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

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:

30 30 ΣΧ-6000; ΣR-150 1-1

(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

30 30 -6000; R-150 1-1

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