Pick a Design, Any Design

by C.J. Keller and Richard Scranton

Most people have heard of Designed Experiments, but have found the inside of your eyelids more pleasant to look at than the books devoted to the topic. This is surely unfortunate, given the wealth of information you could uncover about your process using these techniques. The problem with most of these texts is that they have to choose between a comprehensive coverage with design construction and evaluation of many design types or a simplistic coverage of only one approach. The latter books tend to leave the impression that there is only one way to skin the proverbial cat.

Often times, there are many designs that can be used to estimate the effects of process parameters (factors) on a process outcome (response). The suitability of a design for a given application is limited by the number of runs in the design (i.e. number of conditions you run in the experiment). At most, you can only estimate the effect of the mean, n-1 factors and factor interactions in a design, where n is the number of runs. So if you assume there are no interactions between the factors (sometimes called a screening design), a properly conceived 8-run design can estimate the effect of 7 factors on a response. However, not all designs are created equally, so there are larger designs that can only estimate the same 7 factors. In some cases additional runs are added to improve estimates of error or the precision of estimates.

So what is the difference between these designs? Many times, just the name. Take for example the well known Taguchi L8 designs, shown below with an 8-run Fractional Factorial and an 8-run Plackett-Burman design. Looking in the upper half of these tables, the designs appear to be different. They have, in fact, a common core of three columns (labeled a, b and c), which are easily identified by rearranging the rows as shown in the bottom half of the tables. While the non-core columns in the three formats do not appear to be always identical, the difference is only in which level of the factor is run, resulting in the design estimating the negative sense of the factor (i.e. rather than estimating the ab interaction, it estimates minus ab). The row order is mathematically inconsequential, especially given that run order should be randomized for the experiment.