” via the Test (step 9) and auditing (step 10).

Step 1. Issue. A clear, focused, stand-alone statement that defines the problem.

Step 2. Background. Details that cannot be described in the Current Condition drawing and useful baseline metrics may be included in this section.

Step 3. Current Condition. A drawing that conveys a complete understanding of the current situation is essential in order to realize what improvements may be necessary.

Step 4. Goal. A quantitative statement that will form the basis for how improvement will be measured is provided in this section. In many ways, this statement is the hypothesis for the experiment. Goals in this context are equivalent to Targets, which need to be SMART ( s pecific, m easurable, a ttainable, r elevant and t imely) [17] .

Step 5. Root Cause Analysis. The Root Cause Analysis section can accommodate either a Five Whys analysis or a Ishikawa (fishbone) diagram [18] . These two options give the Author flexibility, depending on the complexity of the problem.

Step 6. Target Condition. A drawing that conveys a complete understanding of what the situation will look like once the improvements have taken hold is placed on this step. The Target Condition describes what is necessary to meet the Goal.

Step 7. Countermeasures. A listing of the improvements needed to attain the Target Condition.

Step 8. Implementation and Cost Analysis. A listing of specific tasks that will lead to improvements, along with timelines, ownership and the expected outcomes is described in this step. The expected outcomes are an essential component of the scientific process because they provide the basis for evaluating whether or not the improvements are successful. This section also contains the cost of completing the A3 report, how much money will be saved after implementation of the Countermeasures, and what types of waste have been removed from the process.

Step 9. Test. A small pilot conducted over 1–2 weeks is recommended. Do the measured results match the predicted results?

Step 10. Follow Up/Audit. This section contains a description of an audit plan (typically 30–90 days), the results of the audit plan, and, if needed, recommendations for how the next A3 Reports will become standard work.

Fifty A3 Problem Solving Questions [19] – [21] populate the back side of the form and are listed as Questions S1 . These questions guide the development of the project's focus and serve to remind the Author that consensus among colleagues is an essential requirement within A3 Thinking.

III. A3 supporting documents

The Four Rules of the Toyota Production System were adopted to guide the A3 Report's Author when asking questions about the Current Condition and when designing the Target Condition [22] . Rule #1 (activities): All work shall be highly specified as to content, sequence, timing and outcome. Rule #2 (connections): Every customer-supplied connection must be direct, and there must be an unambiguous yes-or-no way to send requests and receive responses. Rule #3 (pathways): The pathway for every product and service must be simple and direct. Rule #4: Any improvement must be made in accordance with the scientific method, under the guidance of a teacher, at the lowest possible level in the organization. The 14 Principles of the Toyota Way are presented in Table 1 [23] .

IV. A3 teaching and coaching

A multi-session course in A3 Thinking and Problem Solving was originally developed by the Seattle Children Hospital's Continuous Performance Improvement (CPI) department with consultative guidance by Cindy Jimmerson (Lean Healthcare West, Missoula, Montana, USA). This course was subsequently revised for use at the Research Institute by Research Continuous Performance Improvement (RCPI) consultants. The Research Institute course, currently in its 9 th iteration, was implemented via four 1–2 hour classroom sessions spread over 2–3 months. Each student/Author was assigned a Coach, derived from a pool of RCPI consultants or from colleagues who had successfully completed the course. The Coach provided expertise in scoping, guidance during process walks and data collection, and assistance in understanding A3 Thinking and tools. Each student/Author began the A3 Report process by selecting a Sponsor (typically their supervisor) whose role was to (i) approve the project's commencement and implementation, (ii) support the Author by removing barriers, (iii) ensure the project's completion, and (iv) assure that the Followup/Audit section would be completed. Administratively, all ∼70 employees of the Institute's Research Support Services completed A3 Problem Solving Reports, to varying levels of completeness and sustainment, during FY2012.

V. Cost estimations

In order to determine labor costs associated with (i) completing the A3 report and (ii) labor savings, a quasi-generic calculator in an Excel spreadsheet (Microsoft, Redmond, WA, USA) was used. All jobs at Seattle Children's, the parent organization of the Institute, were placed into 15 groups by the human resources department. A brief description accompanied each job group, providing additional details such as general and specific job titles and functions. After entering the number of hours contributed to the A3 report according to job group ( e.g. , # hours for RCPI consultant, # hours for the A3 Author, # hours for the A3 Sponsor, etc.), the calculator returned a reliable estimate for the sum dollar amount of employee salary plus benefits.

VI. Improvements via rapid Plan-Do-Check-Act (PDCA) process improvement cycles

Improvements were realized after implementation of PDCA cycles, a high level algorithm for solving problems [8] . Foundational to many quality improvement systems, PDCA cycles provide a means to (i) realize continuous change, (ii) achieve better quality in processes, and (iii) sustain the gains brought about by increased efficiency. Such PDCA-dependent improvements are expected to lead to stable, linear processes. After allowing for the collection of baseline data, methods for a hypothesis were developed (“Plan”) and tested (“Do”). Once metrics for the improvement had been captured, results were analyzed against the hypothesis (“Check”). If the observed outcomes failed to meet expectations, then the improvement process was revised (“Act” or “Adopt”) and retested. These cycles were repeated until the target condition was achieved.

VII. Statistical analysis

Statistical analysis was applied to OAC A3 Report #1. The percentage of sick animal cases requiring DVM (Doctor of Veterinary Medicine) input that received DVM input within 2 hours was summarized for baseline, audit 1 and audit 2. We then compared the observed percentages using pair wise Fisher's exact tests. The threshold for statistical significance was set as p <0.05.

