Zero Acceptance Sampling Plans to Reduce Inspection Costs

William A. Levinson

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Why should you attend?

Inspection is a mandatory but non-value-adding activity which means, the less we can do the better provided that the inspection plan deliver an agreed-upon level of protection to the customer. A zero acceptance number (c=0) plan can achieve this with the smallest possible sample size, in comparison to single, double, and multiple sampling plans under ANSI/ASQ Z1.4 (formerly MIL-STD 105). Zero acceptance sampling is essentially a form of discovery sampling in which we have a specified chance of finding at least one nonconforming item, and then rejecting the lot, if the nonconforming fraction exceeds the rejectable quality level (RQL). (ANSI/ASQ Z1.4 plans do not have formal RQLs but we treat the nonconforming fraction for which the chance of rejection is 90% as the RQL for this purpose.)

Nothing is however free in industrial statistics, and the tradeoff for the small sample size is the much larger chance of rejecting lots at the acceptable quality level (AQL). This means the producer must be confident that the quality level is much better than the AQL. When this is not true, alternatives to reduce the sample size include double, multiple, and sequential sampling plans.

Areas Covered in the Session:

1.       Review of ANSI/ASQ Z1.4 including how to define a sampling plan (sample size = n, acceptance number = c) based on (1) the lot size, (2) the inspection level, and (3) the acceptable quality level (AQL).

·         The operating characteristic (OC) curve reflects the acceptance probability as a function of the nonconforming fraction. This is ideally about 95% at the AQL although the exact number may vary depending on the plan.

2.       Convert any ANSI/ASQ Z1.4 plan into a c=0 plan as follows.

·         Determine the rejectable quality level (RQL), the nonconforming fraction for which the acceptance probability is 10%. (ANSI/ASQ Z1.4 plans do not have formal AQLs but we calculate the RQL on this basis. This is also used in sequential sampling plans.) This can be looked up in the standard or calculated by means of the F statistic.

·         Determine the sample size n for which the chance of not finding at least one nonconformance is less than 10% if the nonconforming fraction equals the RQL. This uses the same formula as discovery sampling.

·         The resulting plan has a lower average sample number (ASN) than corresponding ANSI/ASQ Z1.4 single, double, and multiple sampling plans, and also sequential sampling plans that are even more efficient than multiple sampling. The drawback is however a greater chance of rejection at the AQL. If rejection invokes the ANSI/ASQ Z1.4 switching rules, which will be covered in the presentation, this will be counterproductive.

·         Reduced sampling introduces yet another complication because two decisions, one involving acceptance or rejection of the lot, and another the switching rules, are required. It may be administratively simpler to just use the traditional reduced sampling plan.

3.       When a c=0 plan is not practical due to the likelihood of rejection of lots at the AQL, we can use the traditional double or multiple sampling plans to reduce the average sample number somewhat, and sequential sampling is even more efficient.

·         When the quality characteristic is normally distributed, and can be measured by go/no go gages set to specific dimensions, narrow limit gauging can deliver very small sample sizes.

Attendees will receive a handout of the slides and accompanying notes

Who will benefit:

Quality managers, engineers, and technicians, and others with responsibility for acceptance sampling activities


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Speaker: William A. Levinson,

William A. Levinson, P.E., is the principal of Levinson Productivity Systems, P.C. He is an ASQ Fellow, Certified Quality Engineer, Quality Auditor, Quality Manager, Reliability Engineer, and Six Sigma Black Belt. He is also the author of numerous books on quality, productivity, and management.

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