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?

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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?
Transcribed Image Text: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?
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