# Pugh Method: How to decide between different designs?

How can engineers decide systematically between different designs? How can engineers do a concept evaluation and selection?

One method, called Pugh method, helps engineers in design decisions by establishing a procedure to choose the best design from the considered designs.  This method is also known as Decision-Matrix Method or Pugh Concept Selection.  There are variations of the method however I’m going to explain here how I use it.

Step 1:  Make a list of the criteria that you want to compare between different designs.  Each criterion should be an objectively quantifiable measure.

 Criteria Criterion 1 Criterion 2 Criterion M

Step 2: Establish weights factors for each criterion.  A number between 1 and 10 can be chosen for each criteria, the bigger the scale the more experienced you should be to impose the weights.  Other approach can be to distribute a number of points (e.g. 100) between all criterions.  This step can be challenging for novice engineers, one way to overcome this is to just classify them in a 3-point scale where 1 is important, 2 is very important and 3 is extremely important.  The last option is to omit the use of the weights; this would mean that all criterions are equally important.  Whatever weight approach you choose I have to warn that the design selected is influenced by the selection of the weights.  The last issue before passing to the next step is that the order matters when you use this method, establish the weights factor before any analysis is made!  Otherwise you will be unconsciously biased toward one design and assign weights that benefit the strong criterions of that particular design.

 Criteria Weights Criterion 1 3 Criterion 2 2 Criterion M 3

Step 3:  Generation of different designs.  The designs can be generated with Brainstorming, or TRIZ just to mention two examples.  However the way to generate the designs is not the focus here.  The number of designs to evaluate will depend on the complexity of the product being designed.  That being said I would advice not to do a Pugh matrix for just 2 designs, in practice something between 3 to 7 designs could be compared.  At first generate as many designs as possible but then filter them to a manageable quantity.

 Criteria Weights Design 1 Design 2 Design N Criterion 1 3 Criterion 2 2 Criterion M 3

Step 4: Analysis of designs.  This is the step were the classical engineering takes place.  You will quantify mass, energy lost, stress, flow, etc.  All the criterions will need an analysis to quantify it, thus those numbers will have units.

 Criteria Weights Design 1 Design 2 Design N Criterion 1 Analysis 3 #.## [Kg] #.## [Kg] #.## [Kg] Criterion 2Analysis 2 #.## % #.## % #.## % Criterion MAnalysis 3 #.## [MPa] #.## [MPa] #.## [MPa]

Step 5: Fill the matrix.  Now for each design a number has to be calculated to fill its criterion cell.

 Criteria Weights Design 1 Design 2 Design N Criterion 1 3 ? ? ? Criterion 2 2 ? ? ? Criterion M 3 ? ? ?

Again, there is more than one way to do this.  A common way is to establish one of the designs as the Datum design, and compare the other designs criterion analysis numbers (from Step 4) against the Datum design.  A scale is established beforehand, a common one goes from -3 to 3.  If the design is better than the Datum it will get a positive number and the magnitude of the number depends on how much better it is.

After using this approach, I started to modify it in order to have a minimal number of decisions based on the designer assessment of the analysis numbers.  So instead of choosing a number between -3 and 3, I calculated one.  The procedure starts by calculating the average across designs for the criterions.   Then that average is subtracted to each design criterion and that is the number that is input into the decision matrix.

 Criteria Weights Design 1 Design 2 Design N Criterion 1 3 ±#.## ±#.## ±#.## Criterion 2 2 ±#.## ±#.## ±#.## Criterion M 3 ±#.## ±#.## ±#.##

Step 6: Calculate each design score.  This is done by multiplying each criterion weight by the design cell value (±#.##) and summing all the values for the design.  This procedure is repeated for all designs.  Then the design with the higher score is the best design and the decision was made taken into consideration all of the criterions and designs in an objective manner.

 Criteria Weights Design 1 Design 2 Design N Criterion 1 3 ±#.## ±#.## ±#.## Criterion 2 2 ±#.## ±#.## ±#.## Criterion M 3 ±#.## ±#.## ±#.## Total: #.## #.## #.##

Now that the steps are explained, we can go over a specific example.  Since a previous post already discussed Baja and Formula SAE Frame Design we are going to use a frame / chassis as the example for the Pugh Method (decision-matrix method).

Step 1: Make a list of the criteria that you want to compare between different designs.

• Torsional Stiffness
• Torsional Stiffness to Weight ratio
• Frontal Impact (Max Stress)
• Roll Over (Max Stress)
• CG height
• Weight

Step 2: Establish weight factors for each criterion.  In this case choose a number between 1 and 10.

 Criteria Weight (1-10) Torsional Stiffness 9 Torsional Stiffness to weight ratio 10 Frontal Impact 7 Roll Over 8 CG height 8

Step 3: Generate Different Designs.

