The article “Use of Taguchi Methods and Multiple

Chapter 9, Problem 14E

(choose chapter or problem)

The article “Use of Taguchi Methods and Multiple Regression Analysis for Optimal Process Development of High Energy Electron Beam Case Hardening of Cast Iron” (M. Jean and Y. Tzeng, Surface Engineering, 2003:150–156) describes a factorial experiment designed to determine factors in a high-energy electron beam process that affect hardness in metals. Results for two factors, each with three levels, are presented in the following table. Factor A is the travel speed in mm/s, and factor B is accelerating voltage in volts. The outcome is Vickers hardness. There were six replications for each treatment. In the article, a total of seven factors were studied; the two presented here are those that were found to be the most significant.

                   

a. Estimate all main effects and interactions.

b. Construct an ANOVA table. You may give ranges for the P-values.

c. Is the additive model plausible? Provide the value of the test statistic and the P-value.

d. Can the effect of travel speed on the hardness be described by interpreting the main effects of travel speed? If so, interpret the main effects, using multiple comparisons at the 5% level if necessary. If not, explain why not.

e. Can the effect of accelerating voltage on the hardness be described by interpreting the main effects of accelerating voltage? If so, interpret the main effects, using multiple comparisons at the 5% level if necessary. If not, explain why not.