Decisions are part of our daily life, and some choices are harder to make than others. For example, buying a house. When you go to buy a house, you will probably be thinking about the cost, location, number of bedrooms, number of bathrooms, condition, size of the lot, parking, etc. In other words, there are a lot of things to consider when making this type of decision. Therefore, you may be wondering how to factor in each of these criteria when considering which house to buy. This is where the Pugh matrix comes in.
- What is a Pugh matrix?
- When should you use a Pugh matrix?
- What is the difference between a Pugh matrix, FMEA, and correlation matrix?
- Types of Pugh matrices
- How do you create a Pugh matrix?
- Step 1: Gather a team
- Step 2: Choose the options
- Step 3: Choose a baseline/reference design
- Step 4: Determine the CTQs/Criteria
- Step 5: Establish weights for each criterion (if you are creating a weighted Pugh matrix)
- Step 6: Construct the matrix
- Step 7: Rank each alternative against the baseline for each criterion
- Step 8: Determine the score for each alternative
- Step 9: Choose the best option
- Tips to successfully complete a Pugh matrix
- Advantages and disadvantages of the Pugh matrix
- Conclusion
What is a Pugh matrix?
A Pugh matrix is a numerical decision-making tool often used in Design for Six Sigma (DFSS) or during the DMADV process. It is used to determine the best option from a list of alternatives based on certain CTQ (critical-to-quality) criteria. This tool was developed by mechanical engineer Stuart Pugh and is also known by some of the following names:
- Decision matrix/grid
- Selection matrix/grid
- Opportunity analysis
- Problem matrix
- Criteria-based matrix
- Criteria rating form
- Pugh concept selection method
- Pugh controlled convergence
Design teams use Pugh matrices most frequently after determining the Voice of Customer (VOC) and Voice of Business (VOB) and completing Quality Function Deployment (QFD) or House of Quality.
The key benefit of the Pugh matrix is its simplicity. It does not involve complicated mathematics to reach a solution, but often yields the same results as intensive decision-making approaches.
When should you use a Pugh matrix?
You should consider using a Pugh matrix if…
- You have a list of options and need to narrow it down to the single best choice.
- You must make a decision based on a series of criteria.
In general, Pugh matrices are used to aid during new product development processes. However, you can also use them under other circumstances as discussed in the following section.
What is the difference between a Pugh matrix, FMEA, and correlation matrix?
The Pugh matrix is very similar to Failure Mode and Effects Analysis (FMEA) and correlation matrices in that all are numerical decision-making tools. The key difference is that teams typically use the Pugh matrix when designing new products or processes (such as during DFSS and DMADV), while they typically use FMEA and correlation matrices for existing processes (such as during DMAIC).
Pugh matrices are useful in many areas beyond just new product design though, such as:
- Process improvement or project opportunity selection
- Supplier selection
- Financial or investment decisions
Types of Pugh matrices
There are two types of Pugh matrices:
- Unweighted
- Weighted
Unweighted Pugh matrices are the simplest form since they consider all criteria to be of equal importance.
Weighted Pugh matrices are more complex but allow the team to decide if some criteria are more important than others.
In the house hunting example, you may have “must-haves” and “nice-to-haves” when searching for a house. In a weighted Pugh matrix, you would rank the “must-haves” with a higher importance level than the “nice-to-haves”.
Therefore, weighted Pugh matrices are typically more useful since they allow you to consider the relative importance of each criterion. Unweighted Pugh matrices do have their place though when a decision is simpler, or all criteria have similar importance levels.
How do you create a Pugh matrix?
Next time you need to decide between several possible options, try using the below steps to create a Pugh matrix.
Step 1: Gather a team
The team should consist of key stakeholders who are knowledgeable of the process and/or product. In manufacturing environments, this could include roles such as:
- Process engineering
- Quality engineering
- Design engineering
- Scientists
- Marketing
- Sales
- Supply chain
- Management
🔎 EXAMPLE: Let’s explore the house hunting example in more detail. In this case, your team may consist of your family members, your realtor, and a financial advisor.
Step 2: Choose the options
In every decision, there must be options that you are choosing between. Before beginning a Pugh matrix, your team should discuss all potential options and ensure that everyone fully understands each one. Aligning early in the process makes accurately considering criteria and ratings much easier.
The team should consider a brainstorming session for deciding what options to include. There is no limit on the number of options that can be compared using the Pugh matrix. However, your team can consider using a tool like multi-voting to limit lengthy lists to only the most feasible options.
