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Hi, this is Dr. Bamberg, welcome back to our series on the ABCs of Design for the University
of Utah's ME 1000 class. Today we will be talking about the Decide
phase of design. There are two design tools that you will learn
about and use in ME1000. The first tool is Pairwise Comparison Charts,
or PCCs, and the second tool is the Decision Matrix.
You will use PCCs for a variety of tasks in your upcoming design project, including to
organize objectives for your decision matrix. Why do we need these tools? Well, there are
always engineering tradeoffs that make it hard to decide between competing designs.
Consider the tradeoffs between different styles of snowboards.
Traditional snowboards are typically lower in cost, good on groomer days, and lightweight,
whereas Swallowtail snowboards are typically a bit more expensive and heavier, but great
on those beautiful blue sky powder days that turn up in February.
I'm sure you all recognize President Thomas Jefferson, a prolific inventor, who said
"We hold it to be self evident that all objectives are NOT created equal."
Following this wisdom, we know that we must rank objectives in terms of their importance.
To do this, we use pairwise comparison charts (or PCCs).
This tool helps us understand the trade-offs in our objectives, subjectively rank these
objectives, and structure our priorities. We can use PCCs for subjective rankings of
any RELATED group of items.
For instance, you will also use them to rank functions in terms for difficulty.
It is important to remember (just as with morph charts) to apply this tool to rank items
that are at a related level. For instance, we could use a PCC to rank the
top level objectives for a new snowboard design. Our three top objectives might be fast, maneuverable,
and stable (note that these are all adjectives!). To make the PCC, list your objectives in a
single column. Then draw three rows. Next, list your objectives across the top
(in the same order as you listed them going down).
Next, draw columns, with one extra column at the far right. Label this column "Score".
Next, cross out or grey out the squares along the diagonal.
To use the PCC, write a 1 if the row item is MORE important than the column item or
a 0 if the row item is LESS important than the column item.
In the score column, sum the scores for that row.
A final note – be sure to make your scores are consistent!
Let's look at an example. Remember that you should have your users and
clients in mind when you do these rankings. Perhaps you would personally place a priority
on speed, but that might not be what your users and/or clients would desire.
Okay, first we compare Fast and Maneuverable, and as a design team we decide that being
maneuverable is more important than being fast, so we put a 0 in that square.
We similarly, decide that beings stable is more important than being fast, so we put
a 0 in that square as well. Next, we already decided maneuverable is more
important than fast, so we put a 1 in that square.
Our final comparison is between maneuverable and stable, and let's say that we decide maneuverable
is more important, so we put a 1 in that square. Now we fill in the final row to be consistent,
with a 1 showing that we decided stable is more important than fast,
and a 0 showing that stable is less important than maneuverable.
Now you should see why this is called a pairwise comparison chart – we've compared all of
our objectives as individual pairs. Lastly, we add up the scores in each row,
to get a 0 for fast, 2 for maneuverable and 1 for stable.
The highest number, 2, tells us that maneuverable is our most important objective, followed
by the 1 for stable, and the 0 indicates that fast is our least important objective.
That doesn't mean that it is unimportant, after all, we have identified being fast as
an important objective. It just means that we shouldn't sacrifice
stability and maneuverability for speed in this particular design.
Okay, using the PCC allowed us as a team to rank our objectives, and you'll also use it
to rank your functions. What about making decisions about design configurations
that we have developed? Decision Matrices are another design tool,
and are used to help you relate our design configurations to our RANKED design objectives.
We use the decision matrix to rank the design configurations in terms of how well they meet
our objectives. They also provide an organized record of how
your team came to decisions on your design configurations.
First, let's look at the structure of the design matrix you will use in ME1000.
In the left most column, we list our objectives, with the constraints at the top.
You can have more than one constraint and more than three objectives, of course.
In the second column, we list the weights of the objectives.
These should be consistent with your ordinal PCC rankings – they are a crude quantification
of those rankings. You may decide that the weights should be
the same for multiple objectives (for instance here, we could have objective 1 and 2 each
ranked at 25%). Note that the sum of this column should be
100%. Just as we noted with the PCC, these objectives
should all come from a similar level. Note that constraints do note get a weighting
because they are binary You either meet them or you don't, and if
you've decided something should be a constraint, then it is important to meet it.
Okay, along the top row, we list our design configurations, called options here.
Typically you'd have several, say 4 or 5, but just two are shown here due to space.
Now let's look at the results. The first thing you always do is to check
the constraints for each option. Because the constraints are binary, if the
design option fails to satisfy the constraint, you do not fill out the rest of the table.
Enter blanks, as shown here for option 1. For options that do meet the constraints,
you and your team now use your judgment to give the option a score from 0-10 as to how
well it meets the objective. In this case, we see that our team decided
this option got a 9 out of 10 for doing a good job meeting Objective 1,
but only a 1 out of 10 and a 3 out of 10 for meeting Objectives 2 and 3 (try to stick with
whole numbers, since this is already a subjective scale).
Next, we calculate the weighted score by multiplying the weight times the score.
For instance, 30% (or 0.3) times 9 is 2.7. Last, we add up the weighted score to obtain
the total for this design option. You can see that if you had multiple options
that met the constraints, you would now be able to compare these options numerically.
Okay, let's give this a try for our hypothetical snowboard design.
Here we've added a constraint that our marketing department gave us, that the cost must be
under $900. We start with this, and say, yes our traditional
style design will meet this, but unfortunately our swallowtail is going to cost $950.
That means we wouldn't fill out the rest of the table, because the swallowtail design
does not meet the constraints. However, there are four questions you should
always ask after completing a decision matrix, and one of those is whether any of the constraints
are too tight. You might go back to marketing and say that
you'd like to consider designs that cost up to $1000.
Let's assume they agreed that would be acceptable. Now both designs meet that criteria.
Next, we assign weights to the objectives. In our PCC, we found maneuverable to be the
most important, but perhaps we feel that all three objectives are fairly similar, so we
assign it 40%, followed by 35% for our second most important
objective to be stable, and the remaining 25% goes to fast.
Next, we need to assign scores. You can either evaluate each design across
all objectives, or evaluate each objective across all designs.
If we look at fast, we might say decide that the traditional board gets about 6/10 for
being fast under most conditions, with 8/10 for the swallowtail (perhaps we
have another design not shown here that is a racing board that would get 10/10).
For maneuverability, we decide the traditional style gets a 9/10 with 5/10 for the longer
swallowtail. But for stability, perhaps we decide they
are both about an 8, since they are both reasonably stable under the conditions they are designed
for. Next, we calculate the weighted score, multiplying
6*.25 and so on. Last, we add up the scores, and can see that
our total score is slightly higher for our traditional style as compared to the swallowtail.
Although this ostensibly means the traditional style "won," we must remember that these are
subjective rankings, and we must ask ourselves the following four questions.
We already discussed the importance of making sure you have not eliminated any good options
by having too tight of a constraint. Next, any options that are ranked about the
same should be considered equal since these are subjective rankings.
For instance, if you have five designs, with scores of 7.9, 6.8, 4.8, 4.5, and 1.2, you
can probably eliminate the 1.2, and consider the 4.8 and 4.5 as runners-up.
The 7.9 and 6.8 are close enough that you should do some further evaluation – perhaps
with other portions of your objective tree, or by constructing CFPs.
Next, make sure that you have not “fudged” the importance and/or scores to get a desired
result. For instance, as a team, you need to be careful
that no one has strong-armed the group into giving a favored design higher rankings.
Lastly, think about your results and think about what else you may need to consider,
such as modeling, CFPs, or evaluation of other objectives.
Thanks and see you in class!