e

1. Pairwise Comparison Chart
(P.C.C.)
Objectives Goal #1 Goal #2 Goal #3 Goal #4 Score
Goal #1 •••• 0 0 1 1 3rd
Goal #2 1 •••• 1 1 3 1st
Goal #3 1 0 •••• 1 2 2nd
Goal #4 0 0 0 •••• 0 4th
Goal-i is less important than Goal-j
Goal-i is more important than Goal-j
Goal-i is compared to itself (meaningless comparison)
Ranking
of Goals
5036MAA – Design and Sustainability

2. Outline
- What is a Pairwise Comparison Chart (P.C.C.)?
- What is the need that a P.C.C. can cover?
- How does a P.C.C. fit into the design process?
- Methodology
- Examples
- Conclusions / Wrapping up

3. Pairwise Comparison Chart (P.C.C.)
Pairwise: to take two things/items at a time
Example: for a set of three cars {Car-1, Car-2 and Car-3}, one can form the
following pairs: {Car-1, Car-2}, {Car-1, Car-3} and {Car-2, Car-3}
Note: a lot of pairs from a small set of items… Could this be a drawback?
Comparison: to measure/describe the dissimilarity between items
Example: “in motorsport, performance is more important than comfort”;
“in motorsport, comfort is less important than performance”
Note: different expressions (“more important” vs “less important”) but same overall
meaning. I can use two ways to describe the same dissimilarity but must change
the statement accordingly.
Chart: sheet of information in the form of a table, graph, or diagram
Pairwise Comparison Chart: from a set of items, take two, describe the
dissimilarity between them and present the result in a chart; repeat for all pairs that
can be formed from the given set of items

4. What is a Pairwise Comparison Chart (P.C.C.)?
Technique / tool used to:
 rank a set of decision-making criteria (major design objectives)
 rate the criteria on a relative scale of importance
 rank & rate alternative designs
Main idea:
 Take two entities, measure their dissimilarity and judge which entity is more important
 Can be applied to a set of entities, by taking entities two at a time (in pairs)
 The result of the comparison between two different entities A and B is:
 “A is more important than B”; OR
 “B is more important thanA”

5. Pairwise Comparison Chart: used
to rank objectives /
characteristics that should be
included in our design

8. Example: PCC for a ladder
Objectives / Characteristics
• Ladder should be useful
• Used to maintain and repair outlets in high places
• Used to replace light bulbs and fixtures
• Could be a stepladder or short extension ladder
• Could be made of wood or fiberglass, but not aluminium
• Step deflections should be less than 10mm
• Must support weight of an average person + some tools
• Must be safe
• Must not conduct electricity
• Should be relatively inexpensive
• Must be portable between job sites
• Should be light
• Must be durable
• Need not be attractive or stylish
How can I find out which objectives /
characteristics are more important?
I can use PCC (there are other tools as well)

9. Example: PCC for a ladder
Objectives Cost Portability Usefulness Durability Score
Cost
Portability
Usefulness
Durability
N×N (square) matrix
“Row”
objectives
“Column”
objectives
Score for each
“Row” objective
Select N objectives and form a
square matrix as shown below:

10. • First row
– Cost is less important than portability: put “0” in cell
– Cost is less important than usefulness: put “0” in cell
– Cost is more important than durability: put “1” in cell
– Total “Score” for “Row” objective “Cost”: 0 + 0 + 1 = 1
Example: PCC for a ladder
Objectives Cost Portability Usefulness Durability Score
Cost •••• 0 0 1 1
Portability
Usefulness Neutral indicator: it does not make
sense to compare like-with-like
Durability

11. • INVALID values: diagonal entries have a value of “0” or “1”
Example: PCC for a ladder
Value “0” means:
“Row” objective Cost is less important than the “Column” objective Cost,
i.e. cost is less important than itself (does NOT make sense)
Value “1” means:
“Row” objective Cost is more important than the “Column” objective Cost,
i.e. cost is more important than itself (does NOT make sense)
Objectives Cost Portability Usefulness Durability Score
Cost 0 or 1 0 0 1 1
Portability
Usefulness Values wit h no physical meaning
Durability

12. • Second row
– Portability is more important than cost  1
– Portability is more important than usefulness  1
– Portability is more important than durability  1
– Total “Score” for “Row” objective “Portability”: 3
Example: PCC for a ladder
Objectives Cost Portability Usefulness Durability Score
Cost •••• 0 0 1 1
Portability 1 •••• 1 1 3
Usefulness If a cell has a value of “1”, then its
Durability symmetric cell must have a value of “0”

