A decision rule is given here. Assume it applies to a normally distributed quali
ID: 3315140 • Letter: A
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.