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On the conditional residual lifetime of coherent systems under double regularly checking
Author(s) -
Goli Sareh
Publication year - 2019
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.21841
Subject(s) - residual , independent and identically distributed random variables , mathematics , reliability (semiconductor) , conditional expectation , conditional probability , function (biology) , random variable , discrete mathematics , statistics , computer science , algorithm , physics , quantum mechanics , power (physics) , evolutionary biology , biology
In this paper, we consider a coherent system with n independent and identically distributed components under the condition that the system is monitored at time instances t 1 and t 2 ( t 1 < t 2 ). First, various mixture representations for reliability function of the conditional residual lifetime of the coherent system are derived under different scenarios at times t 1 and t 2 ( t 1 < t 2 ). Several stochastic comparisons between two systems are also made based on the proposed conditional random variables. Then, we consider the conditional residual lifetime of the functioning components of the system given that j components have failed at time t 1 and the system has failed at time t 2 . Some stochastic comparisons on the proposed conditional residual lifetimes are investigated. Several illustrative graphs and examples are also provided.