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Pugh matrix: what it is, how to build one, and a worked example

Short answer

A Pugh matrix is a decision tool that compares several solutions with one reference solution, called the datum, one criterion at a time, marking each as better (+), the same (S) or worse (-). It was developed by Stuart Pugh and described in his 1991 book Total Design.

Pick the datum, usually today's way of doing the job. List the criteria the solution must meet. Then, for each concept and each criterion, ask one question: is it better than the datum, the same, or worse? Mark +, S or -. Count the marks. The count is not the answer. It shows where each concept is strong and where it is weak, so the team can fix the weaknesses, borrow the strong features from other concepts and run the matrix again with a better datum. That second pass is why the method is also called controlled convergence. It suits early choices, when the facts are not complete and a score from 1 to 10 would be invented precision.

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What is a Pugh matrix? Meaning, datum and marks

The Pugh matrix is named for Stuart Pugh, who set out the method in Total Design: Integrated Methods for Successful Product Engineering (Addison-Wesley, 1991) as part of a wider approach to design. The method is also called the Pugh method, Pugh concept selection and controlled convergence. Plants use it for more than product design: any choice between a handful of ways to solve one problem, such as how to feed, clamp, convey or inspect a part, or how to cut a changeover.

A Pugh matrix has a few parts. The datum is the reference concept. Every other concept is compared with it, and the datum itself is never marked. The concepts are the options in contention. The criteria are what the solution has to achieve. The marks are +, S and -, where S means the same as the datum (or you cannot tell).

The marks are deliberately coarse. A team that cannot yet say whether a design saves 40 seconds or 50 can usually say whether it is better than today's. That is the point. The method works early, on sketches and descriptions, before anyone has priced the options.

When to use a Pugh matrix

  • You have between three and ten ways to solve one problem and need to narrow them before spending on detail.
  • There is a current solution to measure against. Today's way is the natural datum.
  • The facts are incomplete. The marks are relative, so the matrix works on concepts that are still sketches.
  • The choice has to be defended later. The sheet records which criteria mattered and why a concept was dropped. It fits in the Improve phase of a DMAIC project and on the countermeasures side of an A3.

Do not use it to rank a long backlog of improvement ideas by how much they will deliver. That is a job for a prioritization matrix. And do not use it before the cause of the problem is known: a matrix will happily rank solutions to the wrong problem. Find the cause first with root cause analysis.

How to make a Pugh matrix in seven steps

  1. 1

    State the decision in one line

    For example: how do we cut changeover time on filler 2? A vague decision gives vague criteria.

  2. 2

    List the concepts at the same level of detail

    Describe or sketch each concept to about the same depth. A rough idea marked against a fully detailed one looks worse than it is.

  3. 3

    Write the criteria and flag the must-haves

    Around ten at most, drawn from what the customer, the operator and the plant need. Mark any criterion where a concept that is worse than the datum should not go ahead as it stands. Safety is the usual one. Keep criteria separate, so one benefit is not counted twice under two names.

  4. 4

    Choose the datum

    Today's solution is the obvious choice. Whatever you pick, everyone has to understand it the same way, and it is not marked.

  5. 5

    Mark every concept against the datum, one criterion at a time

    Go across the row for one criterion, then move to the next. Discuss the marks, not the totals. If you cannot decide between S and a mark, write S and note the doubt.

  6. 6

    Count the marks, then study the minuses

    Add up pluses, Ss and minuses per concept. The net is pluses minus minuses. For each minus ask whether it can be accepted, or cured by borrowing a feature from a concept that scored a plus on the same criterion.

  7. 7

    Improve, combine and run round 2

    Make the improved or combined concepts, pick a strong one as the new datum and mark again. Stop when one concept stands out and the team agrees. If nothing beats the datum, the datum may be the best choice.

Pugh matrix example: cutting changeover time on a filler

Illustrative example with made-up marks. A bottling plant wants to shorten the changeover on filler 2. The datum is today's method: operators use wrenches and loose change parts. There are three concepts. A is quick-release clamps on the change parts. B is a change-part cart that the previous shift stages. C is a spare set of change parts kept at the filler. There are seven criteria, and operator safety is flagged as a must-have.

Pugh matrix for the filler 2 changeover (illustrative), datum = wrenches and loose change parts
CriterionA: Quick-release clampsB: Staged change-part cartC: Spare change-part set
1. Cuts changeover time+++
2. Operator safety (must-have)+SS
3. Low capital cost-S-
4. Quick to put in place-S-
5. Fits the existing machine-SS
6. Easy to learnS-S
7. Low upkeep-S-
Pluses211
Sames153
Minuses413
Net (pluses minus minuses)-20-2

Each concept has 7 marks: A is 2 + 1 + 4 = 7, B is 1 + 5 + 1 = 7, C is 1 + 3 + 3 = 7.

