Someone constructs an X chart where the control limits are at 2.0 X rather than at 3

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Someone constructs an X̅ chart where the control limits are at ±2.0σ rather than at ±3σ .

a. If the process is in control, what is the ARL for this chart?

b. If the process mean shifts by 0.5σ , what is the ARL for this chart?

c. In units of σ, how large an upward shift can be detected with an ARL of 10?

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