A shewhart control chart is set up for a quality characteristic of a process. As

Question

A shewhart control chart is set up for a quality characteristic of a process. Assume each Individual in this process follows a normal distribution with a mean of 125 and a standard deviation of 6. Each point on the chart represents the average of a random sample of 9 parts. The control limits of the chart are set at 125 plusminus 5. Calculate sigma_x, the standard deviation of the sample mean of the quality metric. Find the in-control Average Run Length. Find the out-of-control Average Run Length when the mean shifts to 120.

Explanation / Answer

a) Standard error of sample mean = STd dev/rt n

= 6/rt 9 = 2

b) Incontrol aver length

= (125-3*2, 125+3*2)

=(119, 131)

c) Out of control when mean shifts to 120 is

Mean is either below 114 or above 126

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