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

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 multi-objective 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.