Hi - I have been recently trying to compare the experimental powers of 2 models to assess the benefits of one over another in the compare designs tab. One is a concantinated L27 Taguchi array. The other is an augmented model which included the original L27 Taguchi data and 8 extra runs generated in the augment design tab. My experimental power graph does not rank the concantinated L27 main effects powers highly enough for me to believe that the figure is correct, however the augmented powers look correct. I would appreciate any help in relation to attaining the correct powers for the L27 Taguchi for comparison.
Remember that the outer array does not count toward the power. It is merely used to compute the signal-to-noise ratio.
Hi Mark- Thanks for your reply!. In the graphed comparison main effects (all of which are active) KPIVs in the Taguchi model (shown in purple) should have a higher experiemental power that that returned, No?- obviously interactions and quadratics should return values as low as that shown, but I would have thought the main effects would have a higher experimental power as Taguchi method was developed to assess main effects?
Did you try comparing a main effects only model across both designs? As I recall, and I have to admit it's been many years since I used any L arrays, these designs have really funky confounding once you start trying to estimate effects greater than first order that chew up degrees of freedom for effect estimation. Did you try comparing a main effects ONLY model for both designs? I think you might see 'more' power for the L27 only array that is closer to your expectation.
Let's see...L27 is a fractional 3-level design. I don't believe this is a cross product array, so there is no outer array for calculating SN ratios. Taguchi's philosophy towards experimentation has some interesting ideas:
1. Almost all causal relationships are non-linear (e.g., quadratic)
2. Interactions are noise.
Whether you agree with these ideas or not, Taguchi emphasizes quadratic effects more than 2nd order linear effects. As @P_Bartell states, the confounding is quite precarious.
Right, so the Taguchi designs tended to work well when the effects were additive, not interactive. Mechanical assembly versus biochemistry.
I made the un-replicated L27 for the main effects model, with this power assuming an effect at least twice the standard deviation of the response:
I augmented the L27 with 8 runs and no changes to any design definitions otherwise. The power of the new design with the same assumptions is:
The compare design platform yields the same values:
Note: I had to change the Design Role column property from Signal to Categorical in order to open the two data tables with Compare Designs platform.
Hi- Thank you for all of your responses.
Mark- many thanks for making that comparison between the models. I used 2 repeats for the Taguchi L27 .
The original L27 was ran with 4 levels each with 3 level settings. RIE (W) (0, 50, 75). ICP (W) (1600, 1800, 2000). Ar (0, 25, 50) and Pressure (mT) (8,10,12).
I ran the L27 (with 2 repeats) again, i.e. twice in total. Firstly to obtain best case KPOVs predictions for etch rate (ER) (max. is best mean, and max. is for best signal to noise). The second L27 with 2 repeats for Ra (Arithmetic roughness average) (where minimum is best mean and maximum is best case signal to noise). I joined both tables then, to get a single concantinated prediction profile report.
In the augmented RSM design, I changed some of the level settings (i.e. KPIV) bounds to optomise the design space. RIE (25,75), ICP (2000,25000), Ar (0,25), Pressure (8,12)
Does this mean that the graph you have very kindly posted is correct for main effects and that the graph I originally posted shows the correct Powers for the interactions?
I cannot speak to what you did. I simply showed an 'apples to apples' design comparison of the L27 and augmented L27 for the same factor and model definitions.
The nature of the response has no bearing on the design comparison. It is defined while designing the experiment as a convenience to you.
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