1. A film processing service monitors the quality of the developing process with light-sensitive equipment. The accuracy measure is a number with a target value of zero. Suppose that an X chart with subgroups of size five is used to monitor the process and the control limits are UCL - 1.5 and LCL= -1.5. Assume that the estimate for the process mean is zero and for the process standard deviation is 1.30.

a. What is the value ofa for this control chart?

b. Find the UCL and LCL based on three-sigma limits.

c. Suppose that the process mean shifts to 1. What is the probability that the shift is detected on the first subgroup after the shift occurs?