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The Truth About Acceptance Sampling,
Part 1

What can you say about this lot?

Donald J. Wheeler
Wed, 07/02/2014 - 00:00
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Body

One of the common tools of quality assurance is acceptance sampling. Acceptance sampling uses the observed properties of a sample drawn from a lot or batch to make a decision about whether to accept or reject that lot or batch. Textbooks are full of complex descriptions of various acceptance sampling plans, however, there are some very important aspects of acceptance sampling that are not included in the textbooks. These are the topic of this column.

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Extrapolation

In the interest of simplicity, the product that has been measured will be referred to as the “sample,” while the product that has not been measured will be referred to as the “lot.” Every time that we attempt to use a sample to characterize the conformity of a lot, we will be making an extrapolation from the product that has been measured to the product that has not been measured. Now extrapolation is beyond the scope of most courses of instruction and education simply because it is so complex. Yet, typically, it is the one thing that we are called on to do on a daily basis. So how can we extrapolate from the sample to the lot?

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Comments

Submitted by William A. Levinson on Wed, 07/02/2014 - 11:58

This is why attribute data are relatively weak

You can compute a rather wide confidence interval for the nonconforming fraction based on your sample. This is why ANSI/ASQ Z1.4 has acceptable quality levels in the full percentages, which is hardly acceptable quality today. Henry Ford used 100 percent "inspection," except it was actually automated to avoid the prohibitive labor costs. Automatic gages sorted out the bad parts, and may well have let the operators know their equipment was making nonconforming work.
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Submitted by Donald J. Wheeler on Wed, 07/02/2014 - 14:51

Reply to Levinson

In a Technometrics article in 1970 I proved that the minimum variance unbiased estimate of the fraction nonconforming (based upon measurements rather than counts) is only slightly better than the binomial point estimate covered in this paper. While the confidence intervals would be slightly shorter than those given by the Agresti-Coull formula given here, the estimates themselves are much more complex since they involve the either a symmetrical cumulative beta distribution or a cumulative Student's t distribution. So, in practice, and regardless of whether you are using counts or measurements, I recommend using the approach given here for simplicity.
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Submitted by Rip Stauffer on Wed, 07/09/2014 - 03:28

A question...

Wouldn't it be even better if the supplier sent a process behavior chart of the production run that produced the lot, and maybe a capability study?

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Submitted by Donald J. Wheeler on Wed, 07/09/2014 - 04:30

Reply to Rip Stauffer

Absolutely! Trying to discover how good things are after the fact is never as good as knowing what happened while the batch was produced. However, I keep getting questions about how to use acceptance sampling. I even found one plant where they accepted or rejected product internally based on a six piece sample taken every half-hour. Their rejection number was 1, and they were making 2400 pieces per minute. So they made 72,000 pieces every half hour, and then essentially rolled the dice as to whether to accept or reject that half-hour'a production.
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