Reliability analysis of k-out-of-n load-sharing systems

Load-sharing systems have several practical applications. In load-sharing systems, the failure of a component will result in a higher load on each of the surviving components, thereby inducing a higher failure rate for them. This introduces failure dependency among the load-sharing components, which in turn increases the complexity in analyzing these systems. Therefore, in spite of a wide range of applications for load-sharing systems, the methods for computing the reliability of load-sharing systems are limited. In this paper, we first discuss the modeling concepts of load-sharing systems and explain the role of accelerated life testing models in analyzing these systems. We also describe existing analysis methods and their limitations in analyzing load-sharing systems. In modeling load-sharing systems with general failure distributions, it is important to consider an appropriate model to incorporate the effects of loading history. In this paper, we explore using the cumulative exposure model to account for the effects of loading history. We present an efficient method to compute the reliability and mean life of k-out-of-n load-sharing systems with identical or non-identical components following general failure distributions. The method can solve large k-out-of-n systems in a short time. Further, we show how to use the existing computational procedures for solving stochastic reward models for solving load-sharing models. In addition to the exact solutions, we also propose efficient approximations and bounds that can be computed easily. The computational procedure and the bounds proposed in this paper help reliability engineers to accurately model the load-sharing systems that arise in many practical situations.