From: Stan Hilliard
Date: 30 May 2001
Time: 15:11:01
Hi Geoffrey, The operating characteristic curve is the tool that you use to attain statistical relevance for the particular application. See www.samplingplans.com/usingoccurves.htm.
Since you have measured variables, you would want to use either a plan with sampling requirements for levels of the mean or a plan with sampling requirements for levels of the percentage of individual items nonconforming to specification limits.
Sampling plans for both situations can be handled with program TP414.
www.samplingplans.com/software-oc.htm.
You can follow the links from there to the examples and to the tutorial.
If you specify the mean, you need to specify values of the acceptable mean (AQL-mean) and the rejectable mean (RQL-mean). If the situation require rejecting/adjusting for too high and too low then you will have both upper and lower AQLs and RQLs. The oc curve will relate these values of the mean to their probabilities of acceptance -- so that you can predict the performance of the plan in discriminating between acceptable and rejectable levels.
The standard deviation that you would use should be the pooled within-sample standard deviation. It represents the variability that would be realized if you were to repeat the sample in the short-term. I would expect it to be smaller than the per-week value. The pooled standard deviation is calculated as the square root of the pooled variance. The pooled variance is the average variance when weighted by its degrees of freedom (DF). To pool the variance from three samples:
Pooled variance = Vp.
DF = n - 1. (n is the sample size of the particular sample.)
Vp = [DF1*V1 + DF2*V2 + DF3*V3]/ [DF1 + DF2 + DF3]
Then the pooled standard deviation is Sp = SQRT(Vp).
When you design a sampling plan with a known standard deviation like this, it is a good idea to check each sample that its standard deviation is not significantly different. Comparing the sample range to a limit for the range most easily does this. For small sample sizes, TP414 will generate limits for the range.
Stan Hilliard