The technique of multivariable testing (MVT) was discussed in the Journal of the Reliability Analysis Center (First Quarter, 2004). MVT was shown to improve the quality of carbon-foam rings used in nuclear missile housings. The rings are produced via a casting process that involves mixing ingredients, oven curing, and carving the finished part. One type of defect analyzed was the number y of black streaks in the manufactured ring. Two variables found to impact the number of defects were turntable speed (revolutions per minute), x1, and cutting-blade position (inches from center), x2.
a. The researchers discovered "an interaction between blade position and turntable speed." Hypothesize a regression model for E(y) that incorporates this interaction.
b. The researchers reported a positive linear relationship between number of defects (y) and turntable speed (x1) but found that the slope of the relationship was much steeper for lower values of cutting-blade position (x2). What does this imply about the interaction term in the model, part a? Explain.