Reference no: EM131082657
Reconsider the smelting process experiment in Problem 8.23, where a 26 - 3 fractional factorial design was used to study the weight of packing material that is stuck to carbon anodes after baking. Each of the eight runs in the design was replicated three times, and both the average weight and the range of the weights at each test combination were treated as response variables. Is there any indication that a transformation is required for either response?
Problem 8.23
An industrial engineer is conducting an experiment using a Monte Carlo simulation model of an inventory system. The independent variables in her model are the order quantity (A), the reorder point (B), the setup cost (C), the backorder cost (D), and the carrying cost rate (E). The response variable is average annual cost. To conserve computer time, she decides to investigate these factors using a design with I = ABD and I = BCE. The results she obtains are de = 95, ae = 134, b = 158, abd = 190, cd = 92, ac = 187, bce = 155, and abcde = 185.
(a) Verify that the treatment combinations given are correct. Estimate the effects, assuming three-factor and higher interactions are negligible.
(b) Suppose that a second fraction is added to the first, for example, ade = 136, e = 93, ab = 187, bd = 153, acd = 139, c = 99, abce = 191, and bcde = 150. How was this second fraction obtained? Add this data to the original fraction, and estimate the effects.
(c) Suppose that the fraction abc = 189, ce = 96, bcd = 154, acde = 135, abe = 193, bde = 152, ad = 137, and (1) = 98 was run. How was this fraction obtained? Add this data to the original fraction and estimate the effects.
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