I. The A3 Problem Solving Report is a 10-Step Scientific Method based on the P-D-C-A cycle

The 10 sections of the A3 form are aligned with Shewhart's Plan-Do-Check-Act cycle, as illustrated in Figure 1 . Seven sections are devoted to Planning (“Plan”), in alignment with Principle 13 of the Toyota Way. Following nemawashi , the countermeasures are implemented rapidly (“Do”), in order to avoid new problems that could crop up soon after implementation. The “Check” portion of Shewhart's cycle may be the single most important part of the A3 tool, as it examines whether the desired outcomes have been attainable or not. If the desired outcomes have not been reached, then it is time to “Act” by revising the countermeasures.

II. Overview of the A3 Problem Solving scientific method in the OAC

Nine reports were completed by OAC staff between October 1, 2011 and September 30, 2012 ( Table 2 ). All 9 reports represented first-time efforts by the Authors in A3 Problem Solving. Authors interacted with their Sponsors prior to project initiation in order to align the problem statement with departmental and/or institutional goals. Authors “went to gemba” by visiting the location of the problem process and interacting with employees who worked the process. In cases where the problem process directly involved the Author, this was considered beneficial as the problem process was within their sphere of influence. Twice a month, Authors would congregate as a group to practice nemawashi by exchanging perspectives with their colleagues and interact with their Coaches. Once the left side was completed to the satisfaction of the Author, the Sponsor was asked to convey approval by affixing their dated signature to the form. The OAC group continued on to complete the right side by again interacting with each other and with their Sponsors and Coaches. Once the right side was completed, Sponsor approval was gained via dated signature and the “approved” Report was scanned and emailed to the RCPI department, which posted the Report to a SharePoint site. Authors then began their Tests, designed to measure several instances of the process over 1–2 weeks. If any of the Countermeasures failed to meet expectations, then the Author revised the “fix” ( Figure 1 ) and the Test was repeated. Once there was an indication that a stable process had been achieved, then the Author began a 30–90 day Audit Plan. After the results of the Audit Plan were incorporated into the Follow Up section, the “final” Report was scanned, emailed to the RCPI department, which updated its SharePoint site. In this manner, the 9 OAC A3 Reports satisfied an Institutional requirement that all employees of Research Support Services would complete an A3 Problem Solving Report during FY2012.

Since their nine A3 Reports were focused on processes in which OAC Authors were directly involved, it followed that Authors would incorporate the Target Condition into their daily work. In most cases, Authors converted their improvements into their daily work. Presented below are two representative A3 Reports that were judged to be highly successful and sustainable.

III. A3 Report #1: Veterinarian input into treatment of sick animals

The Issue was that the sick animal reporting process limited veterinary input into treatment options, which could impact research and was inconsistent with standard care. The Background section described that 107 sick animal cases were identified in September of 2011 by animal technicians and handled by the veterinarian technician without DVM input. A retrospective analysis determined that 52 of these cases should have received DVM input. This was the current state of the OAC because no full-time DVM was employed prior to August 2011.

The Current Condition illustrated in Figure 2 tells a story of how a convoluted process notified the DVM of the work day's sick animal cases at the end of the work day, a situation that essentially prevented veterinary input into animal care. An Ishikawa diagram (lower right corner) indicated that a combination of historical Methods, communication Machinery (email, telephone), communication Materials (health/cage cards) and People (OAC staff, researchers) all contributed to delay of information to the DVM. A Five Whys Analysis (not shown) revealed that the Root Cause for the convolution was the historical work patterns that existed before the DVM was hired and that modern electronic communication tools had not been fully implemented. The following SMART Goal was therefore developed: “By end of 2011: DVM provides input into treatment of all sick animals requiring DVM consult within 2 hours of detection”.

Animal cases are classified as either “urgent” or “sick” and are typically first detected by one of six animal technicians (AT). In each case, a single veterinary technician (VT) provides the primary interface to the researchers (PI, lab).

The Target Condition ( Figure 2 ) and Countermeasures were then developed (i) to reduce emails to researchers, (ii) for the 6 animal technicians to contact the 1 veterinary technician directly via electronic iPod iTouch (Apple Inc., Cupertino, California, USA) devices, (iii) to update contact info for researchers, and (iv) to gain DVM input within 2 hours after the first instance of sick animal detection. Costs associated with generating the A3 Report included ∼20 and ∼3 hours of DVM and OAC staff time, respectively, which was estimated by the cost calculator to be ∼$925. Expenses associated with implementing the Countermeasures included ∼$1,500 to purchase iPod iTouch devices. Expected benefits, prior to Testing, included (i) improved quality of animal welfare and (ii) improved standard veterinary care.

The quality of OAC responses to sick animal cases was evaluated prior to and after improvement, i.e. successful implementation of the A3 Report #1's Countermeasures ( Table 3 ). The following two definitions of quality were evaluated: (1) Fitness for Use via the customer's assessment and (2) Conformance to Specifications via regulations established by the Institutional Animal Care and Use Committee (IACUC) and the Guide for the Care and Use of Laboratory Animals [24] . At Seattle Children's Research Institute, the customer is the patient/family. Data that associate customer satisfaction with DVM input into sick animal cases are non-existent, other than our assumption that the customer expects that regulations are followed during research into the cures of pediatric disease. Instead, we have assessed customer satisfaction through the eyes of the IACUC as a stakeholder, thus providing this governing body direct input into operational logistics of the OAC that influence quality. Additional stakeholders include the researcher, who designed and conducted the animal experiments, and extramural funding agencies. These stakeholders eventually have, or will, benefit from CPI-dependent improvements. After implementation, 82.4% of sick animal cases requiring DVM input received input within 2 hours – corresponding to a quality level of 1. After a PDCA cycle, the improvement rose to 90.6% – corresponding to a target quality level of 3.

