k-out-of-n systems: An exact formula for the stationary availability and multi-objective configuration design based on mathematical programming and TOPSIS

Abstract

Reliability and availability analyses are recognized as essential for guiding decision makers in the implementation of actions addressed to improve the technical and economical performance of complex systems. For industrial systems with reparable components, the most interesting parameter used to drive maintenance is the stationary availability. In this regard, the present paper proposes an exact formula for computing the system stationary availability of a k-out-of-n system. Such a formula is proved to be in agreement with the fundamental theorem of Markov chains. Then, a multiobjective mathematical model is formulated for choosing the optimal system configuration design. The Pareto front is developed using the Lexicographic Goal Programming (LGP) method, and the TOPSIS method is successively implemented to choose the k-out-of-n configuration that represents the best compromise between the considered objective functions. A numerical example is provided.

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“…As previously underlined, for industrial systems with reparable components, such as production systems, the most interesting parameter (Ahmed et al, 2014) used to drive the maintenance management is the stationary availability , whose maximisation is considered a strategic objective to be pursued. A closed formula has been proposed and validated (Carpitella et al, 2018d) to easily calculate the exact stationary availability for a -out- Being the latter mutually exclusive, the probability of the union is precisely the sum of the probabilities of each functioning state. In the denominator of the proposed formula, all the possible states are considered.…”

“…proposed to obtain the Pareto front (Deb, 2001;Hwang et al, 1993) and to lead the optimal design of a -out-of-system through a MCDM-based approach (Carpitella et al, 2018d).…”