Defects in nuclear missile housing parts. The technique of multivariable testing was discussed in The Journal of the Reliability Analysis Center (First Quarter, 2004). Multivariable testing 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 affect 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. Interpret what it means practically to say that “blade position and turntable speed interact.”

c. 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 you hypothesized in part a? Explain.