Question: Suppose 3 control limits are constructed for the average temperature in a furnace. Sample of size 4 were selected with the average temperature being 5000C

Suppose 3σ control limits are constructed for the average temperature in a furnace. Sample of size 4 were selected with the average temperature being 5000°C and a standard deviation of 50°C.
(a) Find the 3σ control charts.
(b) Suppose that Rules 2 and 3 are used simultaneously to determine out-of-control conditions. What is the overall probability of a type I error assuming independence of the rules?
(c) Approximately how many samples, on average, will be analyzed before detecting a change when Rules 2 and 3 are used simultaneously?
(d) If the process average temperature drops to 4960°C, what is the probability of failing to detect this change by the third sample point drawn after the change?
(e) What is the probability of the shift being detected within the first two samples?

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