A Cumulative-Exposure-Based Algorithm for Failure Data From a Load-Sharing System

In a load-sharing system, total workloads are shared by all components and failure of one component increases stress of the surviving ones. The time interval between two consecutive component failures reflects component reliability under different stress and is of interest to us. This study develops an iterative algorithm for analysis of such data from load-sharing systems. In each iteration, we first obtain the equivalent operating time of each component under a given stress by capitalizing on the cumulative exposure principle. Then the equivalent operating times, which are simply right-censored, are fitted to update the parameter estimates. The conversion has closed forms for most common distributions such as the log-location-scale family and the gamma distribution, and the subsequent fitting of right-censored data is straightforward. Therefore, the algorithm is easy to implement compared with existing methods such as the maximum likelihood estimation. Convergence properties of the algorithm are investigated theoretically and through extensive simulations. Three examples representing different types of real problems are used to demonstrate the proposed algorithm.