Step 4: Analysis of designs.

 Criteria Design 1 Design 2 Design 3 Design 4 Design 5 Design 6 Torsional Stiffness [lbf-deg] 857.81 1057.3 1128.5 1444.9 1009.26 1430.8 Torsional Stiffness to weight ratio 14.767 17.595 18.761 32.293 16.877 23.141 Frontal Impact [psi] 53,011 47,775 38,961 24,444 36,791 26,238 Roll Over [psi] 33,929 28,835 30,995 28,174 36,176 32,705 CG height [in.] 9.64 9.47 9.94 9.78 9.77 9.60

Step 5: Fill in the matrix.  In this case each criteria was averaged across designs.  Then each criteria average was subtracted from each design criterion.  This is known as to center the values.  See the example below.

 Criteria Design 1 Design 2 Design 3 Design 4 Design 5 Design 6 Average Torsional Stiffness [lbf-deg] 857.81 1,057.3 1,128.5 1,444.9 1,009.26 1,430.8 1,154.76 (Average of all designs TS) = Criterion-Average 857.81-1,154.76 =  -296.95

Then the procedure is repeated for the whole table.

 Criteria Design 1 Design 2 Design 3 Design 4 Design 5 Design 6 Average Torsional Stiffness [lbf-deg] 8,57.81 1,057.3 1,128.5 1,444.9 1,009.26 1,430.8 1,154.76 = Criterion-Average -296.95 -97.46 -26.26 290.13 -145.50 276.04 Torsional Stiffness to weight ratio 14.767 17.595 18.761 32.293 16.877 23.141 20.57 = Criterion-Average -5.80 -2.98 -1.81 11.72 -3.69 2.56 Frontal Impact [psi] 53,011 47,775 38,961 24,444 36,791 26238 37,870 = Criterion-Average 15,141 9,905 1,091 -13,426 -1,079 -11632 Roll Over [psi] 33,929 28,835 30,995 28,174 36,176 32705 31,802.33 = Criterion-Average 2,127 -2,967 -807 -3,628 4,374 902.67 CG height [in.] 9.64 9.47 9.94 9.78 9.77 9.6 9.7 = Criterion-Average -0.06 -0.23 0.24 0.08 0.07 -0.1

The only problem now is that each criterion is on different scales, we want to  have all in the same scale.  This can be accomplished by dividing each centered value by the biggest value for that criterion.  The resulting table should look like this:

 Criteria Weight Design 1 Design 2 Design 3 Design 4 Design 5 Design 6 Torsional Stiffness [lbf-deg] 9 -1.0234 -0.3359 -0.0905 1 -0.5014 0.9514 Torsional Stiffness to weight ratio 10 -0.4953 -0.2540 -0.1545 1 -0.3152 0.2191 Frontal Impact [psi] 7 1 0.6541 0.0720 -0.8867 -0.0712 -0.7682 Roll Over [psi] 8 0.4862 -0.6784 -0.1845 -0.8295 1 0.2063 CG height [in.] 8 -0.25 -0.9583 1 0.3333 0.2916 -0.4166

Step 6: Calculate each design score. See the example for Design 1

 Criteria Weight Design 1 Torsional Stiffness [lbf-deg] 9 -1.0234 Torsional Stiffness to weight ratio 10 -0.4953 Frontal Impact [psi] 7 1 Roll Over [psi] 8 0.4862 CG height [in.] 8 -0.25 Totals 9 x (-1.02) +10 x ( -0.49) + 7 x 1 +8 x 0.48 + 8 x (-0.25) = -5.2744

This is the final Pugh Decision Matrix

 Criteria Weight Design 1 Design 2 Design 3 Design 4 Design 5 Design 6 Torsional Stiffness [lbf-deg] 9 -1.0234 -0.3359 -0.0905 1 -0.5014 0.9514 Torsional Stiffness to weight ratio 10 -0.4953 -0.2540 -0.1545 1 -0.3152 0.2191 Frontal Impact [psi] 7 1 0.6541 0.0720 -0.8867 -0.0712 -0.7682 Roll Over [psi] 8 0.4862 -0.6784 -0.1845 -0.8295 1 0.2063 CG height [in.] 8 -0.25 -0.9583 1 0.3333 0.2916 -0.4166 Totals -5.2744 -14.0784 4.6676 8.8228 2.1682 3.6942

Design 4 is the design that the decision matrix chose based in the analysis and weight factors.  With the specific procedure carried here, once the designer establish the criterion weights, all other numbers are calculated without need of the designer to interpret or assign ratings to the designs.

As was mentioned in the description of the general steps there are many variations to the Pugh method.  This is the version that I ended up using, after using it over the years for Formula SAE design decision-making.