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Chan, P. S.; Ng, H. K. T.; Balakrishnan, N.

Statistical inference for start-up demonstration tests with rejection of units upon observing \(d\) failures. (English) Zbl 1169.62349

J. Appl. Stat. 35, No. 8, 867-878 (2008).
Summary: We consider statistical inference for the success probability in the case of start-up demonstration tests where rejection of units is possible when a pre-fixed number of failures is observed before the required number of consecutive successes is 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.

Cited in 5 Documents

MSC:

62N05 Reliability and life testing
62F15 Bayesian inference
62N02 Estimation in survival analysis and censored data
65C60 Computational problems in statistics (MSC2010)
62N03 Testing in survival analysis and censored data

Keywords:

maximum likelihood estimator; EM-algorithm; runs; Bayesian estimation; probability generating function
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References:

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