Question

Two decision rules are given here. Assume that the quality characteristic follows a normal distribution and the control chart has two-sigma control limits, and the sample size is ? = 4.

Rule 1: If one or more of the next 3 samples yield values of the sample average that fall outside the control limits, conclude that the process is out of control.

Rule 2: If all of the next 5 samples fall on the same side of the center line, conclude that the process is out of control.

(a) What is the Type-I error probability for each of these rules?
(b) If the mean of the quality characteristic shifts one process standard deviation, and remains there later, what is the Type-II error probability associated with each decision rule?

Answer 1

a) Sort I blunder likelihood for the first manage is given as underneath:

• Invalid theory: H0: One of a greater amount of the following thre examples
• yield estimations of the example normal that fall inside as far as possible. ​
• Elective theory: Ha: One of a greater amount of the following eight examples .
• yield estimations of the example normal that fall outside as far as possible.
• The sort I mistake likelihood for the principal govern is the likelihood of dismissing the invalid speculation.
• That the procedure is in charge anyway really process is in charge. We dismiss the speculation that the at least one of the following eight examples
• yield estimations of the example normal that fall inside as far as possible anyway really values inside as far as possible.
• At that point the sort I mistake happened.

Sort I mistake likelihood for the second manage is given as beneath:

• Invalid theory: H0 : Next eight example midpoints don't fall on a similar side of the inside line.
• Elective speculation: Ha: Next eight example midpoints fall on a similar side of the middle line.
• The sort I blunder likelihood for the second administer is the likelihood of dismissing
• The speculation that next eight example midpoints don't fall on a similar side of the inside line
• Anyway really eight example midpoints don't fall on a similar side of the middle line.