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

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  • David Scollnik

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.

Suggested Citation

  • David Scollnik, 2010. "Bayesian statistical inference for start-up demonstration tests with rejection of units upon observing d failures," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(7), pages 1113-1121.
    • Handle: RePEc:taf:japsta:v:37:y:2010:i:7:p:1113-1121
    DOI: 10.1080/02664760902914516
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    Cited by:

    1. N. Balakrishnan & M. Koutras & F. Milienos, 2014. "Some binary start-up demonstration tests and associated inferential methods," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(4), pages 759-787, August.

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