# Question

Control charts for x and R are to be established to control the tensile strength of a metal part. Assume that tensile strength is normally distributed. Thirty samples of size n= 6 parts are collected over a period of time with the following results:
(a) Calculate the control limits for x and R .
(b) Both charts exhibit control. The specifications on tensile strength are 200 = – 5. What are your conclusions regarding process capability?
(c) For the above chart, find the β-risk when the true process mean is 199. X

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