Acceptance sampling uses
statistical sampling to determine whether to accept or reject a production lot of material. It has been a common
quality control technique used in industry.
It is usually done as products leave the factory, or in some cases even within the factory. Most often a producer supplies a consumer with several items and a decision to accept or reject the items is made by determining the number of defective items in a sample from the lot. The lot is accepted if the number of defects falls below where the acceptance number or otherwise the lot is rejected.
In general, acceptance sampling is employed when one or several of the following hold:
* testing is destructive;
* the cost of 100% inspection is very high; and
* 100% inspection takes too long.
A wide variety of acceptance
sampling plans is available. For example, multiple sampling plans use more than two samples to reach a conclusion. A shorter examination period and smaller sample sizes are features of this type of plan. Although the samples are taken at random, the sampling procedure is still reliable.
History
Acceptance sampling procedures became common during World War II. Sampling plans, such as
MIL-STD-105, were developed by
Harold F. Dodge and others and became frequently used as
standards.
More recently,
quality assurance broadened the scope beyond final inspection to include all aspects of manufacturing. Broader
quality management systems include methodologies such as
statistical process control
Statistical process control (SPC) or statistical quality control (SQC) is the application of statistical methods to monitor and control the quality of a production process. This helps to ensure that the process operates efficiently, producing ...
,
HACCP,
six sigma, and
ISO 9000
The ISO 9000 family is a set of five quality management systems (QMS) standards that help organizations ensure they meet customer and other Stakeholder (corporate), stakeholder needs within statutory and regulatory requirements related to a pr ...
. Some use of acceptance sampling still remains.
Rationale
Sampling provides one rational means of
verification that a production lot conforms with the requirements of
technical specifications. 100% inspection does not guarantee 100% compliance and is too time-consuming and costly. Rather than evaluating all items, a specified sample is taken, inspected or tested, and a decision is made about accepting or rejecting the entire production lot.
Plans have known risks: an
acceptable quality limit (AQL) and a rejectable quality level, such as lot tolerance percent defective (LTDP), are part of the
operating characteristic curve of the sampling plan. These are primarily statistical risks and do not necessarily imply that a defective product is intentionally being made or accepted. Plans can have a known average outgoing quality limit (AOQL).
Acceptance sampling for attributes
A single sampling plan for attributes is a statistical method by which the lot is accepted or rejected on the basis of one sample.
[Montgomery, D. C. (2009). ''Statistical Quality Control: A Modern Introduction'', Wiley, ] Suppose that we have a lot of sizes
; a random sample of size