Acceptance sampling uses
statistical sampling
In statistics, quality assurance, and survey methodology, sampling is the selection of a subset (a statistical sample) of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians atte ...
to determine whether to accept or reject a production lot of material. It has been a common
quality control
Quality control (QC) is a process by which entities review the quality of all factors involved in production. ISO 9000 defines quality control as "a part of quality management focused on fulfilling quality requirements".
This approach place ...
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
MIL-STD-105 was a United States defense standard that provided procedures and tables for sampling by attributes based on Walter A. Shewhart, Harry Romig, and Harold F. Dodge sampling inspection theories and mathematical formulas. Widely adopted ...
, were developed by
Harold F. Dodge and others and became frequently used as
standards Standard may refer to:
Symbols
* Colours, standards and guidons, kinds of military signs
* Standard (emblem), a type of a large symbol or emblem used for identification
Norms, conventions or requirements
* Standard (metrology), an object t ...
.
More recently,
quality assurance
Quality assurance (QA) is the term used in both manufacturing and service industries to describe the systematic efforts taken to ensure that the product(s) delivered to customer(s) meet with the contractual and other agreed upon performance, design ...
broadened the scope beyond final inspection to include all aspects of manufacturing. Broader
quality management system
A quality management system (QMS) is a collection of business processes focused on consistently meeting customer requirements and enhancing their satisfaction. It is aligned with an organization's purpose and strategic direction (ISO 9001:2015). I ...
s 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
Hazard analysis and critical control points, or HACCP (), is a systematic preventive approach to food safety from biological, chemical, and physical hazards in production processes that can cause the finished product to be unsafe and designs mea ...
,
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 needs within statutory and regulatory requirements related to a product or service. ISO 90 ...
. Some use of acceptance sampling still remains.
Rationale
Sampling provides one rational means of
verification
Verify or verification may refer to:
General
* Verification and validation, in engineering or quality management systems, is the act of reviewing, inspecting or testing, in order to establish and document that a product, service or system meets ...
that a production lot conforms with the requirements of
technical specifications
A specification often refers to a set of documented requirements to be satisfied by a material, design, product, or service. A specification is often a type of technical standard.
There are different types of technical or engineering specificati ...
. 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
The acceptable quality limit (AQL) is the worst tolerable process ''average'' (''mean'') in percentage or ratio that is still considered acceptable; that is, it is at an acceptable quality level.Dodge, Y. (2003) ''The Oxford Dictionary of Statisti ...
(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