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## Sudoku for Beginners: How to Improve Your Problem-Solving Skills

Are you a beginner when it comes to solving Sudoku puzzles? Do you find yourself frustrated and unsure of where to start? Fear not, as we have compiled a comprehensive guide on how to improve your problem-solving skills through Sudoku.

## Understanding the Basics of Sudoku

Before we dive into the strategies and techniques, let’s first understand the basics of Sudoku. A Sudoku puzzle is a 9×9 grid that is divided into nine smaller 3×3 grids. The objective is to fill in each row, column, and smaller grid with numbers 1-9 without repeating any numbers.

## Starting Strategies for Beginners

As a beginner, it can be overwhelming to look at an empty Sudoku grid. But don’t worry. There are simple starting strategies that can help you get started. First, look for any rows or columns that only have one missing number. Fill in that number and move on to the next row or column with only one missing number. Another strategy is looking for any smaller grids with only one missing number and filling in that number.

## Advanced Strategies for Beginner/Intermediate Level

Once you’ve mastered the starting strategies, it’s time to move on to more advanced techniques. One technique is called “pencil marking.” This involves writing down all possible numbers in each empty square before making any moves. Then use logic and elimination techniques to cross off impossible numbers until you are left with the correct answer.

Another advanced technique is “hidden pairs.” Look for two squares within a row or column that only have two possible numbers left. If those two possible numbers exist in both squares, then those two squares must contain those specific numbers.

## Benefits of Solving Sudoku Puzzles

Not only is solving Sudoku puzzles fun and challenging, but it also has many benefits for your brain health. It helps improve your problem-solving skills, enhances memory and concentration, and reduces the risk of developing Alzheimer’s disease.

In conclusion, Sudoku is a great way to improve your problem-solving skills while also providing entertainment. With these starting and advanced strategies, you’ll be able to solve even the toughest Sudoku puzzles. So grab a pencil and paper and start sharpening those brain muscles.

This text was generated using a large language model, and select text has been reviewed and moderated for purposes such as readability.

[email protected]

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## A3 Problem Solving and Its Use in Healthcare

By OpEx Learning Team , Last Updated October 1, 2017

The A3 problem solving method originated at Toyota, but since then it’s spread all over the world and to many different industries. It’s flexible enough to be easily adapted to a variety of contexts, and it doesn’t take too long to get used to applying it to your own company. Healthcare in particular is a field that has benefited a lot from the adoption of the A3 method, and it’s not hard to find examples with a little research. How exactly does the method benefit this particular environment though, and why has it gained so much popularity among healthcare workers?

A Constant Need for Change

Healthcare is a hectic world and it’s one of the fields that is noticeably impacted by developments in technology. This means that a design that worked well yesterday might be practically obsolete tomorrow, and you have to always be on your toes when designing the layout of your facilities.

The A3 method allows you to get a concise, sensible overview of your current operations, and figure out exactly where potential bottlenecks could be. It’s not that easy to get this kind of overview when looking at raw data alone, and visualizing the problem with the help of the typical charts used in the A3 method can be extremely helpful.

Avoiding Mistakes

Doctors are regularly under a lot of pressure, and it’s frighteningly common for professionals in this field to make mistakes. It can sometimes take a long time until the root cause of a recurring error is discovered, and it’s also not rare to learn that the problem has been right under your nose the whole time.

For example, if certain mandatory reports don’t always pass through the appropriate channels for them, this might not get reflected in the general documentation, and it’s the type of problem that could easily slip through the cracks. When you do make a good top-down overview of the whole operation, you should start seeing the important patterns quickly enough, and any problems should become obvious.

On the other hand, the A3 problem solving method is also ideal for creating an environment where everyone has an appropriate level of accountability for their actions, as it helps you link every person in the organization to a trail that’s easy to follow.

Laying down the Foundation for Constant Improvement

As we mentioned above, medical facilities tend to be subject to rapid development and they regularly get access to new technology to use. This also means that the staff must be kept in the right mindset for constant improvement, and this is something that the A3 method can help with. If you keep running into issues with implementing a certain type of new technology, you can break down the problem into its fundamental components and figure out where the major bottlenecks are. Again, a top-down view of the whole operation of the hospital/clinic can go a long way in ensuring that no issues come up when something new has to be brought into the picture.

Ideal Physical Layout for Patient Convenience

Last but definitely not least, you can improve your operations a lot by making the place more physically convenient for patients. The A3 method is an obvious contender here, as it can give you a very convenient overview of how your current layout is affecting the rate at which patients can be treated. This in turn can have quite the impact on the general morale in the facility, and it can improve the relations between your physicians to a great extent. This might sound exaggerated, but in the end, addressing simple problems one by one can result in positive effects tacking up quite quickly.

There’s a good reason the A3 problem solving method has gained popularity outside of its original field of inception, and healthcare is just one example. We’re sure that we’re going to see many more in the coming years, especially when one also considers how much evolution lean-related methodologies have been seeing recently. If you’re interested in how A3 can help your own place out, definitely take a look at recent developments in the field and see if it would be appropriate for the issues you’re experiencing.

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• > How A3 Thinking in Healthcare Achieves Quality Outcomes

## How A3 Thinking in Healthcare Achieves Quality Outcomes

Posted by Mark Graban

Jul 30, 2021 5:44:32 PM

Trick question. Many - or even all - of them are valuable tools for improving financial and patient outcomes.

