A. Gupta [Quality Engineering, 10(2), 347–350, 1997–98] presented a case study involving antibiotic suspension products, with “separated clear volume” (the smaller the better) being the response variable. The objective was to determine the best level of each of five two-level factors so as to minimize the response variable, with the selection of a particular level of a factor being crucial only if the factor is significant. An L16 orthogonal array was used, and that design and the accompanying response values are as follows:

 

(a) Should the data be analyzed in the original units of the factors (with of course some numerical designation for the two levels of factor E)? Why or why not?

(b) Show that this L₁₆ array is equivalent to a suboptimal 2^{5 − 1} design. [Hint: The interaction that is confounded with the mean can be determined using MINITAB, for example, by trying to estimate all the effects. That is, by using a command such as FFACT C₁= (C₂-C₆)⁵, with the response values being in C₁ and the factors being in C₂-C₆.]

(c) Explain the consequences of using this L₁₆ array rather than the 2^{5 − 1} design with maximal resolution in terms of the estimation of the two-factor interactions.

(d) Estimate as many effects as you can with this design and determine the significant effects. With the second level (60) of the second factor considered to be preferable for non statistical reasons, what combination of factor levels appears to be best? Is it necessary to qualify your answer in any way since the L₁₆ design is a resolution IV design whereas a 16-point resolution V design could have been constructed?