# What is Acceptance Sampling?

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Quality Glossary Definition: Acceptance Sampling

Sampling is the selection of a set of elements from a population or product lot. Sampling is frequently used because data on every member of a population are often impossible, impractical or too costly to collect. Sampling lets you draw conclusions or make inferences about the population from which the sample is drawn.

## Sampling error

When used in conjunction with randomization, samples provide virtually identical characteristics relative to those of the population from which the sample was drawn. Users of sampling are cautioned, however, that there are three categories of sampling error:

• bias (lack of accuracy)
• dispersion (lack of precision)
• nonreproducibility (lack of consistency)

These are easily accounted for by knowledgeable practitioners.

## Determining sample size

Determinations of sample sizes for specific situations are readily obtained through the selection and application of the appropriate mathematical equation.

All that is needed to determine the minimum sample size is to specify: if the data are continuous (variable) or discrete (attribute), if the population is finite or infinite, what confidence level is desired or specified, the magnitude of the maximum allowable error (due to bias, dispersion and/or nonresponsibility) and the likelihood of occurrence of a specific event.

Excerpted from Jack B. ReVelle’s Quality Essentials: A Reference Guide from A to Z, ASQ Quality Press, 2004, page 164.

## Sampling at a glance

• Less damage due to handling (inspections)
• More economical than 100% inspection
• Less time than doing 100% inspection
• Especially useful if using destructive testing techniques

Limitations

• Producer's and consumer's risk associated with sampling
• Sampling does not produce the complete picture of the true quality
• Quality cannot be inspected into a product

Excerpted from Mark Allen Durivage’s Practical Engineering, Process, and Reliability Statistics, ASQ Quality Press, 2015, page 145

Acceptance sampling provides the economic advantage of lower inspection costs due to fewer units being inspected. Also, the time required to inspect a sample is substantially less than that required for the entire lot, and there is less risk of damage to the product, due to reduced handling. Most inspectors find that selection and inspection of a random sample is less tedious and monotonous than inspection of a complete lot.

Another advantage of sampling inspection is related to the supplier/customer relationship. By inspecting a small fraction of the lot, and forcing the supplier to screen 100 percent in case of lot rejection (which is the case in rectifying inspection), the customer emphasizes that the supplier must be more concerned about quality.

On the other hand, variability is inherent in acceptance sampling, resulting in sampling errors: rejection of lots of conforming quality and acceptance of lots of nonconforming quality.

## Acceptance sampling vs. 100 percent inspection (screening)

Inspection can be done by acceptance sampling or by screening (also called sorting or 100 percent inspection), in which all units are inspected.

Acceptance sampling is most appropriate when inspection costs are high and when 100 percent inspection is monotonous and can cause inspector fatigue and boredom, resulting in degraded performance and increased error rates. Sampling is the only choice available for destructive inspection.

Rectifying sampling is a form of acceptance sampling. Sample units detected as nonconforming to requirements are discarded from the lot, replaced by conforming units, or repaired. Rejected lots are subject to 100 percent screening, which can involve discarding, replacing, or repairing units detected as nonconforming.

In certain situations, it is preferable to inspect 100 percent of the product. This would be the case for critical or complex products, where the cost of making the wrong decision would be too high. Screening is appropriate when the fraction nonconforming is extremely high. In this case, most of the lots would be rejected under acceptance sampling, and those accepted would be so as a result of statistical variations rather than better quality. Screening is also appropriate when the fraction nonconforming is not known and an estimate based on a large sample is needed.

It should be noted that the philosophy now being espoused in supplier relations is that the supplier is responsible for ensuring that the product shipped meets the user’s requirements. Many larger customers require evidence of product quality through the submission of process control charts showing that the product was produced by a process that was in control and capable of meeting the specifications.

## Sampling plans: Sampling by attributes & variables

The following standards detail acceptance sampling systems:

1. ANSI/ASQ Z1.4 provides tightened, normal, and reduced plans to be applied for attributes inspection for percent nonconforming
2. ANSI/ASQ Z1.9 provides tightened, normal, and reduced plans to be used on measurements which are normally distributed

These standards are based on acceptance quality limit (AQL), which is defined as the maximum percent or fraction of nonconforming units in a lot or batch that, for the purposes of acceptance sampling, can be considered satisfactory as a process average.

Excerpted from The Certified Quality Process Analyst Handbook, Second Edition, ASQ Quality Press, 2014, pages 145-148.