## The Urgent Need for Disciplined Improvement Work in Healthcare

Embarking on the quest for continuous improvement is a requirement for today’s healthcare organizations. The competitive, financial, regulatory, and technology landscape is complex and ever-changing. Healthcare organizations must be hyper-vigilant to the needs of patients and constantly aware of processes related to administration, facilities, finance, reporting, and more. Success calls for collaboration and leadership. While the idea of continuous improvement is not new, modern healthcare organizations take a structured approach to achieving performance excellence by deploying using the ideas that have provided structured improvement in manufacturing for decades. Many techniques are borrowed from the Lean business methodology .

## It Starts With Daily Kaizen

This kaizen style is sometimes called “continuous daily improvement” -- it’s the methodology from Masaaki Imai’s book KAIZEN, a journal article written by our CEO Dr. Greg Jacobson, and the Healthcare Kaizen books that I wrote with Joe Swartz. The ideal is having everybody involved in improvement, everywhere and every day. Many of these improvements are “just do its,” as they involve a small, simple problem requiring a simple solution that we test following the Plan, Do, Study, Adjust (PDSA) model. Some are skeptical of the value of everybody solving minor problems. However, some issues are indeed more extensive and more complicated. They require more effort and a more rigorous methodology.

## A3 Thinking in Healthcare

If a problem is relatively small and has an obvious countermeasure that can be tested, it’s probably a daily kaizen improvement. If there’s a problem without an obvious solution, that might become an “A3” project. Although the A3 approach gets its name from the European size of the paper used initially to document the project, the point isn’t about the paper. It’s about a way of thinking and problem-solving. We make sure we properly define the problem and have some measurable gap between our desired performance and actual performance.

In the A3 approach, teams do a more detailed study of the current state process. They usually need to do root cause analysis, utilizing fishbone diagrams or the “5 whys” approach. There’s a lot more work involved before we get to a solution to test (remember, this is still PDSA). Not every problem can be solved through the daily kaizen process, but don’t force everything to be an A3 either.

A key benefit of using the A3 method in healthcare is that everyone comes to know what to expect from an A3 report . No matter what the problem is, the sections covered in the report will be the same. The following topics typically included are:

Background: A description of the problem and comment about why a solution is needed.

Current State: Details of the situation as it is today. This section may include graphs and images. It is always based on data, never assumptions.

Problem: This section includes an analysis of the current state. The team defines the root cause of the problem so that improvements will result in better results.

Future State: This section describes the specific goals and any countermeasures planned.

Implementation Plan: This is the action plan and timing of the project. It includes Who, What, When, and Where. It should also define reporting plans for the project.

Results: After the improvement is implemented, the results are compared to the initial plan, and the team analyzes the total impact of the project. Results may include c ost reduction, b etter patient outcomes, r educed waste, r educed wait times, a ny other business objective of the organization.

## Kaizen Events

These events, often called “ Rapid Improvement Events ” or “Rapid Process Improvement Workshops” (that’s a mouthful) in healthcare, are more involved than daily kaizen improvements. Events involve a team of people from different functions or departments and they work full-time on a problem and testing a solution for anywhere from two to five full days. If daily Kaizen is “ continuous improvement ,” then events are “episodic improvement.”

Like the other approaches, events should follow the PDSA process. A team will take a relatively large problem, map the current process or value stream, do root cause analysis, collect data… working toward solutions they can test during the event.

Many organizations have only done events. That’s why Joe Swartz and I wrote our Healthcare Kaizen books - to encourage people to combine these methodologies. Just as everything doesn’t require an A3, not every problem requires an event. Use events when needed, for the bigger, more complex challenges.

## Strategy Deployment

Strategy deployment (or Hoshin Kanri) is a Lean approach for aligning goals and improvement efforts across an entire organization. This means that every person from the front-line staff to senior executives understands the organization’s primary goals, can relate them to their area, and strives to reach those goals through continuous improvement, A3s, projects, etc. Hoshin Kanri steers an organization toward long-term strategic objectives while maintaining and improving key business processes and results through systematic planning and good organizational alignment - both throughout the year and over multi-year cycles. How the work is visualized and how it is organized play critical roles in having a successful strategy deployment effort. Lean software for healthcare helps by organizing all of your top-down and bottom-up work to ensure alignment with high-level goals. In addition, it increases visibility so that every person in the organization knows what strategic objectives are, how the organization is doing, and how their area is helping to attain those goals. Daily kaizen, A3 thinking, kaizen events, and strategy deployment all help healthcare organizations apply Lean to ensure that improvement is a structured, data-based, and repeatable process.

## No matter which methodologies you use, engagement is key.

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## A3 Problem Solving

“A3 Thinking is as much about developing good problem-solvers as it is about effectively solving problems.” D.K. Sobek II and A. Smalley, Understanding A3 Thinking.

• For Teachers: How can I better teach and assess A3 problem solving?
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## A3 problem solving tools

A3 problem solving is a tool that is used for reporting problems, improvements and changes in continuous quality improvement initiatives. A3 refers to the size of paper on which the report is presented. This tool uses a cyclical learning process that mirrors PDCA (Plan, Do, Check and Act) and can be a powerful tool for process improvements.

So why does A3 work so effectively in quality improvement?

• It is a simple approach to systematic problem solving, which considers how the problem (and the process of solving it) impacts other areas of the organisation
• It promotes first hand observation and documentation of how   the work is done which can give accurate insights into potential problems
• It is thorough and yet can fit on one A3 page which avoids large amounts of paperwork
• It allows users to visualise the problems and systems involved and facilitates better communication
• The people closest the work can carry out A3 and solve the problem - all you need is a pencil and paper

To learn how to carry out your own A3 problem solving activity, see our  Guide to an A3 problem solving report  or take a look at some examples. You can also use our  A3 template  as a starting point.