🔎 EXAMPLE: While looking for a house, you are considering the following options:
| Option | Building Type | Cost ($/month) | School District Rating | Size (sqft) | Proximity to Work (minutes) |
|---|---|---|---|---|---|
| 1 | Condo | 2,500 | B | 1,200 | 5 |
| 2 | Two-Story House | 6,000 | A | 2,800 | 30 |
| 3 | Apartment | 2,000 | C | 1,000 | 10 |
| 4 | One-Story House | 4,500 | A | 2,000 | 45 |
Step 3: Choose a baseline/reference design
One key aspect of the Pugh matrix is the need for a baseline design to rate all other options against. In many cases, this will be the current product or process. If no current product or process exists, the team should decide which option they want to compare the others to. This is often the most feasible or simplest solution or even a competitor’s design. However, the team can ultimately choose whichever reference design makes the most sense for their process.
🔎 EXAMPLE: In the house hunting example, you may decide to treat your current home as your baseline design. In this case, you live in a 1,200 sqft apartment that is 15 minutes from where you work, has a monthly rent payment of $3,000, and is in a marginal school district with a B rating.
Step 4: Determine the CTQs/Criteria
At this stage, use the VOC and VOB to determine which criteria are necessary for the product to be successful. These are often referred to as CTQs or Critical to Quality factors. It’s important to remember to consider the business needs as well as the customer needs when determining the CTQs. For example, the profit margin of the product may not matter to the customer but will matter greatly to the business.
Ensure the criteria are very specific and clear so your team can accurately evaluate each option. Consider the wording of each criterion to ensure they aren’t ambiguous and that every criterion follows the same rating scale. For example, “cost” is an ambiguous criterion. “Lower cost” is a better option since it clearly defines the goal of the criterion. “Lower cost” also establishes a ranking scale where a positive rating means the option is better than the baseline.
If you find that the list of criteria is very long, consider using multi-voting techniques to narrow the list to the most important criteria.
An alternative to multi-voting is to assign criteria as primary or secondary. Primary criteria are the most critical while secondary criteria may allow for a more granular analysis between the top options. When using this method, evaluate the options against the primary criteria to eliminate obvious losers.
🔎 EXAMPLE: During your house search, you may define the following criteria:
- Lower cost
- Better school district
- Larger living space
- Closer to work
For each of these criteria, you will be comparing your current home to each of the alternative options and rating if the alternative is better or worse than your current home.
Step 5: Establish weights for each criterion (if you are creating a weighted Pugh matrix)
If you are creating a weighted Pugh matrix, you will now need to determine the relative importance of each criterion. The Kano model can be a helpful tool for determining which criteria are “must haves” versus “nice to haves”. Typically, the criteria are rated from 1-10 with the most critical “must have” being weighted the highest. This system works best when you use the full scale of 1 to 10 to establish weights. If you assign a 9 or 10 to all criteria, the weighting scale loses its significance. While all criteria included in the decision-making process are important, it’s critical to rank their importance relative to one another.
It can often be difficult to decide on the weighting for each criterion and teams will often find that this is where the most disagreements occur. For this reason, it is critical to take this stage slowly and ensure that the team is able to come to a full agreement before proceeding with the process. One option for ranking can be to have each team member rank the criteria and then average the ratings.
🔎 EXAMPLE: While house hunting you decide that having a good school district is top priority because you have young children. You also need a larger living space to accommodate your growing family. You would like to stay close to work, but it is not a deal breaker since you can work from home often. Finally, you would always love to save some money, but you just got a decent promotion so finding a lower cost option is not as important as the other criteria. Based on that, let’s assign the following weights to each criterion:
- Lower cost: 1
- Better school district: 4
- Larger living space: 3
- Closer to work: 2
In this case, “better school district” has the highest weight since it is the most important to you while “lower cost” has the lowest weight. The weights also add up to 10 to keep them evenly distributed.
Step 6: Construct the matrix
List all criteria in the first column and the weight for each criterion in the second column. The third column shows the baseline design, and the following columns show each alternative option. Fill in zeroes for each criterion in the baseline column to set up the comparison of the alternative options.
🔎 EXAMPLE: The matrix for our house hunting example might look something like this:
Step 7: Rank each alternative against the baseline for each criterion
When ranking each alternative option, assign a score of +1 if the alternative is better than the baseline for that specific criterion and -1 if it is worse than the baseline. If the alternative is the same as the baseline for a given criterion, assign it a score of 0.
A cross-functional team with deep knowledge of the product or process must participate in the ranking process, as ‘better or worse than baseline’ can be highly subjective. The group should have an open discussion while ranking each alternative against the criteria to ensure all perspectives are considered.
If the team wants to use a finer scale for ranking, consider a five-point scale (-2, -1, 0, +1, +2) or a seven-point scale (-3, -2, -1, 0, +1, +2, +3). Going above a seven-point scale typically adds unnecessary complexity and is not recommended.