13. • INVALID values: symmetric entries have the same value
Example: PCC for a ladder
Symmetric cells have a value of “0” means:
“Row” objective is less important than the “Column” objective and at the
same time the “Column” objective is less important than the “Row”
objective (contradiction; does NOT make sense)
Simply put: “Cost” is less important than “Portability” and at the same time
“Portability” is less important than “Cost” (contradiction; does NOT make
sense)
Objectives Cost Portability Usefulness Durability Score
Cost •••• 0 0 1 1
Portability 0 •••• 1 1 3
Usefulness
Durability Values wi th no physical meaning

14. • INVALID values: symmetric entries have the same value
Example: PCC for a ladder
Symmetric cells have a value of “1” means:
“Row” objective is more important than the “Column” objective and at the
same time the “Column” objective is more important than the “Row”
objective (contradiction; does NOT make sense)
Simply put: “Cost” is more important than “Portability” and at the same time
“Portability” is more important than “Cost” (contradiction; does NOT make
sense)
Objectives Cost Portability Usefulness Durability Score
Cost •••• 1 0 1 1
Portability 1 •••• 1 1 3
Usefulness
Durability Values wi th no physical meaning

15. • Third row
– Usefulness is more important than cost  1
– Usefulness is less important than portability  0
– Usefulness is more important than durability  1
– Total “Score” for “Row” objective “Usefulness”: 2
Objectives Cost Portability Usefulness Durability Score
Cost •••• 0 0 1 1
Portability 1 •••• 1 1 3
Usefulness 1 0 •••• 1 2
Durability
Example: PCC for a ladder

16. • Fourth row
– Durability is less important than cost  0
– Durability is less important than portability  0
– Durability is less important than usefulness  0
– Total “Score” for “Row” objective “Durability”: 0
Example: PCC for a ladder
Objectives Cost Portability Usefulness Durability Score
Cost •••• 0 0 1 1 3rd
Portability 1 •••• 1 1 3 1st
Usefulness 1 0 •••• 1 2 2nd
Durability 0 0 0 •••• 0 4th
NOTE: Due to symmetry, it is NOT necessary to conduct all of the
comparisons; only N×(N-1)/2 comparisons are required

17. • Of the objectives listed, the prioritized list is:
1. Portability
2. Usefulness
3. Cost
4. Durability
• Score for “Durability”: 0
Physical meaning: of the four objectives listed, durability is
the least important (but cannot drop durability from the list
of objectives)
Example: PCC for a ladder

18. PCC: Procedure
Main task: to compare each objective to the others, one at a time
Steps
1. Select N number of key objectives;
2. Create a N×N (square) matrix;
3. Place each of the key objectives in a row across the top of the chart
and in a column down the left-hand side;
4. For each row, compare the “row objective” to each “column objective”;
5. If the “row objective” is more important than the “column objective”,
place a “1” in the cell;
6. If the “column objective” is more important than the “row objective”,
place a “0” in the cell;
7. Add up the values in each row to determine the total “Score” for that
“row objective”;
8. Rank the objectives according to their “Score” (the higher the “Score”,
the higher priority that objective has).

19. Objectives Speed Drive
Power
Lift
Power
Degrees-
of-
freedom
Simple
Controls
Score
Speed •••• 1 1 1 1 4
Drive
Power
0 •••• 1 0 0 1
Lift Power 0 0 •••• 1 0 1
Degrees-
of-freedom
0 1 0 •••• 0 1
Simple
Controls
0 1 1 1 •••• 3
Example: PCC for a robot
Can you identify any problem in this case?
Hint: can you get a “clear-cut” ranking of objectives?

20. At the end of this session I should be able to:
- Understand the purpose of using a Pairwise Comparison Chart
- Describe the main parts of a Pairwise Comparison Chart
- Complete a Pairwise Comparison Chart
- Avoid assigning invalid values for off-diagonal entries of a PCC
- Avoid assigning invalid values for diagonal entries of a PCC
- Preserve symmetry in a PCC
- Rank importance of objectives / characteristics based on a
PCC
- Prepare simple PCCs for devices / services
- Read PCCs and interpret the presented information
- State advantages of using PCCs
- State limitations of using PCCs
Wrapping up