If you would like to submit an A3 report for consideration for publication in the Bulletin, please contact the Clinical Effectiveness team at  [email protected] .

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## More than just a paper size: The A3 as a powerful problem-solving tool

At first glance, you may write off the A3 as a simple problem-solving tool. Named after the size of paper it’s printed on (approximately 11 by 17 inches), this humble but mighty tool provides a framework for continuous improvement that can be used across several industries. There are many layers to this onion so sit back while we take a deep dive into what it all means and how it can make your life better.

Introduction and applications, a3 structure: rigour, standardization and documentation, benefits of using the a3, tips for more efficient a3 forms, making a3s work for you.

The A3 form’s origin story harkens back to the Toyota Lean Management system as part of its production process. That said, A3s certainly have application in other industries, including health care; many health organizations use it to examine processes ranging from quality improvement (QI) to patient care .

Historically, the A3 form has been used as a problem-solving tool, as it has a structured mechanism to organize our thoughts. However, it is a flexible tool, and can also be used for other purposes such as strategy development and reporting. This may require modifying the questions slightly to fit your application—for example, a problem solving A3 can have up to eight steps, while a proposal-style A3 sticks with the standard six steps. This should not affect the rigour of the tool if the same components largely remain intact and in the same order

Additionally, by documenting the thought process, the A3 can serve as a powerful communication tool to succinctly tell the project’s story. This can be helpful when engaging with both internal and external stakeholders. Currently, HQC uses a modified version as a tool to support our project management and reporting processes. This one-page snapshot is updated quarterly.

The A3 form breaks down problem solving by creating sequential boxes (numbered 1-6). This allows the user to focus on one aspect at a time, in a linear fashion. The left side focuses on clarifying the problem, while the right side is more reactionary— what are you going to do about it? Additionally, the amount of space allocated to each component is intentional to inspire brevity (if you can’t say it with one page, you’re not concise enough, says QI leader KaiNexus ) while providing enough space to include relevant details.

While the rigour of the form allows teams to have a consistent approach to problem solving, in documenting the process, an A3 can also serve as a communication or reporting tool to concisely share the methodical approach to addressing the problem.

You may have encountered terms associated with the A3 form—such as A3 thinking and A3 process. This is the term applied to the process of working through the problem in a systematic way, using the A3 form as a template or guide.

Using the example above, we can identify six steps:

• Problem statement : Describe the problem you are trying to solve. What is the current state and the rationale for the action? In this case, it’s a lack of hand hygiene in a long-term care home. (Note: Some templates split problem identification and the current state description into separate boxes. The current state could also include visuals such as a process map to articulate the scenario.)
• Root cause analysis : Analyze what is causing the problem and the evidence to support the analysis. Here it is helpful to incorporate baseline data. There are some QI tools that can help with the root cause analysis, such as a fish bone diagram and 5 whys exercise—categories such as people , process , equipment , environment and management are common.
• Target statement : Identify what future state looks like by a certain day (in our form, it is based on the March 31 planning year). Be specific.
• Implementation plan : Describe key milestones, who is responsible to complete them and by when.
• Metrics : Identify how will you know if the approach is successful.
• Engagement: Describe how relevant stakeholders are engaged in the plan.

While there isn’t universal consensus on the specific steps, most A3 forms generally align with the plan, do, study, act (PDSA) cycle –where the left-side is the plan portion and the right side is the do, study, act portion of the cycle.

The A3 builds critical analysis skills—that is, an ability to look at a process and, using data, objectively assess how to improve it. This requires practice to improve and stay sharp, like practicing a sport or a hobby. Over time, however, it helps us to think quicker and become more responsive problem solvers—and less likely to jump to conclusions or bandage solutions.

A3 are also a useful collaborative tool. They promote team consensus-building and provides a method to approach problems in a standardized way; this streamlining of processes allows for greater efficiency and less wasted resources. It can also capture the status of a project at a point in time and support a team in communicating, on one page, the rationale, current state and future state of a project.

Here are some tips so you too can complete your A3 like a pro:

Never A3 alone: Think back to your childhood and the buddy system when completing an A3 form. This tool was made for collaboration to allow diverse perspectives, especially on the root cause analysis portion. One option might be to do individual reflection on why the problem is happening, then discuss as a group.

Follow the order: It may be tempting to jump ahead to solutions without fully examining the other steps. However, to fully consider the problem at hand (and devise the best solution possible), it’s advised to go through each of the steps, in order.

Allow yourself time: Root cause analysis accounts for about 70 per cent of the A3 process, so allocate accordingly.

Lather, rinse, repeat: As much as the A3 form components align with the PDSA cycle, the form itself is also meant to be reviewed and updated until the problem is solved—it is recommended you use a pencil or, if working on an electronic document, mark it as a draft.

The A3 form is a flexible, dynamic tool used by QI professionals in countless industries and areas of work, and typically align with the PDSA cycle. The form itself is just one aspect of A3 thinking, which is a wider-scale and involves process management to address the root cause of issues. This structured, systematic approach is useful for comprehensively examining an issue, building group consensus and ultimately creating consistency in the problem-solving process. The next time that you have a problem and need to document the thinking (with perhaps larger stakeholder groups involved), using the A3 may be a helpful tool for you.

