Sampling by Variables (ANSI/ASQ Z1.9)

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    Speaker: William Levinson

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    Duration: 60 Minutes
    Product Code: 50259
    Level: Intermediate

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ANSI/ASQ Z1.9 (formerly MIL STD 414) uses sample statistics to determine whether a production lot, or incoming lot, should be accepted or rejected. These statistics also allow estimation of the nonconforming fraction at each specification limit. Attendees will learn how to define a sample plan on the basis of (1) the lot size, (2) the inspection level, and (3) the acceptable quality limit (AQL).

ANSI/ASQ Z1.9 can be used for single specification limits, two-sided specification limits, and even two-sided limits with different AQLs. Attendees will learn everything they need to know to address all three of these applications.

Switching rules meanwhile dictate normal, tightened, or reduced inspection according to production performance. Poor quality results in tightened inspection, while a consistent history of good quality and consistent production conditions allows reduced inspection. In addition, if the process is under control and its standard deviation is known, a considerably smaller sample size is required.


ANSI/ASQ Z1.9 is a widely recognized and generally accepted standard for acceptance sampling by variables. It uses the average and standard deviation (or range) of a sample of n parts to determine whether the lot from which the sample was drawn should be accepted or rejected. The technology is very straightforward, but users must also be aware of the often-overlooked fact that the standard relies on the assumption that the part measurements follow the normal or bell curve distribution. If this is not the case, the standard will not deliver the intended or expected results.

Attendees will also learn pitfalls that are involved in use of the sampling tables, and also use of the range method. It is important to remember that this approach uses the average range of samples of 5, rather than the range of (for example) all 15 parts in the sample.

Handouts will include a technical appendix that shows the derivation of some of the material in the standard such as operating characteristic (OC) curves, and an Excel spreadsheet that duplicates tables B5 and D5, which return estimates of the nonconforming fraction in the lot when the standard deviation is estimated from the sample statistics (B5) or known from prior experience (D5).


• Sampling by variables (ANSI/ASQ Z1.9) requires a far smaller sample than sampling by attributes (ANSI/ASQ Z1.4), but it also requires real number measurements that may be harder to obtain than pass/fail data.
• The sample plan, in terms of sample size n and the acceptance criteria, is a function of (1) the lot size, (2) the inspection level, and (3) the acceptable quality level (AQL). It is important to pay attention to the "chutes and ladders" aspect of some of the tables, in which the intersection of the sample code letter and AQL may contain an arrow that goes to a different row, and therefore a smaller or larger sample size.
• The decision as to whether to accept the lot depends on the sample statistics including its average and also (1) the sample standard deviation, (2) the average range, or (3) the known process standard deviation. If the latter is available, a considerably smaller sample is required. When the range method is used, a sample of n (except 3, 4, or 7) is broken down into groups of 5 whose average range is then calculated.
• The sample statistics can also be used to estimate the nonconforming fraction at each specification limit, and this approach must be used in the more complex applications.
• Switching rules dictate whether inspection must be at the normal, tightened, or reduced level.
• The standard relies on the assumption that the measurements follow the normal or bell curve distribution. The normal probability plot, histogram, and other tests can be used to assess this assumption. If the process standard deviation is known from a process capability study, then these tests should have already been performed.


This webinar will equip attendees to understand and apply the ANSI/ASQ Z1.9 (formerly MIL STD 414) standard for acceptance sampling by variables (real number data), along with vital considerations such as the need to test the measurements for conformance to the normal (bell curve) distribution.


Quality engineers, technicians, and inspectors who use ANSI/ASQ Z1.9 (formerly MIL-STD 414)


Years of Experience: 30+ years

Areas of Expertise: Statistical Process Control, Lean Manufacturing, Quality, ISO 9001, Design Of Experiments, Non-Normal Distributions, Quality Management Systems

William Levinson 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 holds degrees in chemistry and chemical engineering from Penn State and Cornell Universities, and night school degrees in business administration and applied statistics from Union College, and he has given presentations at the ASQ World Conference, ISO/Lean Six Sigma World Conference, and others.

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