This is just an Excerpt from a larger document, click here to view the entire document.Introduction
Determining the sample size "n" required in testing and confidence interval (CI) derivation is of importance for practitioners, as evidenced by the many related queries that we receive at the RIAC in this area. Therefore, we have addressed this topic in a number of START sheets. For example, we discussed the problem of calculating the sample size for deriving a general CI in Reference 1, and for the case of acceptance testing, in Reference 2. The problem of censored sampling has been treated in Reference 3. These cases, however, only treat the situation where fixed samples of predetermined sizes are taken, all at one time.
But sampling is both expensive and time consuming. Hence, there are situations where it is more efficient to take samples sequentially, as opposed to all at one time, and to define a stopping rule to terminate the sampling process. The case where the entire sample is drawn at one instance is known as "single sampling." The case where samples are taken in successive stages, according to the results obtained from the previous samplings, is known as "multiple sampling."
Taking samples sequentially and assessing their results at each stage allows the possibility of stopping the process and reaching an early decision. If the situation is clearly favorable or unfavorable (for example, if the sample shows that a widget's quality is definitely good or poor), then terminating the process early saves time and resources. Only in the case where the data is ambiguous do we continue sampling. Only then, do we require additional information to take a better decision.
The preceding discussion justifies the need to overview multi-stage sampling plans, and we will do so in a sequence of two START sheets. In this first START sheet, we start by exploring double sampling plans. From there, we proceed to higher dimension sampling plans, namely sequential tests. We illustrate their discussion via numerical and practical examples of sequential tests for attributes (pass/fail) data that follow the Binomial distribution. Such plans can be used for Quality Control as well as for Life Testing problems. We conclude with a discussion of the ASN or "average sample number," a performance measure widely used to assess such multi-stage sampling plans. In the second START sheet, we will discuss sequential testing plans for continuous data (variables), following the same scheme used herein.