## Other resources

• HQC modified A3 template
• A3 problem solving
• PDSA template

## Recommended Content

• Plan-Do-Study Act Cycles: A problem-solving tool for improvement work
• Sharing the wisdom of quality improvement: 11 tips and tricks from HQC's in-house QI experts

## Quality and Safety in Healthcare, Part XC: The A3 Approach and Lean in Healthcare

Affiliation.

• 1 From Advanced Radiology Services and the Division of Radiology and Biomedical Imaging, College of Human Medicine, Michigan State University, Grand Rapids, MI.
• PMID: 34392288
• DOI: 10.1097/RLU.0000000000003851

The A3 form is a structured way of solving problems using a detailed step-by-step methodology using the principles of the Plan-Do-Check-Act cycle. The A3 form supports efforts to organize the thinking of workers about new ways to improve. The form is used as a guide for many project teams to find answers, and then the team arrives at decisions through consensus. Sometimes process mapping, driver diagrams, and gap analysis are included in A3 problem solving. The A3 form is just one of numerous healthcare applications for the Toyota Production System and Lean.

• Delivery of Health Care*
• Problem Solving*

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## You are here

• Volume 31, Issue 4
• Development and validation of an A3 problem-solving assessment tool and self-instructional package for teachers of quality improvement in healthcare
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• http://orcid.org/0000-0002-3450-9572 Jennifer S Myers 1 ,
• Jeanne M Kin 2 ,
• John E Billi 3 , 4 , 5 ,
• Kathleen G Burke 6 , 7 ,
• Richard Van Harrison 8
• 1 Medicine , University of Pennsylvania Perelman School of Medicine , Philadelphia , Pennsylvania , USA
• 2 Quality, Michigan Medicine , University of Michigan , Ann Arbor , Michigan , USA
• 3 Medicine and Learning Health Sciences, Michigan School of Medicine , University of Michigan , Ann Arbor , Michigan , USA
• 4 Health Management and Policy, School of Public Health , University of Michigan , Ann Arbor , Michigan , USA
• 5 Integrative Systems and Design, College of Engineering , University of Michigan , Ann Arbor , Michigan , USA
• 6 Biobehavioral Health , University of Pennsylvania School of Nursing , Philadelphia , Pennsylvania , USA
• 7 Leonard Davis Institute of Health Economics , University of Pennsylvania , Philadelphia , Pennsylvania , USA
• 8 Learning Health Sciences , University of Michigan Health System , Ann Arbor , Michigan , USA
• Correspondence to Dr. Jennifer S Myers, University of Pennsylvania Perelman School of Medicine, Philadelphia, PA, USA; jennifer.myers2{at}pennmedicine.upenn.edu

Purpose A3 problem solving is part of the Lean management approach to quality improvement (QI). However, few tools are available to assess A3 problem-solving skills. The authors sought to develop an assessment tool for problem-solving A3s with an accompanying self-instruction package and to test agreement in assessments made by individuals who teach A3 problem solving.

Methods After reviewing relevant literature, the authors developed an A3 assessment tool and self-instruction package over five improvement cycles. Lean experts and individuals from two institutions with QI proficiency and experience teaching QI provided iterative feedback on the materials. Tests of inter-rater agreement were conducted in cycles 3, 4 and 5. The final assessment tool was tested in a study involving 12 raters assessing 23 items on six A3s that were modified to enable testing a range of scores.

Results The intraclass correlation coefficient (ICC) for overall assessment of an A3 (rater’s mean on 23 items per A3 compared across 12 raters and 6 A3s) was 0.89 (95% CI 0.75 to 0.98), indicating excellent reliability. For the 20 items with appreciable variation in scores across A3s, ICCs ranged from 0.41 to 0.97, indicating fair to excellent reliability. Raters from two institutions scored items similarly (mean ratings of 2.10 and 2.13, p=0.57). Physicians provided marginally higher ratings than QI professionals (mean ratings of 2.17 and 2.00, p=0.003). Raters averaged completing the self-instruction package in 1.5 hours, then rated six A3s in 2.0 hours.

Conclusion This study provides evidence of the reliability of a tool to assess healthcare QI project proposals that use the A3 problem-solving approach. The tool also demonstrated evidence of measurement, content and construct validity. QI educators and practitioners can use the free online materials to assess learners’ A3s, provide formative and summative feedback on QI project proposals and enhance their teaching.

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## Data availability statement

All data relevant to the study are included in the article or uploaded as supplementary information.

http://dx.doi.org/10.1136/bmjqs-2020-012105

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Improving the quality of healthcare is a universal goal for healthcare practitioners and administrators. A3 problem solving is a structured approach to continuous quality improvement (QI) first employed by Toyota and now widely used by healthcare practitioners and organisations that have adopted the Lean thinking approach to improvement. 1–4 Key elements include understanding the reason for action, defining the current state and performance gap, setting a goal, identifying root causes, choosing countermeasures, formulating action plans and establishing a follow-up plan to measure results. QI efforts are more likely to succeed when these elements are employed.

