Reliability analysis and redundancy optimization of k-out-of-n systems with random variable k using continuous time Markov chain and Monte Carlo simulation

This article discusses the problems associated with the redundancy of structures k-out-of-n as a method of increasing system availability. A parallel k-out-of-n system was considered, with k repairable and homogeneous components. The other (n – k) objects are in hot redundancy mode. Failures and repairs are independent processes, and each repaired object is treated as full-fledged in terms of operation. The system operates under dynamically changing conditions, so the minimum number of operable components essential for its proper operation is a random variable with a specific distribution. Component damages and repairs are independent stochastic processes. A probabilistic and simulation approach based on Continuous Time Markov Chain and Monte Carlo simulation is proposed. This study aims to optimize the number of components in the k-out-of-n structure, which will ensure the system operation with a certain availability and performance. The proposed methods were applied to real transport systems, for which models were developed with parameters estimated on the basis of empirical data. The convergence of the results obtained, using two methods, testifies to the correctness of the methodology used and the reliability of the models developed. The risk to system performance associated with changing input parameters was assessed using model sensitivity analysis. As indicated, the model is not susceptible to changes in the damage and repair intensity. It has also been shown that optimization of the k-out-of-n structure brings a significant reduction in the costs incurred for system development and operation.