Problem #4 (Alpha and Beta risks, ARL): An x-bar chart has a center line of 100, uses three-sigma control limits, and is based on a sample size of four. The process standard deviation is known to be six. If the process mean shifts from 100 to 92, what is the probability of detecting this shift on the first sample following the shift? What is the average run length for the chart to detect the shift?

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Problem #4 (Alpha and Beta risks, ARL): An x-bar chart has a center line of 100, uses
three-sigma control limits, and is based on a sample size of four. The process standard
deviation is known to be six. If the process mean shifts from 100 to 92, what is the
probability of detecting this shift on the first sample following the shift? What is the
average run length for the chart to detect the shift?
Transcribed Image Text:Problem #4 (Alpha and Beta risks, ARL): An x-bar chart has a center line of 100, uses three-sigma control limits, and is based on a sample size of four. The process standard deviation is known to be six. If the process mean shifts from 100 to 92, what is the probability of detecting this shift on the first sample following the shift? What is the average run length for the chart to detect the shift?
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