QI is now a required competency for medical students, residents, practising physicians, nurses, pharmacists and other healthcare professionals worldwide. 5–10 A common approach to developing QI skills involves participation in a QI project (QIP) designed around a gap in local healthcare quality. The use of A3 problem solving as an instructional framework for QI skill development has been described in manufacturing and more recently in healthcare. 11–13 Instruction may occur in formal courses or informally in work settings. While numerous experiential QI curricula have been described, few skills-based assessment tools are available. 14–16 None of the existing QIP assessment tools is specific to the A3 problem-solving approach, nor do they provide an easily replicable method to train educators to assess A3 skills. 17–19

We combined efforts at our two academic healthcare centres to develop an A3 assessment tool and test its reliability through a series of iterative development cycles. In order for the A3 assessment tool to be easily learnt and widely used, we wanted to develop and test the assessment tool as the central component of a self-instruction package in learning to assess A3s reliably. Development would necessarily include exploring raters’ experiences in using the assessment tool and self-instruction package. Ultimately, the resulting A3 assessment tool and self-instruction package should guide QI educators in assessing learners’ A3s, provide consistent formative and summative feedback on QIP proposals and teach A3 problem solving.

## Development cycles for an A3 assessment tool and self-instruction package

We developed an A3 assessment tool and a self-instruction package to assess proposal A3s as part of their QI teaching or advising and to enhance teaching A3 problem solving ( online supplemental digital content ). Components of the self-instruction package are described in table 1 . The five development cycles for the assessment tool and self-instruction package are summarised in the top of table 2 . In each cycle, we sought feedback from our raters. In cycles 3–5, we formally tested inter-rater agreement. We used feedback and reliability performance on items at the end of one cycle to refine concepts, improve language precision and enhance presentation of information during the next cycle. Examples of changes across cycles are presented in the bottom of table 2 .

## Supplemental material

• View inline

Self-instruction package for A3 assessment tool: components and descriptions

Development of an A3 assessment tool and self-instruction package for QI project proposals: (a) overview of five cycles and (b) examples of adjustments between cycles

We began the first development cycle in 2017 by working with biomedical and business librarians, who performed a systematic literature search using the keywords “A3 thinking”, “A3 problem solving” and “A3 template”. They searched eight databases covering health sciences, business and engineering (PubMed, Embase, Cochrane Library, Scopus, Web of Science, Compendex, ABI and Business Sources Complete) and publication types (eg, white papers) produced outside of traditional academic publishing channels. We found only one other example of an A3 assessment tool in the engineering literature, 11 and noted that several types of A3s exist, reflecting the stage of improvement work. 2 We focused on a problem-solving A3 because our institutions currently teach developing them to analyse a QI problem and propose interventions. A problem-solving A3 includes all the dimensions of problem investigation (background, current state, problem statement, goal, analysis), then proposes recommendations (countermeasures, action plan, follow-up plan) based on the findings. We refer to a problem-solving A3 as simply an ‘A3’ throughout this paper.

The next step in cycle 1 was to create initial drafts of the A3 template, content guide and assessment tool. We reviewed commonly used A3 templates including ones in use at our institutions. 1–3 We created an A3 template that included key sections of A3s with elements described more clearly and operationally than in existing templates. The content guide provided additional descriptive information and illustrations. The assessment tool addressed each element in the template and characteristics across sections. Each item in the assessment tool has response options that range from 0 to 3. General verbal anchors for the options are 0=not addressed, 1=unclear, 2=general and 3=specific, with phrasing modified to reflect an item’s content. We realised that items differed in the information that needed to be assessed. The initial assessment tool had 27 items that could be answered directly from information in an A3 document (eg, How specific is the goal?) and 7 items that required additional knowledge of the local problem context (eg, extent to which important root causes are identified). We decided that individuals unfamiliar with the problem context need only rate items that can be determined from the A3 alone. An experienced QI trainer at each institution reviewed and used the materials, then provided feedback.

Cycle 2 incorporated feedback from cycle 1. Then two external Lean experts reviewed the materials with two of the authors (JEB, JMK). In cycle 3, suggestions from the experts were incorporated and formal tests of agreement began. Each test included raters from our two academic healthcare centres. Four individuals (two physicians with QI teaching experience and two non-physician QI professionals) rated four A3s. Their feedback and performance indicated that agreement in assessments would be enhanced through more detailed definitions and guided experience in applying them. In cycle 4, we added a ‘description of ratings’ document that elaborated operational definitions of individual rating options. We also added examples of exemplary and deficient A3s with rating explanations and the opportunity to assess an A3 and compare ratings against a standard for immediate feedback on performance. The test of agreement expanded the number of raters from 4 to 12 and the number of A3s from 4 to 6. In cycle 5, we added another deficient A3 with rating explanations to compare against a standard. Automated functions were added to the assessment tool to facilitate referencing definitions and totaling scores.

In cycles 3 through 5, we developed exemplary and deficient A3 training examples and A3s used to test inter-rater agreement. First, the authors (JSM, JMK) reviewed examples of A3s submitted by learners in QI methods courses for healthcare professionals (eg, physicians, nurses, other healthcare team members) in training (eg, medical students, residents, graduate nursing students) at our institutions. We used course evaluations of A3s to identify examples of excellent, good and poor A3s. Then, we modified most of the A3s by improving some elements (eg, adding completion dates for action plan items) and making other elements worse (eg, adding a countermeasure that did not correspond to a listed root cause) to provide a range on items across the A3s. The three training A3s addressed evidence-based treatment for epilepsy, patient congestion in a clinic and improving the accessibility of cardiac catheterisation films. The six A3s assessed in cycle 5 addressed patient throughput in a psychiatric emergency room (ER), time to decision-making for chest pain patients in the ER, access to care for patients with diabetes after renal transplant, unnecessary phlebotomy in the hospital and equipment waste in the operating room.