Reading the matrix

No concept wins on the count. B comes out level with the datum at a net of 0 and the others sit at -2. But the sheet says more than the net. A is the only concept that improves safety, and its minuses are cost, speed to install, fit and upkeep. B costs almost nothing but offers no safety gain and asks operators to learn a routine. Since safety is a must-have, none of the concepts is worse than the datum on it, so none is dropped.

That is where the second round starts. The team takes B as the new datum and makes a hybrid, D: B's staged cart plus quick-release clamps on only the two clamps that put hands in the danger zone. D keeps most of B's low cost and adds A's safety gain where it counts. The team marks D, and any other improved concept, against B on the same seven criteria, and repeats until one stands out.

The weighted view

A weighted view is an optional second look, and it is not part of the plain method. The team gives each criterion a weight from 1 to 5, set before marking: time 5, safety 5, capital cost 3, quick to install 2, fit 3, easy to learn 2, upkeep 2. The weighted net multiplies each mark (+1, 0 for S, -1) by its weight and adds them up.

A: +5 (time) +5 (safety) -3 (cost) -2 (install) -3 (fit) -2 (upkeep) = 10 - 10 = 0. B: +5 (time) -2 (learn) = 3. C: +5 (time) -3 (cost) -2 (install) -2 (upkeep) = 5 - 7 = -2. So the weighted net is 0 for A, 3 for B and -2 for C. A moves from -2 up to 0 because safety carries weight 5. B still leads. If the weighted and plain views named different leaders, the team would talk about the weights first, not the totals.

Pugh matrix vs decision matrix vs prioritization matrix

These three get mixed up. Search results often use the names for each other. The difference is what you are choosing between and how you score.

Three matrices and when each fits
MatrixChoosing betweenHow it scoresUse it when
Pugh matrixA few competing concepts for one problem+, S or - against a datumEarly, with incomplete facts, to improve and narrow concepts
Weighted decision matrixOptions that are already well definedA score, often 1 to 5 or 1 to 10, times a weight for each criterionFacts are in and the team needs a ranked list to defend a choice
Prioritization matrixA long list of improvement ideasUsually impact against effortDeciding which ideas to do first

See the glossary entry for the [weighted decision matrix](/learn/glossary) and the guide to the [prioritization matrix](/blogs/prioritization-matrix-lean-manufacturing).

Common Pugh matrix mistakes

  • Treating the total as the answer. The count is a prompt for discussion, not a verdict.
  • A weak or unclear datum. If people read it differently, the marks mean different things.
  • Concepts at different levels of detail, so a vague one gets marked down for what is not yet drawn.
  • Overlapping criteria. Cost and payback, or speed and cycle time, double count the same thing.
  • Changing the criteria after seeing the marks. Set them and the weights first.
  • Choosing on a tie. Tied concepts mean the criteria do not separate them yet. Add detail, or improve them.
  • Using it on a problem whose cause is unknown. Fix that first.

Pugh matrix template

The Pugh matrix template comes as Excel and PDF. It holds up to 8 concepts and 12 criteria, counts pluses, Ss and minuses, shows the net and an optional weighted net, flags a minus on a must-have criterion, and has a second sheet for round 2 with a new datum. The weights, the must-have flag and the round 2 sheet are the template's own additions to the classic method.

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FAQ

Questions about pugh matrix

  1. A Pugh matrix is a decision tool that compares several concepts with one reference concept, the datum, one criterion at a time, marking each as better (+), the same (S) or worse (-). The team counts the marks, studies the weaknesses, improves or combines the concepts and repeats the comparison. It comes from Stuart Pugh's Total Design (Addison-Wesley, 1991).

  2. The datum is the reference concept that all the others are compared with. It is usually today's solution, or a strong concept the team already knows well. The datum is never marked itself, and the team has to read it the same way. In round 2 the strongest concept from round 1 often becomes the new datum.

  3. State the decision, list the concepts at the same level of detail, write the criteria and flag the must-haves, choose the datum, and mark every concept against the datum as +, S or - one criterion at a time. Count the marks, study the minuses, improve or combine the concepts and run the matrix again with a stronger datum until one concept stands out.

  4. A Pugh matrix marks each concept as better, the same or worse than a datum and is used early, with incomplete facts, to narrow and improve concepts. A weighted decision matrix scores each option, often from 1 to 5 or 1 to 10, multiplies by a weight for each criterion and adds up the totals. It suits options that are already well defined.

  5. A plus means the concept is better than the datum on that criterion, a minus means it is worse, and S means the same, or that the team cannot tell. Counting the pluses and minuses gives the net for each concept. The count is a prompt for discussion, not the decision.

  6. Do not use it to rank a long list of improvement ideas, which is a job for an impact and effort prioritization matrix, and do not use it before the cause of the problem is known. A matrix can rank solutions to the wrong problem just as easily as to the right one.

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