Operating System

A process is known to be in-control with the N(100, 25 ) distribution for individual part dimensions. Amanufacture decided to define its own rules for process monitoring based on 3 consecutive sampleinspections, where each sample consists of 4 individual measurements.

Rule 1: The control chart concludes an out-of-control condition by “finding anyone of these threeconsecutive samples beyond 2-sigma control limits in the X-bar control chart”.

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Rule 2: The control chart concludes an out-of-control condition by “finding three consecutive samples, onthe same side of the centerline, exceeding the centerline by 1.0 sigma limits in the X-bar control chart.If the process shifts to an out-of-control condition with N(103, 27 ),

1. What is the average number of samples needed to detect this process shift on the X-bar controlchart when using

Rule1? (10 points)

2. What is the average number of samples needed to detect this process shift on the X-bar controlchart when using Rule2?

 

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