During improvement work, procedures were redesigned to remove waiting and to bring flow to the sick animal process (Toyota Way Principle 2), the workflow was modified to include the DVM (Principle 4), processes were addressed such that quality was achieved the first time in gaining the timely input of the DVM (Principle 5), standardized tasks were implemented to bring stability to how the OAC responds to sick animals (Principle 6), and trusted technologies such as the iPod iTouch were brought in to enhance flow (Principle 8).

Waste removal metrics, prior to and after improvement, were also assessed. Wait time for researchers to respond to telephone calls was reduced from 2–6 hours to <2 hours ( Table 4 , waste #2). Multiple handling steps of sick animal information were reduced from 5 to 2 ( Table 4 , waste #3). Unnecessary steps, such as Animal Technicians contacting laboratory researchers directly, were eliminated through the introduction of iPod iTouch devices, a proven and reliable technology (waste #4). The number of queues in which sick animal information was communicated tallied 5 prior to improvement and 2 afterwards ( Table 4 , waste #5). Searching for correct researcher contact information was eliminated from the Animal Technician's role and reduced to <2 hours for the overall process ( Table 4 , waste #6). The defect of not involving the DVM in animal care decisions was reduced ( Table 4 , waste #7), as described below.

Two 30-day audits were performed to determine the number of sick animal cases requiring DVM input that actually received DVM input within 2 hours ( Table 5 ). The baseline metric was 0%. Following several rapid PDCA cycles that optimized communication among six Animal Technicians, one Veterinary Technician, one DVM and dozens of researchers, the results of the first audit realized a significant improvement to 82.4% ( p <0.0001). After an additional PDCA cycle, a trend towards improvement was observed (8.2% to 90.6%, p  = 0.11).

IV. A3 Report #7: Weekend checking process of animal health and habitat in the vivarium

The Issue focused on the confusing process to keep track of what has been completed and not completed during weekend/holiday checks. Such checks involved animals, feeds, treatments and reports – the types of activities that could be fit into an 8–10 hour shift by one OAC staff individual. The significance of this problem was that, if left unsolved, the obligation of not meeting IACUC expectations could be compromised.

As Background, the vivarium at SCRI consists of 22 rodent, 2 large animal, 4 fish and 3 satellite animal rooms spread over multiple floors in the same building. Responsibilities involve an overall health check of animals, mechanical functionality, and the feeding and treatment of animals. The Current Condition described a linear process where the OAC staff individual could be called away for emergencies or to procure treatment medications, thus triggering a lapse in where the checking left off and where it needed to be picked back up. As the Institute grows by adding investigators who use animal models in their research, a true need for optimization of the weekend/holiday check is essential.

A Five Whys analysis concluded that the Root Cause of the dysfunction was that the OAC had variation in the process for weekend/holiday checks. Accordingly, the Goal of this A3 Report was to “create/maintain a process to find where staff had left off in the routine facility check and know what had been completed/not completed”.

The Target Condition and Countermeasures specified (i) the creation of a “Weekend Check Log” that contained all responsibilities in reusable, laminated check forms that clearly delineated a standard process of checking, (ii) training of OAC staff in use of the log, and (iii) maintaining an updated log for all weekend/holiday checks.

Engagement with OAC staff by the Author was via nemawashi . The Countermeasures were carefully planned through 8 Implementation Steps and then rapidly implemented (“do”), in alignment with Shewhart's Plan-Do-Check-Act cycle. The Cost of improvement was minimal (7 hrs of staff time) while the Cost Benefits were organizational, time management and 1–2 hours of time saved each holiday or weekend day.

Testing of the improvement took place over a 2-day weekend and identified minor problems and inconsistencies. A rapid PDCA cycle was performed, followed by re-testing over the next weekend. After another round of rapid PDCA, the improvement was subjected to a 73-day audit period that spanned 10 weekends and 1 holiday. After a final round of rapid PDCA, the improvement was incorporated into standard work for all OAC staff assigned to such responsibilities.

Because, in part, of the quality and pace at which this Author pursued this A3 Problem Solving Report, he was promoted to be an OAC CPI team leader in a manner consistent with Principle 9 of the Toyota Way: “Grow leaders who thoroughly understand the work, live the philosophy, and teach it to others.”

The usefulness of the A3 Problem Solving Tool has been validated as the OAC undergoes a productive transformation, in alignment with Principle 14 of the Toyota Way: “Becoming a lean organization through relentless reflection ( hansei ) and continuous improvement ( kaizen ).” Being able to complete 9 A3 Problem Solving Reports in a manner that utilizes rapid PDCA cycles and downstream incorporation into daily standard work is a solid foundation as the OAC breaks down silos and implements cross-training. The OAC, as a department within Research Support Services, has begun its CPI journey in a manner consistent with the following 4P Model developed in The Toyota Way [25] . Philosophy : Dr. Ida Washington, OAC Director, and Dr. James Hendricks, Research Institute President, view the OAC as a means to adding value to patients of Seattle Children's Hospital – namely supporting research into cures of pediatric diseases and conditions. People and Partners : Dr. Washington has team-empowered the OAC staff in the department's CPI journey. These nine A3 Problem Solving Reports certainly support the Research Institute as a learning organization. Process : Elimination of waste in the OAC has been accomplished by applying CPI principles such as A3 Reports and standard work. Problem solving : The CPI toolbox to solve problems within the OAC is growing and currently consists of A3 Reports, 5S organizing systems, a Kaizen board, a Daily Management System, and Heijunka and pitch boards.

