A Start-Up Demonstration Test Using a Simple Scan-Based Statistic

Recently, start-up demonstration tests and various extensions of them (in order to accommodate dependence between the trials, to allow for corrective action to be taken once the equipment fails for the first time, etc.) have been discussed in the literature. In this chapter, we propose a start-up demonstration test using a simple scan-based statistic that would facilitate an early rejection of a potentially bad equipment. We then derive the probability generating function of the waiting time for rejection of an equipment and the mean and variance of the waiting time. We also present some recurrence relations satisfied by the probability mass function and the moments. In addition, we indicate how the moment estimator for the unknown probability of success(p)of the individual trials can be derived. The case of start-up demonstration testing when consecutive attempts are dependent in a Markovian fashion is discussed next. Finally, we present a numerical example to illustrate the test proposed and the usefulness of the results established in this chapter.