Consider the alloy cracking experiment in Problem 6.15. Suppose that temperature (A) is a noise variable. Find the response model, and the model for the mean response, and the model for the transmitted variability. Can you find settings for the controllable factors that minimize crack length and make the transmitted variability small?
Problem 6.15:
A nickel-titanium alloy is used to make components for jet turbine aircraft engines. Cracking is a potentially serious problem in the final part because it can lead to nonrecoverable failure. A test is run at the parts producer to determine the effect of four factors on cracks. The four factors are pouring temperature (A), titanium content (B), heat treatment method (C), and amount of grain refiner used (D). Two replicates of a 24 design are run, and the length of crack (in mm ×10-2 ) induced in a sample coupon subjected to a standard test is measured. The data are shown in Table P6.2
(a) Estimate the factor effects. Which factor effects appear to be large?
(b) Conduct an analysis of variance. Do any of the factors affect cracking? Use α = 0.05.
(c) Write down a regression model that can be used to predict crack length as a function of the significant main effects and interactions you have identified in part (b).
(d) Analyze the residuals from this experiment.
(e) Is there an indication that any of the factors affect the variability in cracking?
(f) What recommendations would you make regarding process operations? Use interaction and/or main effect plots to assist in drawing conclusions.