Implementation of the Countermeasures in an A3 Problem Solving Report is often expected to lead to incorporation into standard work. For OAC A3 Report #7 (“Weekend checking process of animal health and habitat in the vivarium”), the weekend check log is now a stable of standard work on weekends and holidays. The log is described in the standard work document for OAC huddles, and is discussed on the day prior to and after its use. Typical data that populate the log include special feeding or handling instructions for any given animal, technical procedures such as injections, or logistical considerations in the aquatic center. The collective data indicate that A3 Thinking has taken hold for A3 Report #7 in a manner aligned with Principle 14. Consistent with this A3 Thinking is a new PDCA proposal to convert the written log into an electronic log in order to reduce errors attributable to handwriting legibility issues.

The format of A3 Problem Solving Report form that is currently in use at the Research Institute lacks sufficient white space for documentation of observed outcomes ( Figure 1 , step 7) and for the results of the testing process ( Figure 1 , step 9). This brevity contrasts with the typical results section of a scientific manuscript, which is the most important part of peer-reviewed, published studies. While this brevity is probably founded on the notion that A3 Thinking is paramount to the A3 Problem Solving Report, there is no formal restriction that prevents appending additional outcomes and results to the Report – other than the overall requirement to present the entire Report on one side of an 11×17 inch piece of paper. The Author is faced with aligning these results with the basis for comparison that is stated in the Goal section ( Figure 1 , step 4). It then follows that A3 Thinking provides a platform for establishing a causal linkage between the action items of the Countermeasures and the outcomes of the Implementation Plan. In this perspective, the A3 Problem Solving Report does align quite well with traditional hypothesis-driven scientific experimentation.

A conventional position in laboratory animal care is that compliance equals quality. But that attitude is misplaced, especially in the new Guide's allowance for performance standards that permit flexibility in designing and evaluating evidence-based approaches for desired outcomes [24] . Being able to implement CPI-dependent improvements that specifically address Toyota's definition of quality can only serve to benefit the OAC's stakeholders: the IACUC, the researcher and the extramural funding agency. The ultimate beneficiary, of course, is Seattle Children's customer – the patient/family who awaits new cures for pediatric disease.

Veterinary medical care is an essential part of any animal care and use program. Such a program includes, at a minimum, effective plans for preventive medicine, monitoring and treatment of disease, surgery and post-op care, and anesthesia, analgesia and euthanasia [24] . Given that parts of each plan can be carried out by OAC staff, the communication within the OAC during the assessment and treatment of sick animals becomes paramount. Likewise, the daily observations of animals for signs of illness, injury or abnormal behavior need to be conducted by trained personnel. Such observations include holidays and weekends, a process in which a single OAC staff member is expected to visit every cage in the facility – a somewhat daunting task that was standardized by OAC A3 Report #7.

Being able to reduce the time it takes for veterinary input in sick animal cases has brought the OAC closer to realizing one-piece flow for that process. An important assessment of the sick animal Current Condition (OAC A3 Report #1) was to identify what was value added, using the Three Toyota Categories: (i) value added, (ii) non-value added and (iii) non-value added but required [26] . In the context of waste, Seattle Children's lists the following three categories: (i) muda , non-value added, (ii) mura , unevenness or variation in work processes, and (iii) muri , overburdening people or equipment [27] . Seattle Children's teaches that there are 9 types of waste contained within the muda category (see Table 4 ). Step by step, the OAC is pursuing its True North by acting as a tortoise and not the hare. Removal of waste can only lead to increased efficiencies while allowing OAC staff to increase supportive interactions with Institute researchers. Lean improvements do not happen overnight. Instead, they are a transformative process – and for a complex healthcare organization like Seattle Children's, this CPI journey is expected to demonstrate constant planning, doing, checking and acting.

Supporting Information

Questions s1.

Fifty A3 Problem Solving Questions [19] – [21] populate the back side of the A3 form. These questions guide the development of the project's focus and serve to remind the Author that consensus among colleagues is an essential requirement within A3 Thinking.

Acknowledgments

The Authors acknowledge the expert instruction and coaching in A3 Thinking by Delila Katzka and Lucinda Getz, CPI consultants and project managers in the Department of Research Continuous Performance Improvement at Seattle Children's Research Institute. The suggestion by Stephanie Axelrod that the IACUC is a stakeholder at the Institute is also acknowledged. The OAC staff is also acknowledged, specifically the OAC CPI team (Jonathan “JD” Pedersen and Lindsey Jackson) and Euclid Curioso, for helpful support while CPI was reintroduced to their department. Statistical analysis was provided by the Seattle Children's Core for Biomedical Statistics, which is supported by the Center for Clinical and Translational Research at Seattle Children's Research Institute and grant UL1RR025014 from the NIH National Center for Research Resources. The authors appreciate a critical reading of the manuscript by Lucinda Getz, Stephanie Axelrod and Delila Katzka, and a proofreading review by Kori J. Flajole.

