Reliability analysis of load sharing systems under unequal load-sharing rule with applications

We are examining a setup consisting of several parallel-connected k-out-of-m load sharing systems. The load sharing is modeled using proportional conditional failure rates for component failures and load sharing under the unequal load-sharing rule. We have derived the system reliability for the entire setup. To illustrate this, we examine two cases: one with n systems connected in parallel, each following a 1-out-of-2 configuration, and the other with n systems connected in parallel, each following a 2-out-of-4 configuration. The system components are assumed to be identical with an exponential as well as Weibull baseline distributions. We propose two methods to estimate the baseline parameter and load-sharing parameters. Additionally, we present a confidence interval using bootstrapping techniques, specifically the percentile bootstrap (boot-p). We assess the performance of these parameter estimation and interval estimation methods through simulation studies. Furthermore, we evaluate the practical applicability of the proposed techniques by analyzing two real datasets. The same approach can be applied to a system that includes multiple k-out-of-m load sharing systems, where these systems are connected in either a series or a p-out-of-q configuration.