Abstract
Reliability importance of components of various systems is an important part in the reliability study. In this paper Birnbaum-reliability importance (B-importance) of components of three popular consecutive-type systems as consecutive-k-out-of-n: F-system, m-consecutive-k-out-of-n: F system and r-within-consecutive-k-out-of-n: F system is studied. The B-importance is studied when the survival probabilities of components of the system are Markov dependent. This study is based on conditional distribution of number of occurrences of failure runs of length k and number of occurrences of scanning windows of length k containing r failures in the sequence of Markov Bernoulli trials. Simplified formulae for calculation of B-importance of each component of the three consecutive-type systems are developed in terms of survival probabilities. To demonstrate the simplicity of the derived results, numerical study is also included.
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