A decision rule is given here. Assume it applies to a normally distributed quali

Question

A decision rule is given here. Assume it applies to a normally distributed quality characteristic, the control chart has 3-sigma control limits, and the sample size is n = 5.

Rule: If at least one out of the next two sample averages fall outside the contorl limits, conclude that the process is out of control.

What is the type I error of this rule? The below is defined as follows:

= P(one point outside the contol limits | process out of control)

(a) 2(1-)2

(b) 2(1-)+2

(c) 2(1-)

(d) none of the above

Continued from question above, what is the type II err of the rule? Suppose the process has a mean shift of one process standard deviation. The below is defined as follows:

= P(one point inside the contorl limits | process out of control)

(a) 1-2

(b) (1-)2

(c) 2

(d) none of the above

Explanation / Answer

= P(one point outside the contol limits | process out of control)

Option (c) is correct choice. That is, 2(1-).

= P(one point inside the contorl limits | process out of control)

Option (b) is correct choice. That is, (1-)2.

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