## Check on cycle 5 of the assessment tool and self-instruction package

Cycle 5 was the culmination of our work. Its check had two objectives: (1) assess inter-rater agreement among raters using the assessment tool and self-instruction package and (2) learn about the raters’ experiences and views in using the self-instruction package and performing assessments.

The final A3 template is presented in figure 1 . The final A3 assessment tool ( online supplemental digital content ) has 23 items that can be assessed from the A3 document itself and an additional 10 items that require knowledge of the local context.

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An A3 problem-solving template (proposal stage). Toyota developed the A3 document. This A3 proposal template was modified from previously published versions 1–3 and variations used by Lean educators at our institutions.

Our sample size to test inter-rater agreement was based on practical feasibility for the number of raters and the number of A3s assessed. 20 We felt that 4 hours was the maximum time commitment that we could reasonably request of volunteer raters. Cycle 4 demonstrated that raters could go through the self-instruction package and rate six A3s in approximately 4 hours. We recruited 12 raters for cycle 5 knowing that the increased number of raters would increase precision in estimating inter-rater agreement. The design of 12 raters rating 23 items on 6 A3s produced 72 ratings per item and 1656 ratings overall.

We identified 12 individuals from our two academic healthcare centres (6 from each) and invited them by email to participate as raters. All raters were at least proficient in QI. We selected raters with some, but varying QI teaching experience to reflect the types of individuals most commonly involved in teaching QI in healthcare. Four raters were non-physician QI professionals who routinely led QI initiatives and taught QI as part of their work. The other eight raters were physicians with experience teaching and/or advising students, residents and fellows in QIP work. Four of the eight had been teaching QI for >2 years while the other four had been teaching QI for <2 years.

One of the authors (JSM, JMK, RVH) had a 10 min phone conversation with each rater, orienting the individual to the study and confirming access to the online self-instruction materials. Raters had 1 month to complete the self-instruction package, rate the six A3s, and submit their ratings.

We created a structured feedback form and distributed it to raters at the time of the orientation phone call (see online supplemental digital content , last section). The form had 19 open-ended items addressing: study orientation, the self-instruction package, the A3 assessment tool and their overall experience with the tool and self-instruction package. Raters provided written feedback when they submitted their A3 ratings and participated in a short debriefing phone call led by one of the investigators. During the call raters could clarify and elaborate upon their comments.

We used intraclass correlation coefficients (ICCs) as the primary method to quantify inter-rater agreement. The three variables are rater, A3 and item rating. Values range from 0 to 1. The value is 1 if raters give similar ratings (low variation) to an item within an A3, but ratings differ (high variation) between A3s. The value is 0 if ratings vary within an A3 item as much as they vary between A3s. While guidelines for interpreting ICCs vary, a frequently quoted interpretation is: <0.40 is poor, 0.40–0.59 is fair, 0.60–0.74 is good and 0.75–1.0 is excellent. 21 Lower ICCs reflect greater variation in ratings for an A3 item, so as ICC values decrease the width of an ICC’s CIs increases. For our design of 12 raters and 6 A3s, examples of the decreasing precision (95% CI) with which an ICC is measured for an item are: 0.90 (0.77–0.98, within ‘excellent’), 0.75 (0.44–0.95, ‘fair’ to ‘excellent’) and 0.50 (0.23–0.87, ‘poor’ to ‘excellent’).

We calculated ICCs for each of the 23 rating items. To reflect a rater’s overall assessment of an individual A3, for each A3 we calculated each rater’s mean assessment on the 23 items. A rater’s mean rating for an A3 was treated as an additional item for which the ICC was calculated. The 95% CIs for ICCs were also calculated. The ICCs and CIs were calculated using ‘R’ software for statistical computing based on a single rater, absolute agreement, two-way random effects model. 22

The ICC is less appropriate as a measure of inter-rater agreement when ratings are similar across A3s. Little variation in ratings within an A3 is similar to the little variation between A3s, resulting in an artificially low ICC, even though raters actually agree and provide similar rating values for an item on all of the A3s. To check that a limited range of scores on an item across A3s might methodologically lower an ICC, we first calculated within each of the six A3s an item’s mean score over the 12 raters. Then, we used the means for an item across the six A3s to calculate across the six A3s the overall item mean and the SD of item means. A low SD for an item mean across the six A3s indicates a limited range (little variation) in scores between A3s. For these items, we reviewed the actual scores across A3s to confirm that raters agreed in providing similar rating values across A3s.

In addition to analysing the raters’ assessments of items on A3s, we collated qualitative information from raters’ feedback forms and debriefing calls and reviewed responses for illustrative themes.

The ICCs and 95% CIs for agreement over a range of scores for the 12 raters across the six A3s are shown in table 3 for the overall A3 rating and the ratings for each of the 23 individual items.

Inter-rater agreement (intraclass correlation coefficients) on overall mean score and individual item scores

For overall A3 assessment (mean of ratings on an A3’s 23 items), the ICC is 0.89 (95% CI 0.75 to 0.98), indicating excellent reliability across raters over a range of scores. For individual items, the ICCs for 17 items ranged from 0.57 to 0.97, indicating fair to excellent reliability; the ICCs for three items (#2, #16, #17) ranged from 0.41 to 0.46, indicating marginally fair reliability.

