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

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  • P. S. Chan
  • H. K. T. Ng
  • N. Balakrishnan

Abstract

In this paper, we consider the statistical inference for the success probability in the case of start-up demonstration tests in which rejection of units is possible when a pre-fixed number of failures is observed before the required number of consecutive successes are achieved for acceptance of the unit. Since the expected value of the stopping time is not a monotone function of the unknown parameter, the method of moments is not useful in this situation. Therefore, we discuss two estimation methods for the success probability: (1) the maximum likelihood estimation (MLE) via the expectation-maximization (EM) algorithm and (2) Bayesian estimation with a beta prior. We examine the small-sample properties of the MLE and Bayesian estimator. Finally, we present an example to illustrate the method of inference discussed here.

Suggested Citation

  • P. S. Chan & H. K. T. Ng & N. Balakrishnan, 2008. "Statistical inference for start-up demonstration tests with rejection of units upon observing d failures," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(8), pages 867-878.
    • Handle: RePEc:taf:japsta:v:35:y:2008:i:8:p:867-878
    DOI: 10.1080/02664760802124455
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    References listed on IDEAS

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    1. Philippou, Andreas N. & Georghiou, Costas & Philippou, George N., 1983. "A generalized geometric distribution and some of its properties," Statistics & Probability Letters, Elsevier, vol. 1(4), pages 171-175, June.
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    3. N. Balakrishnan & S. Mohanty & S. Aki, 1997. "Start-Up Demonstration Tests Under Markov Dependence Model with Corrective Actions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 155-169, March.
    4. S. Aki & N. Balakrishnan & S. Mohanty, 1996. "Sooner and later waiting time problems for success and failure runs in higher order Markov dependent trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(4), pages 773-787, December.
    5. Ebneshahrashoob, M. & Sobel, Milton, 1990. "Sooner and later waiting time problems for Bernoulli trials: frequency and run quotas," Statistics & Probability Letters, Elsevier, vol. 9(1), pages 5-11, January.
    6. Balasubramanian, K. & Viveros, R. & Balakrishnan, N., 1993. "Sooner and later waiting time problems for Markovian Bernoulli trials," Statistics & Probability Letters, Elsevier, vol. 18(2), pages 153-161, September.
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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.
    2. Athanasios Rakitzis & Demetrios Antzoulakos, 2015. "Start-up demonstration tests with three-level classification," Statistical Papers, Springer, vol. 56(1), pages 1-21, February.

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