# Sequential sampling

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]:

1. to obtain precise estimates of the parameters
2. 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]:

1. lots having 20 percent or fewer infested ears are good lots, and it is very important that they be so classified
2. lots having 80 percent or more infested ears are bad lots, and it is very important that they be co classified
3. 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].

## Examples of Sequential sampling

• Chain Sampling: This technique involves a chain of sampling steps. At each step in the chain, a sample is selected and the results of the sample are analyzed. If the results indicate that the population is homogeneous, then the sampling process is complete. If the results show that the population is heterogeneous, then additional samples may be taken to further refine the results.
• Adaptive Sampling: This is a type of sequential sampling where the sample size is adjusted based on the results of the previous sample. For example, if the results of the first sample indicate that the population is heterogeneous, then the sample size may be increased in order to obtain more precise results.
• Stratified Sampling: This technique involves dividing the population into strata according to some predetermined criteria and then randomly selecting a sample from each stratum. This type of sequential sampling is often used when the population is known to be heterogeneous.

Sequential sampling offers a number of advantages over traditional sampling techniques. These include:

• Cost savings: Since the sample size is not fixed in advance, it can be adjusted according to the degree of precision required. This eliminates the need to collect excess data and helps to reduce costs.
• Time efficiency: Sequential sampling eliminates the need for multiple data collection cycles, thus reducing the amount of time needed to collect data.
• Flexibility: Sequential sampling can be adjusted to different scenarios according to the requirements of the study. This allows for a more tailored approach to data collection.
• Accuracy: The results of sequential sampling are more accurate than those of traditional sampling techniques due to the smaller sample size. This allows for better decision-making.

## Limitations of Sequential sampling

Sequential sampling has several limitations that can hinder its effectiveness. These include:

• The sample size is not fixed in advance, which can lead to unpredictable results.
• The predetermined rules that decide when sampling terminates may be insufficiently precise.
• The samples are drawn in order, which can lead to bias if individuals with certain characteristics are more likely to be drawn earlier or later in the sample.
• Sequential sampling can be costly and time consuming, as it requires collecting and analysing data from each successive sample.
• It can be difficult to interpret the results of sequential sampling, as the sample size is constantly changing and the rule for termination is predetermined.

## Other approaches related to Sequential sampling

• Stratified Sampling: A type of sampling where the population is divided into strata or homogeneous subgroups and then a sample is taken from each stratum.
• Cluster Sampling: A sampling technique in which a sample is taken from groups or clusters of elements that are similar to each other.
• Systematic Sampling: A sampling technique in which a sample is taken by selecting elements at regular intervals from the population.
• Multistage Sampling: A sampling technique in which several stages of samples are selected from the population.

In summary, Sequential sampling is a type of sampling technique in which elements are drawn one by one or in groups in order, and the results of the drawing at any stage decides whether sampling is to continue. Other approaches related to Sequential sampling include Stratified Sampling, Cluster Sampling, Systematic Sampling, and Multistage Sampling.

## Footnotes

1. Y. Dodge, D. Commenges 2011, p.368
2. L. L. Young 2010, p.153
3. J.A. Onsager 2000, p.3
4. P. Erto 2010, p.149

 Sequential sampling — recommended articles Np chart — Experimental error — Adjusted mean — Statistical power — CUSUM chart — Control chart — Central tendency error — Random error — Decision tree

## References

Author: Natalia Hajduk