Quality in Design - Medical Device Design: Innovation from Concept to Market - page 123

Table 7.2: Optimal Result Obtained Using Microsoft Excel® Solver Routine

Diameter (mm) Length (mm) Mass (kg)

50.32 50.32 0.47

7.3 Design of Experiments/2 k Factorial Experiments
Sometimes it is difficult to ascertain which parameter in your design is the most important.
Equally sometimes you need to ascertain which parameter determines the quality of your
design. So, for example, if we were to examine the performance of a sphygmomanometer
(used to measure blood pressure) we would have many variables to consider, but which are
insignificant? Which have a detrimental effect on performance? Which have a beneficial
effect on performance? When the Japanese were tussling with improving quality an engineer
named Taguchi realized that it was important to design out problems. Hence he needed
a simple experiment to determine which parameter of a design has the greatest effect on
quality, and if it is detrimental get rid of it. To do this he invented factorial experiments .
There are whole textbooks on this subject so I can only give an introduction. However, the
tool I am about to share can be used for most design problems. It should be noted that you
do not need to have complex mathematical models for this to work; testing real things is
possible too.

Consider the injection molding of a syringe body. The variables we have on the injection
molding machine are T = temperature of the injected plastic, P = the pressure of the injected
plastic, and Tm = the mould temperature. Now this is where Taguchi was clever; instead
of looking at a whole range of values he proposed we should only look at maximum and
minimum values of all parameters. So if we could set the mould temperature to be anywhere
between −5 °C and 20 °C these would be the extremes. As there are three variables (T, P, and
Tm) that can only be set at two values, the total number of experiments required is 8 (2 3 ).
Hence for any system with k variables the total number of experiments is 2 k . To design the
experiment we use −1 to signify a minimum, and +1 to signify the maximum. The design of
the experiment is simple (see Table 7.3 ).

It is pretty obvious that beyond four variables 2 k experiment design is time-consuming and,
if you are doing real experiments, costly. If, however, you are doing numerical-based models
then the only cost is time; and this can be reduced by using a computer-based model. I have
further highlighted the subsets for three variables and two variables for your information.
For systems with more than variables it is common to use k-n experiment design, but that is
beyond the scope of this text.

Now let us return to our original example with three variables; how does this affect
Table 7.3 ?