Funding Statement

This work was supported by internal funding. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

8D report preparation in Downloadable PPT, Excel and PDF templates| with Example |

Tiago Aparecido Rodrigues Rita

8D report communicates how 8D methodology is used to solve a recurring problem or customer complaints . Most of the customers ask 8D report as a proof of the implementation of solution to their complaints. Hence lets learn how to prepare a 8D report through an easy example. You will also get downloadable and editable 8D report templates with example. You will be able to find 8D templates in Excel, PPT and PDF formats.

Before continuing with this its recommended to learn our article on 8D problem solving in which we have clearly explained the 8 steps in 8D and when to use 8D. In this article we are doing its practical side.

Let’s do it.

An Example for the preparation of 8D report

Let’s imagine that you are a chef at a diner restaurant, and suddenly an order has returned. The customer is complaining that the snack was carried out scorched.

You quickly need to carry out an analysis to understand what actually happened at the time of snack production, take the appropriate actions and prevent this from happening more often in the future.

Then, you decide to use the 8D in order to solve the problem.

let’s see how the resolution of this analogy would be using the 8D methodology .

Check below in 9 steps how to apply it easy with a simple practical example.

Before we begin, download the templates in excel, PPT and PDF to support you in you daily routine. Excel and PPT template are editable, which you can use for other projects.

8D report templates with example (Download)

8d problem solving step 1 – customer complaint.

We need to describe the problem related by the customer , according to customer´s language. Tip: In this step it is very important to faithfully describe what the customer complained about, how the information was passed on.

8D Problem solving STEP 2 – Team Building

We need to build the multifunctional team that will work in the investigation, this can be performed by the responsible persons for the area affected. Tip: Create a strong team that has knowledge on the related subject, if possible, extend participation to everyone who, at some point, has any contact related to the problem

8D Problem solving STEP 3 – Problem Description

Problem description with details, characterize and transform from the customer language to our language. Tip: Be as detailed in the description of the problem as possible, include images, videos if possible to help the understanding the problem.

8D Problem solving STEP 4 – Containment action

In this step we need to develop or propose / containment action in order or Take action so that the customer does not continue to receive products with the same problem. ***Give a destiny to the snack returned. Tip: Try to develop a containment action where the customer is satisfied and safe for that moment, unfortunately the failure has already occurred now we need to restore the image with the customer.

8D Problem solving STEP 5 – Finding the root cause and corrective action

Now we need to find the root cause, using auxiliary tools, if you read our article about 8D , you can find some kind of tools to support the analysis to find and confirm the root cause. Tip: During the analysis you can use the following tools to support the team to solve the problem:

• Tendency Chart
• Brainstorming
• Affinity Diagram
• Cause and Effect Diagram
• Why Why Analysis
• FTA – Fault Tree Analysis
• SIPOC / Flowchart
• Capability Studies

To support us, we´ll use fish bone diagram and the why why analysis:

In conjunction with the multifunctional team, we need to raise the possibilities that may have contributed to the problem having occurred, taking into account the 6M’s After that we score according to the potential using Highly likely / low probability or Improbable. This score will support us on focus just the high potential causes.

After we find the most potential root causes, we use the Why Most analysis in order to confirm if in fact this happened because of the potential cause raised by the team. 

The more common way to use the Why-Why analysis, it´s just asking 5 times the “Why” to the potential root causing, until we no longer have an answer to the 5 Why´s. Normally after that, we´ll find the root cause inside the potential cause. But, to support us on this analysis we´ll use the Why-Why to find 3 kind of root cause:

Occurrence Root Cause

Why did the problem occur?

Detection Root Cause

Why did not detect the problem?

Systematic Root Cause

Why did not prevent the problem?

8D Problem solving STEP 6 – Validation of the proposed root cause and corrective action

The team need to create plan in order to confirm / validate the proposed solutions in step 5º . Depend on the problem you are facing, you can use tests in low scale to get a feedback quickly. Tip: Use short scale tests / use auxiliary tools tools to proof the effectiveness of corrective actions. This step is very important to avoid gap and in the future the problem appear again.

Tools to support the validation of root cause

• Correlation
• Simulations

8D Problem solving STEP 7 – Implementation of Corrective action

According to the results in the step 6º, you can make official what was has been proven during the validations of solutions, this step is very important because is from this topic will you systematize the actions to the future.

8D Problem solving STEP 8 – Preventive action

Now we need implement the actions on the system, and make a plan in order to avoid the re-incidence of the fail. In this step it´s very important that all documentation be update, to ensure that all analysis was implemented to all internal process. Tip: Use preventive actions to avoid recidivism / transform the actions in best practices and update all documentations related with the process.

8D Problem solving STEP 9 – Closure

In the last step we need to present all results, recognition about all participants, lessons learned to Others areas, and 8D Finalization

Bellow you can find the template filled with the example:

We hope you have enjoyed the article on 8D report templates with example.

Thank you. Hope you have noticed downloadable and editable 8D PPT template. Go and download it, present before your team and solve your customer complaints.

You may refer more 8D report preparation example from here .

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Introduction

Mathematicians love a good puzzle. Even something as abstract as multiplying matrices (two-dimensional tables of numbers) can feel like a game when you try to find the most efficient way to do it. It’s a little like trying to solve a Rubik’s Cube in as few moves as possible — challenging, but alluring. Except that for a Rubik’s Cube, the number of possible moves at each step is 18; for matrix multiplication, even in relatively simple cases, every step can present more than 10 12 options.

