Question: A normally distributed quality characteristic is controlled by x and R charts having the following parameters (n = 4, both charts are in control): (a)

A normally distributed quality characteristic is controlled by x and R charts having the following parameters (n = 4, both charts are in control):

(a) What is the estimated standard deviation of the quality characteristic x?
(b) If specifications are 610 ±15, what is your estimate of the fraction of nonconforming material produced by this process when it is in control at the given level?
(c) Suppose you wish to establish a modified x chart to substitute for the original x chart. The process mean is to be controlled so that the fraction nonconforming is less than 0.005. The probability of type I error is to be 0.01. What control limits do you recommend?

R Chart r Chart UCL- 18.795 Ccnter linc: 8.236 Ccater linc 620.00 LCL-0 UCL = 62600 614.00

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