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Reliability of systems with dependent components based on lattice polynomial description ; Marichal, Jean-Luc in Stochastic Models (2012), 28(1), 167-184 Reliability of a system is considered where the components' random lifetimes may be dependent. The structure of the system is described by an associated "lattice polynomial" function. Based on that ... [more ▼] Reliability of a system is considered where the components' random lifetimes may be dependent. The structure of the system is described by an associated "lattice polynomial" function. Based on that descriptor, general framework formulas are developed and used to obtain direct results for the cases where a) the lifetimes are "Bayes-dependent", that is, their interdependence is due to external factors (in particular, where the factor is the "preliminary phase" duration) and b) where the lifetimes' dependence is implied by upper or lower bounds on lifetimes of components in some subsets of the system. (The bounds may be imposed externally based, say, on the connections environment.) Several special cases are investigated in detail. [less ▲] Detailed reference viewed: 130 (8 UL)Analyse de fiabilité des systèmes semicohérents et description par des polynômes latticiels ; Marichal, Jean-Luc Scientific Conference (2009, February 10) Detailed reference viewed: 36 (0 UL)Reliability analysis and lattice polynomial system representation ; Marichal, Jean-Luc Scientific Conference (2008, October 17) Detailed reference viewed: 39 (0 UL)System reliability and weighted lattice polynomials ; Marichal, Jean-Luc in Probability in the Engineering and Informational Sciences (2008), 22(3), 373-388 The lifetime of a system of connected units under some natural assumptions can be represented as a random variable Y defined as a weighted lattice polynomial of random lifetimes of its components. As such ... [more ▼] The lifetime of a system of connected units under some natural assumptions can be represented as a random variable Y defined as a weighted lattice polynomial of random lifetimes of its components. As such, the concept of a random variable Y defined by a weighted lattice polynomial of (lattice-valued) random variables is considered in general and in some special cases. The central object of interest is the cumulative distribution function of Y. In particular, numerous results are obtained for lattice polynomials and weighted lattice polynomials in case of independent arguments and in general. For the general case, the technique consists in considering the joint probability generating function of "indicator" variables. A connection is studied between Y and order statistics of the set of arguments. [less ▲] Detailed reference viewed: 113 (6 UL) |
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