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Statistical inference for coherent systems with Weibull distributed component lifetimes under complete and incomplete information

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  • A. Jablonka
  • E. Cramer
  • M. Hermanns

Abstract

Point estimators for the parameters of the component lifetime distribution in coherent systems are evolved assuming to be independently and identically Weibull distributed component lifetimes. We study both complete and incomplete information under continuous monitoring of the essential component lifetimes. First, we prove that the maximum likelihood estimator (MLE) under complete information based on progressively Type‐II censored system lifetimes uniquely exists and we present two approaches to compute the estimates. Furthermore, we consider an ad hoc estimator, a max‐probability plan estimator and the MLE for the parameters under incomplete information. In order to compute the MLEs, we consider a direct maximization of the likelihood and an EM‐algorithm–type approach, respectively. In all cases, we illustrate the results by simulations of the five‐component bridge system and the 10‐component parallel system, respectively.

Suggested Citation

  • A. Jablonka & E. Cramer & M. Hermanns, 2019. "Statistical inference for coherent systems with Weibull distributed component lifetimes under complete and incomplete information," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(4), pages 1011-1027, July.
    • Handle: RePEc:wly:apsmbi:v:35:y:2019:i:4:p:1011-1027
    DOI: 10.1002/asmb.2440
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