Randomization of Taguchi arrays and Covering arrays in JMP

[#1]

Hi dear Community,

Investigating the potential use of orthogonal arrays/covering arrays/Taguchi arrays, I have found that the platforms Covering Array and Taguchi Designs do not offer the option to randomize the order of the runs when creating a design (before making the datatable). But if you build a robust design with Custom Design platform (and add categorical factor(s) for noise factor(s): Experiments for Robust Process and Product Design), then the design can be randomized.

Is there any justification to run the experiments in the same design construction order (no randomization) for these two platforms (Covering Array and Taguchi designs) ?

For Taguchi arrays for example, I found the lack of randomization quite disturbing, as the first factor will be split in two "blocks" of runs, the first half at the low level and the second half at the high level. Even if we are considering noise factors in this design scenario (and measuring responses to account for these noise effects), running the experiments with this schema could create or increase bias coming from non-specified noise factors: for example, a bias coming from temperature during the day, where the first half of the experiments are done the morning with relatively low temperatures and the other half in the afternoon with relatively high temperature, biasing and potentially inflating ou neutralising the effect of the first factor.

Looking forward to any inputs, and if it's not intended, I will create a JMP Wish :)

Thank you !

[#2 · Accepted solution]

Victor, AFAIK, Taguchi didn't emphasize using the randomization you speak of as he calculates a SN ratio across the outer array (This is a function of mean and standard deviation estimates across the changing noise...essentially as if those responses were repeats).  He was more interested in exposing the treatments to manipulated noise to create robust designs and created on response that was indicative of such robustness.  There are , of course, arguments about the effectiveness (or statistically, the "correctness") of this technique.  I am biased to treating those cross (inner and outer arrays) as split-plots.

Of course, you can do your own randomization, but if you can both identify the noise and manage it for the course of the experiment you will be better off.

"Block what you can, randomize what you cannot" G.E.P. Box

[#3]

Thanks a lot for your answer, it makes a lot of sense !

I have read in several papers showing the limitations of Taguchi designs that Taguchi did create design in a practical and "engineer"-focused way, to the detriment of "statistical correcteness". JMP provide the same format as you mentions when creating Taguchi designs, with noise factors considered as "repeats" and using the response average and standard deviation to calculate a S/N ratio (example with L4):

Without considering the inner and outer arrays cross as a split-plot experiment, I'm afraid that running the analysis in the same order as the table is provided would cause a potential bias in the experimentation, because of the possible influence of external (and not considered) noise factors. Also Covering array platform has the same challenge with the ordering of the runs, but it could be possible to consider it as a split-plot experiment, so thanks for this good advice. 

I'm quite reassured to see that my understanding of these designs is not completely off.

Best,

[#4]

There is a lot of misunderstanding of Taguchi's philosophy.  Much of his work was translated into English and that is not often easy to do.  I remember teaching with him in Tokyo many years ago his emphasis on response variable selection/creation was very engineering like.  He preferred response variables that were robust to extraneous noise and interactions (e.g., in the form of energy or mass due to laws of conservation).