Bayesian statistical inference for start-up demonstration tests with rejection of units upon observing d failures

David Scollnik

Journal of Applied Statistics, 2010, vol. 37, issue 7, 1113-1121

Abstract: This paper is concerned with Bayesian estimation and prediction in the context of start-up demonstration tests in which rejection of a unit is possible when a pre-specified number of failures is observed prior to obtaining the number of consecutive successes required for acceptance of the unit. A method for implementing Bayesian inference on the probability of success is developed for use when the test result of each start-up is not reported or even recorded, and only the number of trials until termination of the testing is available. Some errors in the related literature on the Bayesian analysis of start-up demonstration tests are corrected. The method developed in this paper is a Markov chain Monte Carlo (MCMC) method incorporating data augmentation, and it additionally enables Bayesian posterior inference on the number of failures given the number of start-up trials until termination to be made, along with Bayesian predictive inferences on the number of start-up trials and the number of failures until termination for any future run of the start-up demonstration test. An illustrative example is also included.

Keywords: start-up demonstration test; Bayesian estimation; MCMC; data augmentation (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1080/02664760902914516

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