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 of α 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?
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 of α 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?
Given:
UCL = 1.5
LCL = -1.5
(a)
The type I error is:
The type I error is 0.00988.
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