From: Stan Hilliard
Date: 06 Jul 2000
Time: 17:38:20
Hi Dot,
First, what is AS1199 Sampling Procedures? If I were to guess, I would say it is a Company document that uses sampling plans from Mil-Std-105.
ASQC standard Z1.4 (same as Mil-Std-105E) says that for inspection level II and batch size of N=250 to use a sample size code letter of G, for which the fixed sample size n, is 32 under normal inspection. For an AQL of 2.5%, the acceptance number, Ac is 2 defectives.
ASQC standard Z1.4 also gives a matched double sampling plan of:
Sample 1: n1=20, Ac1=0, Re1=3
Sample 2: n1+n2=40, Ac2=3, Ac4=3
This is the technical answer to your question, but that approach is outdated methodology. I do not recommend it except when you are required by a customer who is on that system. A more "rational" approach is to specify the performance that you desire for the plan.
The performance of a sampling plan is completely determined by four numbers: (1) the acceptable quality level (AQL), (2) the rejectable quality level (RQL), (3) the producers risk (Alpha), and (4) the Consumers risk (Beta). These four numbers determine two points - the producers point and the consumers point - on the oc- curve.
This oc curve shows everything that you can know about the performance of that specific sampling plan with respect ot accepting and rejecting various quality lots. You should view the oc curve from the standpoint of the probability that the sampling plan will reject off-grade lots, and accept lots that are fit for use.
For details on using the oc curve to develop sampling plans see:
See www.samplingplans.com/usingoccurves.htm
The sampling plan program TP105 provides the following probabilities for the sampling plan that you specified above( p'=lot fraction defective, Pa=Probability of acceptance:
p' Pa
0.0000(0.00%) 1.0000
0.0220(2.20%) 0.9637
0.0503(5.00%) 0.7998
0.0838(8.39%) 0.4927
0.1508(15.8%) 0.1114
0.1843(18.4%) 0.0495
Note from the table above that for the purpose of detecting off-grade lots, AQL does not do the job. The sampling plan that you specified was for AQL=2.5% defective. Yet a lot that is 8.38% defective would have nearly a 50% chance of passing. A lot would have to be 18.4% defective or more before you could be quite confident that the plan would catch it!
This is why I do not recommend the AQL & inspection-level approach - too many people get fooled by it. This problem can be avoided by using the oc curve method to design sampling plans.
The program TP105 that I used to perform the oc curve analysis (above) is descibed here:
www.samplingplans.com/software.htm
Sincerely, Stan Hilliard