🔎 EXAMPLE: Let’s rank each option in our house hunting example against the baseline based on the information given in the example from step 2. It is important to do some research before ranking the options so that the rankings are based on real information. In this case, I decided to use a five-point scale to more finely rank the options.
Step 8: Determine the score for each alternative
If using a weighted Pugh matrix, multiply each value by the associated criteria weight and then sum each column. If using an unweighted Pugh matrix, simply find the sum of each column.
The baseline design should always have a score of zero and each alternative should either have a positive or negative score based on the results of the ranking. The alternatives with a negative score are “worse” than the baseline and those with a positive score are “better” than the baseline.
🔎 EXAMPLE: The scores for each option in our example are given at the bottom of the matrix below.
Step 9: Choose the best option
In theory, the alternative with the highest weighted sum after completing the Pugh matrix should be the winner. At this point it is important to use common sense though. The team should review the results and make sure the decision makes sense.
In many cases, the Pugh matrix will identify a few obvious losers and one or more potential winners that rank closely to each other. At this point, evaluate if the highest ranked option is the best one to go with or if a hybrid solution between two or more of the top options is a better option.
If, after completing the Pugh matrix, the team finds that several alternatives all have the same high score, you may want to consider reevaluating either the criteria weights or the rankings. This is also a good situation to move from a three-point rating scale to a five or seven-point rating scale to get more sensitive results.
🔎 EXAMPLE: We can now rank the options in our house hunting example from best to worst with 1 being the best and 4 being the worst. In this case, there is an obvious loser in option #3. The apartment scored lower than our baseline which means it is not a good choice. On the other hand, the condo and the two-story house scored +5 and +6, respectively. Does this mean the two-story house is the clear winner? Not necessarily. Since these options had a similar score, you may want to define some additional criteria to compare the options. In this case, that could be “nice-to-haves” such as a large yard, proximity to stores, etc.
Tips to successfully complete a Pugh matrix
Before attempting a Pugh matrix, consider the following to have the best chance of success:
- A well-versed, unbiased team is critical for evaluating each concept and the criteria. Cross-functional teams of 4-8 members are optimal to capture all perspectives while minimizing the noise of too many voices. You may also want to consider including someone with limited experience to gain an outsider’s perspective.
- An experienced facilitator who has no stake in the product or process can help ensure the team stays on track and can help settle disputes in an unbiased manner.
- Plan enough time for the activity to ensure the team does not feel rushed into making a decision. The time needed will depend on the complexity of the problem. If needed, it is better to schedule a follow-up meeting than to rush into a decision prematurely.
- Clearly define the goal before starting so that there are no misconceptions among the team.
- Perform other assessments ahead of time to clearly define the VOC and VOB. This can include assessments such as QFD and the Kano model, among others.
- Use data as much as possible when ranking alternatives. For example, if you know the actual cost to implement each design, use that data to rank each option accordingly. Using opinions solely to complete the Pugh matrix often results in inaccuracies due to misconceptions by the team.
- Complete sanity checks after finishing the Pugh matrix to make sure the results are reasonable. Often, the best option is to create an optimal hybrid solution from a few of the highest-ranking alternatives.
- Document any disagreements or reasons for certain decisions for reference in future work.
Advantages and disadvantages of the Pugh matrix
Some advantages of using the Pugh matrix for decision-making are:
✔️ It is a simple and non-technical approach to decision-making.
✔️ Pairwise comparison against a baseline allows for easier differentiation between options.
✔️ It creates structure for the decision-making process.
✔️ Using a Pugh matrix encourages a team-based process to minimize individual bias.
✔️ It can be made more or less sensitive depending on the complexity you choose (unweighted vs weighted, three-point ranking scale vs seven-point ranking scale).
✔️ The Pugh matrix can handle a large number of decision criteria and alternatives.
On the other hand, some disadvantages of using a Pugh matrix for decision-making are:
❌ It may not consider interrelationships or other dependencies
❌ You may be forced to make assumptions about how a potential design will perform if you do not have supporting data. Be sure to make note of any assumptions so these can be considered in the final decision.
❌ An internal team may weigh criteria differently than a customer which can affect the outcome and potentially lead to an undesirable decision for the end user.
Conclusion
Overall, the Pugh matrix is a great option if you need to make any type of decision between different options. Due to its simplicity, the Pugh matrix is ideal for both complex technical decisions as well as more mundane examples like the house hunting case study that we explored in this article. Can you think of a time when a Pugh matrix could be a useful tool in your work or life? We’d love to hear from you in the comments below!
