Two decision rules are given here. Assume they apply to normally distributed qua

Question

Two decision rules are given here. Assume they apply to normally distributed quality characteristic, the control chart has three-sigma control limits, and the sample size is n 5. Rule 1: If one or more of the next eight 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 eight sample averages fall on the same side of the center line, conclude that the process is out of control. What is the type I error probability for each of these rules?

Explanation / Answer

Formula of probability of type 1 error is

P( type 1 error ) =P( rejecting H0 when H0 is true)

For rule 1:

H0 : one or more points are lies outside the control limits .

H1:one or more points are not lies outside the control limit.

P( Type 1 error ) =The process is control when one or more points outside the control limits.

For rule 2:

H0: If all of the next eight sample averages fall on the same side of the center line.

H1: if all of the next eight sample averages not fall on the same side of the center line

P( type 1 error ) = The process is control when if all all points fall on the same side of the center line.

problem 4)

Beta=type 2 error

type two error =failed to reject H0 when H0 is false

Type 2 error = Process is out of control when remaining 7 samples lies in control limits.

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