6.59. Control charts for and s have been maintained on a process and have exhibited statistical control. The sample size is n = 6. The control chart parameters are as follows: I Chart s Chart UCL = 708.20 UCL = 3.420 Center line = 706.00 Center line = 1.738 LCL = 703.80 LCL = 0.052 (a) Estimate the mean and standard deviation of the process. (b) Estimate the natural tolerance limits for the process. (c) Assume that the process output is well modeled by a normal distribution. If specifications are 703 and 709, estimate the fraction nonconforming. (d) Suppose the process mean shifts to 702.00 while the standard deviation remains constant. What is the probability of an out-of-control signal occur- ring on the first sample following the shift? (e) For the shift in part (d), what is the probability of detecting the shift by at least the third subsequent sample?
6.59. Control charts for and s have been maintained on a process and have exhibited statistical control. The sample size is n = 6. The control chart parameters are as follows: I Chart s Chart UCL = 708.20 UCL = 3.420 Center line = 706.00 Center line = 1.738 LCL = 703.80 LCL = 0.052 (a) Estimate the mean and standard deviation of the process. (b) Estimate the natural tolerance limits for the process. (c) Assume that the process output is well modeled by a normal distribution. If specifications are 703 and 709, estimate the fraction nonconforming. (d) Suppose the process mean shifts to 702.00 while the standard deviation remains constant. What is the probability of an out-of-control signal occur- ring on the first sample following the shift? (e) For the shift in part (d), what is the probability of detecting the shift by at least the third subsequent sample?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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