Inference with progressively censored k-out-of-n system lifetime data

M. Hermanns and E. Cramer ()
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M. Hermanns: RWTH Aachen University
E. Cramer: RWTH Aachen University

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2018, vol. 27, issue 4, No 6, 787-810

Abstract: Abstract A system with n independent components which works if and only if a least k of its n components work is called a k-out-of-n system. For exponentially distributed component lifetimes, we obtain point and interval estimators for the scale parameter of the component lifetime distribution of a k-out-of-n system when the system failure time is observed only. In particular, we prove that the maximum likelihood estimator (MLE) of the scale parameter based on progressively Type-II censored system lifetimes is unique. Further, we propose a fixed-point iteration procedure to compute the MLE for k-out-of-n systems data. In addition, we illustrate that the Newton–Raphson method does not converge for any initial value. Finally, exact confidence intervals for the scale parameter are constructed based on progressively Type-II censored system lifetimes.

Keywords: Progressive Type-II censoring; k-out-of-n system; MLE; Fixed-point iteration; Exact confidence intervals; Exponential distribution; 62F10; 62N01; 62N05 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11749-017-0569-8

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