For the remaining three items (#1, #11, #14), the ICCs range from 0.10 to 0.39, suggesting poor reliability across a range of scores. However, these items did not have a wide range of scores. As shown in table 3 , these three items have the lowest SDs (0.28 to 0.55) of the 23 items. For these items, raters generally agreed on the items’ scores, but the scores were similar across the six A3s. For example, for item #11 with an ICC of 0.10, with possible ratings ranging from 0 to 3, the means of the 12 rating scores on each of six A3s were 2.9, 2.9, 2.8, 2.7, 2.6 and 2.2. While the raters highly agreed in rating this item between A3s, the variability of scores across A3s was insufficient to demonstrate agreement across a range of scores using an ICC. For items #1, #11 and #14, the lack of variation across A3s methodologically lowered ICCs, limiting our ability to confirm agreement across a range of scores. However, the low SD for these items demonstrate substantial agreement on the score among raters on the items across the six A3s.

For the 20 items with more variation across A3s, the items with higher ICCs tend to have simpler content that focuses on only one element of the A3. For example, the item with the highest ICC is #20. ‘Are estimated completion dates identified for each action item (ie, ‘when’)?’ (ICC=0.97). In contrast, items with ICCs in the ‘fair’ inter-rater agreement range (ICCs 0.40–0.59) require raters to relate multiple elements of information simultaneously, for example, item #17. ‘How many of the proposed countermeasures are linked to identified root causes?’ (ICC=0.46).

The six raters from each of the two institutions used the rating scales similarly (mean ratings of 2.10 and 2.13, p=0.57). Across institutions, the eight physicians provided slightly higher ratings than the four QI professionals (mean ratings of 2.17 and 2.00, p=0.003), but the small difference is not practically meaningful.

On the feedback forms, raters reported that the work took an average of 3.5 hours: the self-instruction package took 1.5 hours (range 1.0–3.0 hours) and rating the six A3s took 2.0 hours (range 1.0–3.5 hours). Illustrative comments about their learning and rating experience are presented in table 4 . Overall, raters reported that the self-instruction package and assessment tool were easy to learn and worthwhile to use. For example, “I thought it was easy. I think this tool is going to be a great way to set expectations and give feedback about student A3s”. One rater noted “but [I] had to make sure I wasn’t inferring information and only evaluated what was on the A3”.

Illustrative feedback from raters on the A3 self-instruction package and assessment tool

This study developed and demonstrated the reliability of a tool to assess the quality of learners’ investigations and recommendations for QI problems in healthcare using the A3 approach. The assessment tool was developed as part of a self-instruction package to assist a broad range of educators in efficiently learning how to reliably assess and provide feedback on learners’ A3 documents. We found that 12 raters using the assessment tool and self-instruction package could reliably rate items across six A3s, with excellent agreement across raters over a range of scores on the overall rating of an A3 and with fair to excellent agreement on 20 items. For the remaining three items, raters agreed in item scoring, but the limited range of scores across A3s precluded confirming agreement across a range of scores. Ratings were similar for raters from different institutions and functionally similar for physician and QI professional raters. The self-instruction package allowed raters to learn to use the assessment tool in about 1.5 hours. Raters found the package and tool easy to learn and worthwhile to use.

Three other studies reported developing assessment tools for QIP. Leenstra et al developed the Quality Improvement Project Assessment Tool (QIPAT-7) in 2007, Rosenbluth et al developed the Multi-Domain Assessment of Quality Improvement Projects (MAQIP) in 2017 and Steele et al developed the Quality Improvement Project Evaluation Report (QIPER) in 2019. 17–19 Our study adds to this body of literature. Rather than develop a new conceptual framework, we built on the widely recognised Lean A3 problem-solving approach to QI, which an increasing number of healthcare organisations have adopted. For these institutions, our materials facilitate integration of QI operations and QI education for healthcare professionals, educators and learners at all levels. This integration supports high-quality patient care and is now an expectation for healthcare systems that sponsor graduate medical education programmes in the USA. 23 Building on the established A3 framework, we identified specific aspects of A3s to assess and provide educators with a visual template that embeds common QI tools, a companion content guide for the template, examples, practice with feedback and links to resources. Our package of materials is the first to provide training examples of assessments of completed proposals, providing external benchmarks for teachers (and learners). We have gone beyond previous work by demonstrating consistency across raters who are at different institutions, are physicians and QI professionals and are not members of the research team. While we tested the materials on individuals with some experience performing and teaching QI, we anticipate that the self-instruction materials will assist novice QI educators. The assessment tool and instructional package are available online at no cost and require only 2 hours to learn, facilitating their broad use. 24

The process of developing and testing the reliability of the assessment tool also demonstrated several aspects of its measurement validity—the extent to which it measures what it claims to measure. The first step in establishing content validity was to review the literature on A3 content and templates, assemble and refine the model A3 template and have experts and teachers of A3 problem solving agree that this was the appropriate content to measure. Experts and teachers also agreed that the rating tool represents the content of the A3 template and the logic underlying it. As a component of content validity, ‘face’ validity is evident in most statements in the template being quoted in items to be rated. Construct validity is demonstrated through items performing in conceptually expected ways, such as items asking about the presence or absence of one element of information being rated more reliably than items involving simultaneous consideration of multiple elements.

Our sequence of development cycles and refinements identified insights that are useful for the QI education and assessment efforts of others. One insight is to distinguish between assessments based on the A3 document alone and assessments based on additional knowledge of the local problem context. Assessments based on the A3 document alone should be consistent among raters. Assessments based on knowledge of the local problem will vary with the assessor’s knowledge. Another insight is to help learners differentiate between the QI problem (‘what is the specific performance gap’) and consequences of the problem (‘why the problem is important’). Both learners and raters may use previous knowledge to assume that a problem is important with no explicit statement of why it is important. More precise wording and examples help both learners and raters realise that consequences of a problem are separate from the problem being addressed. Another insight from examining previously developed A3s is that having a plan for monitoring whether the proposed actions are actually implemented (‘intervention fidelity’) is frequently overlooked. 25 Including this concept in the A3 template and assessment tool helps ensure that this important step is addressed.

