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## Re: C=0 Sampling plan from AQL

**From: **Stan Hilliard

**Date: **16 Nov 2002

**Time: **23:16:59

### Comments

Roland, I received this email from you and I am posting in the forum so that others can follow the discussion.

=========== Start of Quote: from Roland Hng

Thank you for your help so far on C=0 sampling conversion plan.

(See attached file: Sampling Plan Table.tif)

Stan, I have a copy of table which is suppose to correlate AQL to C=0 sampling size. But this plan does not match the AQL level in the sampling analyser print out.

Example : for AQL 1.5% on the above table, corresponding C=0 sample size should be 46. But, the sampling analyser software show that for C=0 and n=46, corresponding AQL is 0.111%.

I am confused. Why is there a difference??
Could you help explain, Sir.

=========== End of quote from Roland Hng

I agree with your analysis. For the sampling plan n=46, C=0, TP105 calculates the producer's point and consumer's point as: [Alpha=0.05, AQL=0.001114(fraction)] and [Beta=0.05, RQL=0.063050(fraction)]. The fractions correspond to the percentages AQL=0.111%, RQL=6.30%.

To illustrate why the universal C=0 approach is misleading and could cost your company a lot of money, I calculated the complete oc curve for n=46, c=0. The oc curve revealed that the producer's risk of that plan is 0.4917(fraction). I used alpha=(1-Pa) at p'=AQL=1.5%. In other words, 49% of the AQL lots will be rejected. If you base AQL on process capability, then the yield will be 50%. You could double the price of the product to recover the expected loss due to rejecting half of the AQL lots.

I received the C = zero sampling plan table that you e-mailed to me. You will find that all of the sampling plans in that table have 50% chance of rejecting AQL lots. The article by R. C. Baker that I mailed to you contains a thorough analysis of the expected cost increases due to this type of C=0 sampling plan.

You might ask why this type of sampling plan is required by QS9000. I do not know except to note that QS9000 is written by a consumer to be used by producers. The consumer's point did not change appreciably in the conversion to C=0.

RQL Original: RQL=5.3% at alpha=5%.

RQL Final: RQL=6.30 at beta=5%.

AQL Original: AQL=1.9704% at alpha=5%.

AQL Final: AQL=0.111% at alpha=5%.

AQL Final: AQL=1.5% at alpha=49%.

I hope that this helps you to understand and to avoid the potential cost increase to your company that could occur from using C=0 sampling plans without being aware of the 50% producer's risk.

Sincerely, Stan Hilliard

##### Last changed: November 20, 2007