Mixture Representations of Inactivity Times of Conditional Coherent Systems and their Applications

In this paper we obtain several mixture representations of the reliability function of the inactivity time of a coherent system under the condition that the system has failed at time t (> 0) in terms of the reliability functions of inactivity times of order statistics. Some ordering properties of...

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Bibliographic Details
Published in:Journal of applied probability 2010-09, Vol.47 (3), p.876-885
Main Author: Zhang, Zhengcheng
Format: Article
Language:English
Subjects:
60K10
62E15
Applications
Coefficients
Coherence
Coherence coefficient
Coherent system
Distribution theory
Exact sciences and technology
inactivity time
Mathematical analysis
Mathematical functions
Mathematical vectors
Mathematics
Military logistics
mixture representation
Nonparametric inference
Order disorder
Probability and statistics
Probability distribution
Probability theory
Probability theory and stochastic processes
Random variables
Randomness
Reliability
Reliability functions
Reliability, life testing, quality control
Representations
Sciences and techniques of general use
signature
Signatures
Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications)
Statistics
Stochastic models
stochastic order
Studies
System failures
Time signatures
Vectors (mathematics)
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Description
Summary:In this paper we obtain several mixture representations of the reliability function of the inactivity time of a coherent system under the condition that the system has failed at time t (> 0) in terms of the reliability functions of inactivity times of order statistics. Some ordering properties of the inactivity times of coherent systems with independent and identically distributed components are obtained, based on the stochastically ordered coefficient vectors between systems.
ISSN:0021-9002
1475-6072
DOI:10.1239/jap/1285335415