Over the past 50 years, researchers have approached this problem in many ways, all based on computer searches aided by human intuition. Last month, a team at the artificial intelligence company DeepMind showed how to tackle the problem from a new direction, reporting in a paper in Nature that they’d successfully trained a neural network to discover new fast algorithms for matrix multiplication. It was as if the AI had found an unknown strategy for solving a monstrously complex Rubik’s Cube.

“It’s a very neat result,” said Josh Alman , a computer scientist at Columbia University. But he and other matrix multiplication specialists also emphasized that such AI assistance will complement rather than replace existing methods — at least in the near term. “It’s like a proof of concept for something that could become a breakthrough,” Alman said. The result will simply help researchers on their quest.

As if to prove the point, three days after the Nature paper came out, a pair of Austrian researchers illustrated how new and old methods might complement each other. They used a conventional computer-aided search to further improve one of the algorithms that the neural network had discovered.

The results suggest that, like the process of solving a Rubik’s Cube, the path to better algorithms will be full of twists and turns.

Video : DeepMind researchers trained an AI system called AlphaTensor to find new, faster algorithms for matrix multiplication. AlphaTensor quickly rediscovered — and surpassed, for some cases — the reigning algorithm discovered by German mathematician Volker Strassen in 1969.

Christopher Webb Young/ Quanta Magazine ; Emily Zhang for Quanta Magazine

Multiplying Matrices

Matrix multiplication is one of the most fundamental and ubiquitous operations in all of mathematics. To multiply a pair of n -by- n matrices, each with n 2 elements, you multiply and add these elements together in particular combinations to generate the product, a third n -by- n matrix. The standard recipe for multiplying two n -by- n matrices requires n 3 multiplication operations, so a 2-by-2 matrix, for example, requires eight multiplications.

For larger matrices, with thousands of rows and columns, this process quickly becomes cumbersome. But in 1969, the mathematician Volker Strassen discovered a procedure for multiplying a pair of 2-by-2 matrices using seven rather than eight multiplication steps, at the cost of introducing more addition steps.

Strassen’s algorithm is needlessly convoluted if you just want to multiply a pair of 2-by-2 matrices. But he realized it would also work for bigger matrices. That’s because the elements of a matrix can themselves be matrices. For example, a matrix with 20,000 rows and 20,000 columns can be reimagined as a 2-by-2 matrix whose four elements are each 10,000-by-10,000 matrices. Each of these matrices can then be subdivided into four 5,000-by-5,000 blocks, and so on. Strassen could apply his method to multiply 2-by-2 matrices at each level of this nested hierarchy. As the matrix size increases, the savings from fewer multiplications grows.

Strassen’s discovery led to a search for efficient algorithms for matrix multiplication, which has since inspired two distinct subfields. One focuses on a question of principle: If you imagine multiplying two n -by- n matrices and let n run toward infinity, how does the number of multiplication steps in the fastest possible algorithm scale with n ? The current record for the best scaling, n 2.3728596 , belongs to Alman and Virginia Vassilevska Williams , a computer scientist at the Massachusetts Institute of Technology. (A recent unpublished preprint reported a tiny improvement using a new technique.) But these algorithms are of purely theoretical interest, winning out over methods like Strassen’s only for absurdly large matrices.

The second subfield thinks on a smaller scale. Soon after Strassen’s work, the Israeli American computer scientist Shmuel Winograd showed that Strassen had reached a theoretical limit: It’s not possible to multiply 2-by-2 matrices with fewer than seven multiplication steps. But for all other matrix sizes, the minimum number of required multiplications remains an open question. And fast algorithms for small matrices could have an outsize impact, since repeated iterations of such an algorithm might beat Strassen’s algorithm when reasonably sized matrices are being multiplied.

Unfortunately, the sheer number of possibilities is huge. Even for 3-by-3 matrices, “the number of possible algorithms exceeds the number of atoms in the universe,” said Alhussein Fawzi , a DeepMind researcher and one of the leaders of the new work.

Faced with this dizzying menu of options, researchers have made progress by transforming matrix multiplication into what seems like a totally different math problem — one that is easier for computers to handle. It’s possible to represent the abstract task of multiplying two matrices as a specific kind of mathematical object: a three-dimensional array of numbers called a tensor. Researchers can then break this tensor up into a sum of elementary components, called “rank-1” tensors; each of these will represent a different step in the corresponding matrix multiplication algorithm. That means that finding an efficient multiplication algorithm amounts to minimizing the number of terms in a tensor decomposition — the fewer the terms, the fewer the steps involved.

In this way, researchers have discovered new algorithms that multiply n -by- n matrices using fewer than the standard n 3 multiplication steps for many small matrix sizes. But algorithms that outperform not only the standard but also Strassen’s algorithm for small matrices have remained out of reach — until now.

The DeepMind team approached the problem by turning tensor decomposition into a single-player game. They started with a deep learning algorithm descended from AlphaGo — another DeepMind AI that in 2016 learned to play the board game Go well enough to beat the top human players.

All deep learning algorithms are built around neural networks: webs of artificial neurons sorted into layers, with connections that can vary in strength representing how much each neuron influences those in the next layer. The strength of these connections is tweaked over many iterations of a training procedure, during which the neural network learns to transform each input it receives into an output that helps the algorithm accomplish its overall goal.

In DeepMind’s new algorithm, dubbed AlphaTensor, the inputs represent steps along the way to a valid matrix multiplication scheme. The first input to the neural network is the original matrix multiplication tensor, and its output is the rank-1 tensor that AlphaTensor has chosen for its first move. The algorithm subtracts this rank-1 tensor from the initial input, yielding an updated tensor that is fed back into the network as a new input. The process repeats until eventually every element in the starting tensor has been reduced to zero, meaning there are no more rank-1 tensors to take out.

