From: Stan Hilliard
Date: 10/25/2005
Time: 2:53:13 PM
Hi Rick,
You asked if an acceptance sampling approach would be better in your case. I think so.
The dilemma that you face is common when sampling small populations for a low fraction defective. The following sampling strategy might addresses that issue.
Stage (1) First, draw a monthly sample from a global population that consists of all 275 of the business's branches. The statistics of this sample apply at the level of the total business.
Stage (2) Second, use defectives in the global sample to decide if/where to "drill down" on specific branches that may be exceptional sources of error.
Here is how I think I would choose a sample size for stage (1). Consider various sample sizes in multiples of 275. For example, for AQL=0.04 (4%), Producers risk=0.05, Consumer's risk=0.05, Calculate RQL and base your choice on that. RQL is the population fraction defective that, if true, has (1-Beta)= 0.95 chance of being rejected.
1) n=1 per branch=275, RQL=0.0875 (8.75%), Ac=16
2) n=1 per branch=550, RQL=0.0722 (7.22%), Ac=30
And so on. Our new software version 3 of TP105 does the calculations and allows you to try out various schemes. TP105 also calculates and plots performance curves like the OC and AOQ curves.
The stage (1) decision rule is that if the number of defectives in the global sample is less than or equal to Ac, accept the global population. Otherwise, reject it.
Stage (2)
If the stage (1) plan rejects the global population, stage (2) is to drill down on offending branches.
2a) Define a rule for "offending branch". For example, sample fraction defective (p') greater than AQL=0.04.
2b) By "drill down, I mean to rectify, meaning 100% inspect.
If the stage (1) plan accepts the global population, stage (2) is to do no further inspection, but to notify and increase next month's sample size for branches with high sample percent defective.
The method that I outlined for stage (2) is not based on statistical analysis because the small populations do not allow for good precision. You should adjust/modify it based on your ongoing experience and judgement. A corrective action plan will improve future branch performance.