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Optimal replacement and allocation of multi‐state elements in k ‐within‐ m ‐from‐ r / n sliding window systems
Author(s) -
Xiao Hui,
Peng Rui,
Levitin Gregory
Publication year - 2015
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2143
Subject(s) - sliding window protocol , reliability (semiconductor) , mathematical optimization , state (computer science) , element (criminal law) , genetic algorithm , computer science , joint (building) , order (exchange) , window (computing) , mathematics , algorithm , engineering , structural engineering , physics , power (physics) , quantum mechanics , political science , law , operating system , finance , economics
This paper proposes a new model that generalizes the linear sliding window system to the case of multiple failures. The considered k ‐within‐ m ‐from‐ r / n sliding window system consists of n linearly ordered multi‐state elements and fails if at least k groups out of m consecutive groups of r consecutive multi‐state elements have cumulative performance lower than the demand W . A reliability evaluation algorithm is suggested for the proposed system. In order to increase the system availability, maintenance actions can be performed, and the elements can be optimally allocated. A joint element allocation and maintenance optimization model is formulated with the objective of minimizing the total maintenance cost subjected to the pre‐specified system availability requirement. Basic procedures of genetic algorithms are adapted to solve the optimization problem. Numerical experiments are presented to illustrate the applications. Copyright © 2015 John Wiley & Sons, Ltd.