Failure Time Distributions: Estimates and Asymptotic Results
The paper deals with life distributions for coherent systems of components. Two major questions are discussed: (i) estimation of system life in terms of component lives, and (ii) asymptotic models. Both questions are related to extremes of a sequence of random variables through the path set and cut set decomposition of coherent systems, which reduce a coherent system to either a parallel or a series system. It is pointed out that the classical theory of extremes of independent and identically distributed random variables does not provide an acceptable approximation. Hence, the emphasis is on dependence or on the case when the random variables are not identically distributed. The inequalities presented when discussing question (i) are applicable not only to extreme value problems but to an arbitrary multivariate distribution when lower dimensional marginals are specified. The asymptotic models are also discussed in the light of hazard rate properties of the limiting distributions for the extremes in a particular model.
Key Wordscoherent system component life system life extreme value distribution dependent model inequalities multivariate distribution Weibull distribution hazard rate
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