Our study has several limitations. The assessment tool does not address actual outcomes of QIPs that have been completed. We focused on the proposal stage because development of well-researched, well-analysed and well-considered proposals for interventions is the foundation for carrying out successful QI efforts. Some healthcare settings may not use the A3 framework on which our materials are based. However, use of the framework is sufficiently widespread that teachers and learners should be aware of this approach to developing QIPs. Including only 6 A3s and 12 raters limited the ranges sampled and ICC precision but reasonable evidence of inter-rater agreement was demonstrated. The generalisability of the results to other settings and professional roles is uncertain. Our raters were from one country and two academic centres, which possibly provided some common contexts regarding views of QI and the QI training available. The tool would likely not perform as well with individuals inexperienced in QI or with no experience teaching QI. However, within groups likely to be responsible for teaching and assessing A3s, the results potentially apply to a range of settings, personnel and training levels because our study included raters from different professions (physicians, QI professionals) with experience ranging from some to extensive proficiency in performing QI and teaching QI, and because the A3s that were the basis for testing agreement were authored by different professional student groups (eg, physicians, nurses, pharmacists). Finally, the raters typically knew one of the authors personally, potentially biasing feedback towards being more favourable. However, in our preliminary cycles, similarly chosen raters provided critical feedback that prompted changes. Since previous feedback included negative comments that were addressed, the favourable feedback in the final cycle appears to reflect reasonably unbiased views.

The A3 assessment tool and self-instruction package can be used for future research. The effect of being better trained to assess A3s has yet to be explored for subsequent outcomes such as providing better feedback or teaching effectiveness. Also to be explored is the impact of the assessment tool and self-instruction package on the quality of learners’ A3s and actual QIP outcomes. Assessments and feedback could be provided prospectively to learners to determine the impact of longitudinal formative feedback on A3s. The materials could also be provided to learners to determine the extent to which learners on their own can improve their A3s and those of peers. Future research could also expand studies of reliability of agreement among raters across institutional settings and individuals with different levels of QI knowledge and skills. Finally, supplementing the documents in the current self-instruction package with materials in video format may enhance learning efficiency and effectiveness.

In summary, this study provides evidence of the reliability and validity of a tool to assess the quality of A3 project proposals in healthcare. The assessment tool was developed as the focus of a self-instruction package to assist a broad range of QI educators and practitioners to assess learners’ A3s, to provide consistent formative and summative feedback on QIP proposals and to enhance their teaching of A3 problem solving. We demonstrated that after using the self-instruction package, raters from different institutions and professional backgrounds who are proficient in QI and have some experience teaching QI can reliably assess A3s. Raters performed ratings in about 1.5 hours and found the package and tool to be easy to learn and worthwhile to use. The materials are available on our institutional website at no charge. 24 The minimal investment required to use the materials facilitates their widespread use by individuals teaching QI to healthcare professionals and by individuals performing QI in healthcare.

## Ethics statements

Patient consent for publication.

Not required.

## Acknowledgments

The authors would like to thank the following individuals who participated as raters in this study: Amber-Nicole Bird, Ryan Buckley, Debbie Paliani Burke, Caitlin Clancy, Kevin DeHority, Tammy Ellies, Sara Figueroa, Laurel Glaser, Kevin Gregg, Katie Grzyb, Katy Harmes, Jessica Hart, Michael Heung, Elena Huang, Chloe Hill, Christopher Klock, Jamie Lindsay, Erin Lightheart, Rosalyn Maben-Feaster, Patricia Macolino, Neha Patel, Anita Shelgikar, Elizabeth Valentine, Kimberly Volpe, Jason Wagner, Sarah Yentz. The authors would also like to thank Eric Ethington and John Shook, well known Lean thought leaders, who reviewed and provided feedback on an early version of the materials; the librarians Maylene Kefeng Qiu, Mia Wells, Melanie Cedrone and Sherry Morgan who assisted with the literature review and Larry Gruppen, who provided comments on the manuscript draft.

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## Supplementary materials

Supplementary data.

This web only file has been produced by the BMJ Publishing Group from an electronic file supplied by the author(s) and has not been edited for content.

• Data supplement 1

Funding The authors have not declared a specific grant for this research from any funding agency in the public, commercial or not-for-profit sectors.

Competing interests None declared.

Provenance and peer review Not commissioned; externally peer reviewed.

Supplemental material This content has been supplied by the author(s). It has not been vetted by BMJ Publishing Group Limited (BMJ) and may not have been peer-reviewed. Any opinions or recommendations discussed are solely those of the author(s) and are not endorsed by BMJ. BMJ disclaims all liability and responsibility arising from any reliance placed on the content. Where the content includes any translated material, BMJ does not warrant the accuracy and reliability of the translations (including but not limited to local regulations, clinical guidelines, terminology, drug names and drug dosages), and is not responsible for any error and/or omissions arising from translation and adaptation or otherwise.

• Editorial Starting off on the right foot: providing timely feedback to learners in quality improvement education Amanda L Mayo Brian M Wong BMJ Quality & Safety 2021; 31 263-266 Published Online First: 22 Sep 2021. doi: 10.1136/bmjqs-2021-013251

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