Two decision rules are given here. Assume they apply to a normally distributed quality characteristic and the sample size is n = 5. Rule 2: If all of the next seven sample averages fall on the same side of the center line, conclude that the process is out of control. i) What is the probability of a sample average fall on the upper side of the center line? ii) What is the α-error probability for the control chart under Rule 2?
Two decision rules are given here. Assume they apply to a
Rule 2: If all of the next seven sample averages fall on the same side of the center line, conclude that the process is out of control.
i) What is the
ii) What is the α-error probability for the control chart under Rule 2?
Sol:-
i) Assuming that the quality characteristic is normally distributed, the probability of a sample average falling on the upper side of the center line can be calculated using the standard normal distribution.
The center line represents the mean of the process, so if the process is in control, the probability of a sample average falling on the upper side of the center line is 0.5.
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