At that point, the neural network has discovered a valid tensor decomposition, since it’s mathematically guaranteed that the sum of all the rank-1 tensors is exactly equal to the starting tensor. And the steps it took to get there can be translated back into steps of the corresponding matrix multiplication algorithm.

Here’s the game: AlphaTensor repeatedly decomposes a tensor to a set of rank-1 components. Each time, AlphaTensor gets rewarded if it finds a way to reduce the number of steps. But shortcuts to victory are not at all intuitive, just as you sometimes must scramble a perfectly ordered face on a Rubik’s Cube before you can solve the whole thing.

The team now had an algorithm that could, theoretically, solve their problem. They just had to train it first.

Like all neural networks, AlphaTensor needs a lot of data to train on, but tensor decomposition is a notoriously hard problem. There were few examples of efficient decompositions that the researchers could feed the network. Instead, they helped the algorithm get started by training it on the much easier inverse problem: adding up a bunch of randomly generated rank-1 tensors.

“They’re using the easy problem to produce more data for the hard problem,” said Michael Littman , a computer scientist at Brown University. Combining this backward training procedure with reinforcement learning, wherein AlphaTensor generated its own training data as it blundered around looking for efficient decompositions, worked much better than either training method on its own.

The DeepMind team trained AlphaTensor to decompose tensors representing the multiplication of matrices up to 12-by-12. It sought fast algorithms for multiplying matrices of ordinary real numbers and also algorithms specific to a more constrained setting known as modulo 2 arithmetic. (This is math based on only two numbers, so matrix elements can only be 0 or 1, and 1 + 1 = 0.) Researchers often start with this more restricted but still vast space, in hopes that algorithms discovered here can be adapted to work on matrices of real numbers.

After training, AlphaTensor rediscovered Strassen’s algorithm within minutes. It then discovered up to thousands of new fast algorithms for each matrix size. These were different from the best-known algorithms but had the same number of multiplication steps.

In a few cases, AlphaTensor even beat existing records. Its most surprising discoveries happened in modulo 2 arithmetic, where it found a new algorithm for multiplying 4-by-4 matrices in 47 multiplication steps, an improvement over the 49 steps required for two iterations of Strassen’s algorithm. It also beat the best-known algorithm for 5-by-5 modulo 2 matrices, reducing the number of required multiplications from the previous record of 98 to 96. (But this new record still lags behind the 91 steps that would be required to beat Strassen’s algorithm using 5-by-5 matrices.)

The new high-profile result created a lot of excitement, with some researchers heaping praise on the AI-based improvement on the status quo. But not everyone in the matrix multiplication community was so impressed. “I felt like it was a little overhyped,” said Vassilevska Williams. “It’s another tool. It’s not like, ‘Oh, the computers beat the humans,’ you know?”

Researchers also emphasized that immediate applications of the record-breaking 4-by-4 algorithm would be limited: Not only is it valid only in modulo 2 arithmetic, but in real life there are important considerations besides speed.

Fawzi agreed that really, this is just the beginning. “There is a lot of room for improvement and research, and that’s a good thing,” he said.

A Final Twist

AlphaTensor’s greatest strength relative to well-established computer search methods is also its greatest weakness: It’s not constrained by human intuition about what good algorithms look like, so it can’t explain its choices. That makes it difficult for researchers to learn from its achievements.

But this may not be as big a drawback as it seems. A few days after the AlphaTensor result, the mathematician Manuel Kauers and his graduate student Jakob Moosbauer , both of Johannes Kepler University Linz in Austria, reported another step forward.

Manuel Kauers tweaked the DeepMind approach to generate further improvements.

Jakob Moosbauer

When the DeepMind paper came out, Kauers and Moosbauer were in the process of searching for new multiplication algorithms using a conventional computer-aided search. But unlike most such searches, which start afresh with a new guiding principle, their method works by repeatedly tweaking an existing algorithm in hopes of squeezing more multiplication savings out of it. Taking AlphaTensor’s algorithm for 5-by-5 modulo 2 matrices as a starting point, they were surprised to find that their method reduced the number of multiplication steps from 96 to 95 after just a few seconds of computation.

AlphaTensor also helped them make another improvement indirectly. Previously, Kauers and Moosbauer hadn’t bothered to explore the space of 4-by-4 matrices, believing that it would not be possible to beat two iterations of Strassen’s algorithm. The AlphaTensor result prompted them to reconsider, and after a week of computation time starting from scratch, their method turned up another 47-step algorithm unrelated to the one AlphaTensor had discovered. “If somebody had told us that there is something to discover for 4-by-4, we could have done that earlier,” said Kauers. “But OK, well, that’s how it works.”

Littman expects more such surprises, likening the situation to the first time a runner finished a mile in under four minutes, a feat that had widely been considered impossible. “People were like, ‘Oh, wait, we can do this,’ and now lots of people can do it,” he said.

Looking forward, Fawzi hopes to generalize AlphaTensor to tackle a broader range of mathematical and computational tasks, just as its ancestor AlphaGo eventually branched out into other games.

Kauers sees this as the true litmus test for the application of machine learning to discovering new algorithms. He points out that the quest for fast matrix multiplication algorithms is a combinatorial problem to which computer searches, with or without human assistance, are well suited. But not all mathematical problems are so easy to pin down. If machine learning can discover a qualitatively new algorithmic idea, he said, “this would then be a game changer.”

