Progressive Type‐II censoring and coherent systems |
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| Authors: | Erhard Cramer Jorge Navarro |
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| Affiliation: | 1. Institute of Statistics, Department of Mathematics, RWTH Aachen University, Aachen, Germany;2. Department of Statistics and Operations Research, Facultad de Matematicas, Universidad de Murcia, Murcia, Spain |
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| Abstract: | A new connection between the distribution of component failure times of a coherent system and (adaptive) progressively Type‐II censored order statistics is established. Utilizing this property, we develop inferential procedures when the data is given by all component failures until system failure in two scenarios: In the case of complete information, we assume that the failed component is also observed whereas in the case of incomplete information, we have only information about the failure times but not about the components which have failed. In the first setting, we show that inferential methods for adaptive progressively Type‐II censored data can directly be applied to the problem. For incomplete information, we face the problem that the corresponding censoring plan is not observed and that the available inferential procedures depend on the knowledge of the used censoring plan. To get estimates for distributional parameters, we propose maximum likelihood estimators which can be obtained by solving the likelihood equations directly or via an Expectation‐Maximization‐algorithm type procedure. For an exponential distribution, we discuss also a linear estimator to estimate the mean. Moreover, we establish exact distributions for some estimators in the exponential case which can be used, for example, to construct exact confidence intervals. The results are illustrated by a five component bridge system. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 512–530, 2015 |
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| Keywords: | progressive Type‐II censoring progressive censoring with random removals coherent systems likelihood inference EM‐algorithm bridge system signature |
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