Suppose that a quality characteristic is normally distributed with specifications at 120 ± 20. The process standard deviation is 6.5.

(a) Suppose that the process mean is 120. What are the natural tolerance limits? What is the fraction defective? Calculate PCR and PCR_k and interpret these ratios.

(b) Suppose that the process mean shifts off-center by 1.5 standard deviations toward the upper specification limit. Recalculate the quantities in part (a).

(c) Compare the results in parts (a) and (b) and comment on any differences.