Inspection lot

In quality management , the inspection lot is the identification of a product sample as part of production quality monitoring . It is considered a request from (ongoing or completed) production to take a sample and check it in accordance with the internal quality standards.

This is also used for incoming and outgoing goods inspections. The values agreed between the supplier and the customer (AQL, RQL see below) then apply as a quality standard. How the parameters for this inspection lot (acceptance number and lot size or sample size ) are determined is explained below. A sampling plan is also often mentioned . ${\ displaystyle c}$ ${\ displaystyle n}$ ${\ displaystyle (n, c)}$

Action

Relationship between AQL / type 1 error and RQL / type 2 error to the operating characteristics function

The following figures are mostly determined with the customer (RQL and error of the 2nd type ) and the production (AQL and error of the 1st type ) and the operational characteristic function must then fall below (consumer point) or exceed (producer point) these points. The operating characteristics function can be influenced by the acceptance number and the sample size , thus determining the parameters for the inspection lot. ${\ displaystyle c}$ ${\ displaystyle n}$

IQL

IQL is the abbreviation for Indifferent Quality Level . This is the quality level at which the acceptance probability is 50%; this value is of little importance in practice.

AQL

AQL is the abbreviation for acceptance quality limit (dt. Acceptable Quality Level , a numerical value) - if agreed between customer and supplier - indicates how high the reject rate at which the lot with the probability is assumed (producer risk). ${\ displaystyle 1- \ alpha}$

Example: With a delivery quantity of 10,000 pieces from a production with the agreed quality level, the size of the sample is 200 pieces. The following test shows “often” (with the probability ) that the number of errors in the sample is below the number of rejections; the lot is thus accepted. The probability that the number of defects found in the sample is greater than the acceptance number, although the proportion of defects in the lot meets the agreed "limit position". The lot is to be withdrawn by the producer, even though a complete inspection of the remaining units beyond the sample does not exceed the agreed error rate. ${\ displaystyle 1- \ alpha}$ ${\ displaystyle \ alpha}$

RQL

RQL is the abbreviation for rejectable quality limit (dt. Rejectable quality limit ) . A numerical value that - if agreed between the customer and the supplier - indicates how high the scrap portion is for which the lot is mistakenly accepted with the probability of type 2 error ( error) (consumer risk). ${\ displaystyle \ beta}$

Example: With a delivery quantity of 10,000 pieces, the size of the inspection lot is 2 pieces. Both samples do not meet the test conditions. The entire delivery is rejected. With the probability of error of the 2nd type ( error), the lot can still meet the requirements. ${\ displaystyle \ beta}$

Explanation

As is clear from the example, errors of the 1st and 2nd type influence each other. In addition, the steepness of the operating characteristic function is determined by the sample size, so that errors of the 1st and 2nd type can be reduced.

Two-stage examination

In a two-stage test, a first test lot is taken from the scope and one of three decisions is made: ${\ displaystyle n_ {1}}$

Accept delivery (if the inspection lot turns out convincingly good)
Reject delivery (if the test lot turns out terribly bad)
Take another inspection lot from the scope (if you cannot decide yet) ${\ displaystyle n_ {2}}$

In the case of two-stage testing, the sample size is random, either or . The mean sample size ( ASN , average sample number ) of a two-stage test is usually smaller than the sample size of a single-stage test, assuming the same requirements for the operating characteristics are assumed. ${\ displaystyle n_ {1}}$ ${\ displaystyle n_ {1} + n_ {2}}$

Sequential testing

The sequential check is an application of the sequential likelihood ratio test . Here, after each test element drawn, a decision is made as to whether the delivery is accepted, rejected or whether another test element is drawn. This results in a further reduction in the ASN compared to the two-stage test.

Individual evidence

↑ ISO 2859-1: 1999
↑ ^a ^b Uhlmann, W. (1982): Statistical Quality Control , BGTeubner, Stuttgart

[1] ISO 2859-1: 1999

[U-2] Uhlmann, W. (1982): Statistical Quality Control , BGTeubner, Stuttgart