The length of industrial filters is a quality characteristic of
interest. Thirty samples,
each of size 5,...
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The length of industrial filters is a quality characteristic ofinterest. Thirty samples, each of size 5, are chosen from the process. The data yields anaverage length of 110 mm, with the process standard deviation estimated to be 4mm. (a) Find the warning limits for a control chart for the averagelength. (b) Find the 3sigma control limits. What is the probability of atype I error? (c) If the process mean shifts to 112 mm, what are the chances ofdetecting this shift by the third sample drawn after the shift? (d) What is the chance of detecting the shift for the first time onthe second sample point drawn after the shift? (e) What is the ARL for a shift in the process mean to 112 mm? Howmany samples, on average, would it take to detect a change in the process mean to116 mm?
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Here X Length of industrial filter is a quality characteristic Given that thirty samples each of size five gave the process average 110 mm with process standard 4 mm Warning limits are 2 limits therefore UCL of warning limit Process
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