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Statistical inference for coherent systems with Weibull distributed component lifetimes under complete and incomplete information
Author(s) -
Jablonka A.,
Cramer E.,
Hermanns M.
Publication year - 2019
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2440
Subject(s) - estimator , component (thermodynamics) , weibull distribution , expectation–maximization algorithm , independent and identically distributed random variables , inference , mathematics , order statistic , statistics , computer science , point estimation , mathematical optimization , algorithm , maximum likelihood , random variable , artificial intelligence , physics , thermodynamics
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.