Analyzing DOE With Statistical Software Packages: Controversies and Proposals

Consequences of using estimated response values from negligible interactions in factorial designs

“…For a confidence level of 95%, Lenth proposed the values of 3.76 and 2.57 for designs with eight and 16 experiments, respectively. These values have been discussed by authors such as Loughin, Ye and Hamada, and Fontdecaba et al, all of whom show that a type I error closer to 5% is obtained and that there is a notable decrease in type II errors when using lower values of t . In our study, we used the values proposed by Ye and Hamada: 2.297 and 2.156 for eight and 16 experiments, respectively.…”

“…When all the runs have been carried out, this task can be done manually representing the effects in an NPP-a task that requires the analyst's judgment, by using the variability of effects based on the values of those that can be considered null or by using the method of Lenth. 7 An analysis of how some well-known statistical software packages address the issue of assessing the significance of the effects can be found in Fontdecaba et al 9 Neither of these methods are appropriate in our case. The judgment by representing the effects in NPP cannot be automated.…”

Estimating missing values from negligible interactions in factorial designs

“…For eigth-run designs we use the same testing scenarios that were used by Fontdecaba et al (2015): And for 16-run designs the same that were used by Venter and Steel (1998), and later also by Ye et al (2001) and Fontdecaba et al (2014): S16-1: 1 = ⋯ = 14 = 0, 15 = Δ S16-2: 1 = ⋯ = 12 = 0, 13 = 14 = 15 = Δ S16-3: 1 = ⋯ = 10 = 0, 11 = ⋯ = 15 = Δ S16-4: 1 = ⋯ = 8 = 0, 9 = ⋯ = 15 = Δ S16-5: 1 = ⋯ = 12 = 0, 13 = Δ, 14 = 2Δ, 15 = 3Δ S16-6: 1 = ⋯ = 10 = 0, 11 = Δ, 12 = 2Δ, 13 = 3Δ, 14 = 4Δ, 15 = 5Δ…”

“…They are explained in commonly used textbooks as Montgomery (2013) and Box et al (2005), and implemented in the most common statistical software packages for industrial applications (Fontdecaba et al, 2014). Accepting to reduce the problem to choose among these two methods, it seems reasonable to suppose that it will be more adequate to apply one or the other according to the characteristics of the situation; for instance, depending on the number of interactions that can be considered negligible.…”

“…Accepting to reduce the problem to choose among these two methods, it seems reasonable to suppose that it will be more adequate to apply one or the other according to the characteristics of the situation; for instance, depending on the number of interactions that can be considered negligible. However, several statistical software packages use always by default the same method regardless of the characteristics of the case being analyzed (Fontdecaba et al, 2014).…”