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. 

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

Many real-world systems are heterogeneous k-out-of-n cold standby systems, like unmanned aerial vehicles performing a reconnaissance mission along multiple routes exposed to different environmental conditions. Reliability analysis of such systems is difficult and complicated. In this paper, efficient complete and partial approximation methods based on the central limit theorem are proposed for reliability analysis of k-out-of-n cold standby systems with position-dependent component lifetime distributions. Particularly, there are k online positions in the considered system with varying operating conditions and stress levels. The time-to-failure distribution of a component depends on the online position at which the component is working. The system fails when more than (n − k) components have failed. Case studies are performed to demonstrate the efficiency and accuracy of the proposed complete and partial approximation methods as compared to the existing convolution method. Influences of system parameters k and n and the component time-to-failure distribution parameter on the accuracy of the proposed complete approximation method are also demonstrated through empirical studies. Practice guidelines are provided based on performance studies of the proposed methods. The proposed approximation methods are also generalized by considering imperfect switchover. 

Efficient reliability approximation for large k-out-of-n cold standby systems with position-dependent component lifetime distributions

Standby mode transfer schedule minimizing downtime of 1-out-of-N system with storage

A lifetime estimation method for multi-component degrading systems with deteriorating spare parts

Optimising resource-constrained fleet selective maintenance with asynchronous maintenance breaks

Availability for multi-component k-out-of-n: G warm-standby system in series with shut-off rule of suspended animation

The train braking system with redundant components has an essential effect on driver safety. In this paper, we consider the failure of K-out-of-N brake motors during operation and the redundant recovery by preventive maintenance. Two Continuous Time Markov Chains (CTMC) are used to model the working process and the preventive maintenance process of the braking system corresponding to the real situation of the train. Considering the maintenance effect of intermittent daily and cyclical overhaul with nested relationships, a new operation risk assessment model of the K-out-of-N system is developed to evaluate the effectiveness of the preventive maintenance of the train. Some safety parameters are solved based on the two coupled preventive maintenance periods, which conveniently design the safety of the train braking system. Finally, a case study illustrates the effectiveness of the safety evaluation method. The results show that we can trade off the effects of the multiple PM intervals on train safety considering the redundancy structure of the braking system by the proposed model.

/pdf/a-method-for-safety-evaluation-of-train-braking-system-2ykoxx32.pdf

A Method for Safety Evaluation of Train Braking System Considering Multiple Types of Preventive Maintenance Cycles

Uncertain process-based integration of ADT and field data of PCB in airborne equipment and PCB residual lifetime evaluation

Deadline-constrained multi-commodity flow routing and scheduling optimization with consideration of edge lengths and capacities

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Papers

Availability for multi-component k-out-of-n: G warm-standby system in series with shut-off rule of suspended animation

A Method for Safety Evaluation of Train Braking System Considering Multiple Types of Preventive Maintenance Cycles

Uncertain process-based integration of ADT and field data of PCB in airborne equipment and PCB residual lifetime evaluation

Deadline-constrained multi-commodity flow routing and scheduling optimization with consideration of edge lengths and capacities