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1. Government’s scope, efficiency and role in regulating business

Table of contents.

• Views on the efficiency of government
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American s are evenly divided in their preferences for the size of government. Yet a somewhat greater share wants the government to do more to solve problems than say it is doing too much better left to others.

There is a persistent belief that government is wasteful: 56% say it is “almost always wasteful and inefficient.”

However, a majority of Americans (58%) say government regulation of business is necessary to protect the public good.

Divisions on government’s size, scope

Overall, 49% say they would prefer a smaller government providing fewer services, while 48% say they would rather have a bigger government providing more services.

Most Democrats prefer a larger government. For nearly half a century, Democrats and Republicans have differed in their preferences for the size of government. Today, those differences are as wide as they have ever been:

• Nearly three-quarters of Democrats and Democratic-leaning independents (74%) favor a bigger government, providing more services. By comparison, in 2015, a smaller majority of Democrats (59%) said they preferred a bigger government.
• Just 20% of Republicans and Republican leaners prefer a bigger government; nearly four times as many want smaller government with fewer services. Republicans’ views of the size of government have changed less than Democrats’. Still, when George W. Bush was running for reelection in 2004, roughly a third of Republicans favored a bigger government.

When asked about the proper role of government, about half of Americans (53%) say the government should do more to solve problems, while 46% say the government is doing too many things better left to businesses and individuals.

An overwhelming share of Democrats (76%) say government should do more to solve problems, while about a quarter (23%) say it is doing too many things better left to individuals and businesses.

By contrast, Republicans prefer a more limited role for government: 71% say government is doing too many things better left to businesses and individuals, while 28% say government should do more to solve problems.

There are also sizable demographic differences in these views:

• White adults (54%) are the most likely to say government is doing too many things better left to businesses and individuals, while smaller shares of Asian (34%), Black (31%) and Hispanic (29%) adults say the same.
• Younger adults are more likely than older adults to favor a larger role for government, with adults ages 18 to 29 (66%) being the most likely to say government should do more to solve problems.
• Among income groups, a majority of lower-income adults (61%) say government should do more to solve problems, while smaller shares of upper- and middle-income adults (53% and 48%, respectively) say the same.

Views among partisans by race, ethnicity and income

Among partisans, there are wide demographic differences on the preferred role of government – especially among Republicans.

Hispanic Republicans (58%) are much more likely than White Republicans (21%) to favor a larger role for government.

Views among Democrats are much less divided, with at least seven-in-ten Democrats in each racial and ethnic group saying government should do more to solve problems.

Nearly half of lower-income Republicans (46%) say that the government should do more to solve problems, while smaller shares of middle- (22%) and upper-income (19%) Republicans say the same.

Wide majorities of Democrats across income groups say government should do more to solve problems.

In assessments of the efficiency of the government, a majority of Americans (56%) find it to be “almost always wasteful and inefficient.” A smaller share (42%) say government “often does a better job than people give it credit for.”

Overall, views on the efficiency of government have remained somewhat steady since 2019, with views today mirroring those five years ago.

Among partisans, a majority of Democrats (63%) say the government often does a better job than people give it credit for, while a large majority of Republicans (77%) say government is often wasteful and inefficient.

Views on the efficiency of government in both parties have remained steady since 2021.

While Democrats are generally more likely than Republicans to say government does not get enough credit, these views vary somewhat depending on which party holds the presidency:

• Democrats are now more likely to give credit to the government than they were during the Trump administration.
• Among Republicans, views of government efficiency were more positive during the Trump administration.

This is consistent with shifts in views during prior administrations .

On the topic of government regulation of business, about six-in-ten Americans (58%) say that government regulation of business is necessary to protect the public interest. Four-in-ten, however, say government regulation of business usually does more harm than good.

These views have remained largely unchanged since 2017.

As with other attitudes about government, Republicans and Democrats differ on the impact of government regulation of business:

• About two-thirds of Republicans (65%) say government regulation does more harm than good.
• Roughly eight-in-ten Democrats (82%) say government regulation is necessary to protect the public interest.

Among other demographic differences:

• White adults (45%) are the most likely to say government regulation does more harm than good, while smaller shares of Hispanic (32%), Asian (29%) and Black (27%) adults say the same.
• Younger adults are more likely than older adults to say government regulation of business is necessary to protect the public interest, with adults ages 18 to 29 (64%) being the most likely to say this.

Americans are divided in their views on the country’s ability to solve important problems. About half (52%) of Americans say “this country can’t solve many of its important problems,” while 47% say that “as Americans, we can always find ways to solve our problems and get what we want.”

More Americans express confidence in the country’s ability to solve problems now than a year ago (47% now, 43% then). Still, the share saying this is lower than it was from 2019 to 2022.

Unlike assessments of government, there are no partisan differences in views on the country’s ability to solve its important problems.

In both parties, about half say the U.S. can’t solve many of its important problems, while slightly narrower shares say Americans can always find ways to solve the country’s problems.

Views among age groups

Among age groups, younger adults are the most likely to express skepticism in the country’s ability to solve its important problems. About six-in-ten adults ages 18 to 29 (62%) say the U.S. can’t solve many of its important problems, while smaller shares of older adults say the same.

Overall, the shares of adults in each age group who voice skepticism on the country’s ability to solve its problems remain higher than they were in 2022.

However, older adults have grown slightly more optimistic on this issue in the past year. Views among the youngest adults are relatively unchanged from 2022.

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