# Sequential sampling

Sequential sampling | |
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See also |

**Sequential sampling**- a sampling in which the members are drawn one by one or in groups in order, and the results of the drawing at any stage decide whether sampling is to continue. The sample size is thus not fixed in advance but depends on the actual results and varies from one sample to another. The sampling terminates according to predetermined rules which are decided by the degree of precision required^{[1]}.

Sequential sampling is a fast efficient tool for many sampling problems. Sequential sampling may be used^{[2]}:

**to obtain precise estimates**of the parameters**to test hypotheses concerning**the parameters

## Mechanic of sequential sampling

All dichotomous sequential plans begin with the establishment of two alternative hypotheses, here designated H1 and H2. Consecutive samples are examined and evaluated until cumulative results dictate that one hypothesis is more likely to be correct than the other at some preestablished degree of reliability.

Suppose we are examining ears of sweet corn for the presence of corn earworm larvae. We expect to find no larvae in noninfested ears, and exactly one larva per infested ear, because the larvae are cannibalistic. Let us assume that^{[3]}:

- lots having 20 percent or fewer infested ears are
*good*lots, and it is very important that they be so classified - lots having 80 percent or more infested ears are
*bad*lots, and it is very important that they be co classified - lots having more than 20 percent but less than 80 percent infestation can be classified as either
*good*or*bad*without serious consequence.

## Sequential acceptance sampling

In quality control by acceptance sampling, the maximum number of samples is fixed in advance. In sequential acceptance sampling, a sequence of samples is selected from the lot and, at each stage, a decision is taken about whether to accept or reject the lot or whether to select a further sample. This process continues until a decision to either accept or reject the lot is made.

Theoretically, the sequential sampling may continue indefinitely, until the while lot has been inspected. If the sample size at each step is equal to one, this procedure is usually called item-by-item sequential sampling. If the sample size at each step is greater than one, the procedure is defined as group sequential sampling. The item-by-item sequential sampling procedure can be illustrated by means of a Cartesian diagram where the abscissa is the total number of items selected up to that time, and rejection are drawn on the basis of the sequential probability ratio test theory.

If the plotted points stay within the boundaries, another sample is selected; if a point falls above the upper line, the lot is rejected; if a point falls below the lower line, the lot is accepted^{[4]}.

## Footnotes

## References

- Dodge Y., Commenges D., (2011),
*The Oxford Dictionary of Statistical Terms*, Oxford University Press, New York. - Erto P., (2010),
*Statistics for Innovation*, Springer Science & Business Media, Milano. - Onsager J.A., (2000),
*The Rationale of Sequential Sampling*, U.S. Department of Agriculture, Washington. - Young L.L. (2010),
*Statistical Ecology*, Springer Science & Business Media, Boston.

**Author:** Natalia Hajduk