Control Chart Process: Detecting Shifts with 3 Sigma Limits and Mean Changes

[axnman]

Process is Out of control if 1 point plots outside 3-sigma limits or 2 consecutive points between 2-sigma & 3-sigma on same side...

if mean changes to mean1=mean0 + 9...what is probability to detect shift on 1st or 2nd sample following shift?

Point outside 3 sigma is ok but what @ the 2 consecutive points between...please help!

 

[HallsofIvy]

This is absolutely opaque. I think you are dealing with a statistics situation but it's not clear from what you have said. Please try to clarify exactly what your problem says.

 

[axnman]

Ya statistics situation...sorry @ that,...

basically want to calculate the probability of detecting the shift on the first or the second sample when mean (say 200) shifts to a new value = mean + 9 (say 209)...(an out control situation is given as : if 1 point plots outside 3-sigma limits or 2 consecutive points between 2-sigma & 3-sigma on same side)

 

[axnman]

here is the actual question :

Samples of n=4 items are taken from a process at regular intervals. Suppose process mean is 200 and stnd. dev. =10

Assume the following rule is applied to control chart with 3-sigma limits:

The process is declared out of control when either a point plots outside of the 3-sigma limit OR 2 consecutive points plot between the 2-sigma & 3-sigma limits on the same side of the chart. If the process mean shifts to 209, what is the probability that the shift will be detected on the first or the second sample following the shift?