Start‐up demonstration tests: models, methods and applications, with some unifications

Abstract

Start‐up demonstration tests were first discussed in the quality/reliability literature about three decades ago. Since then, many variations of these tests have been introduced, and the corresponding distributional characteristics and inferential methods have also been studied. All these developments, based on independent and identically distributed binary trials, have been further generalized to some other forms of trials such as Markov‐dependent trials, exchangeable trials and multistate trials. In this paper, we provide a comprehensive review of all these results and highlight some unifications of the results. We also describe a general estimation method and then present several numerical examples to illustrate some of the models and methods described here. Finally, a number of open issues in this area of research are pointed out. Copyright © 2014 John Wiley & Sons, Ltd.

A Comparison of Start-Up Demonstration Test Procedures Based on a Combinatorial Approach

“…These include using generating functions, the Markov Chain Embedding technique (MCE) and the present combinatorial approach. An extensive survey of the various start-up procedures has been presented in a paper by Balakrishnan et al (2014). At first, the CS (Consecutive Successes) procedure was introduced by Hahn and Gage (1983) and by Viveros and Balakrishnan (1993).…”

An Approach for Reliability Demonstration Test Based on Power‐Law Growth Model

“…Generally, the proposed methods can be classified into two categories on the basis of the type of data involved: test plans based on failures and those based on degradation. Zhao, Kleyner et al , Zhang et al , Jensen and Balakrishnan et al are among the recent scholars studying demonstration tests under different conditions and test schemes.…”

Asymptotic results for the multiple scan statistic

“…The scan statistic has been fruitfully exploited in a diverse spectrum of research areas such as quality control, reliability theory, biosurveillance, molecular biology, start-up demonstration testing, actuarial science, and so on (see, e.g. Glaz and Naus (1991), Koutras (1996), Boutsikas and Koutras (2002), (2003), Balakrishnan and Koutras (2002), Glaz et al (2009), and Balakrishnan et al (2014)).…”