A stochastic expectation-maximization algorithm for the analysis of system lifetime data with known signature

Statistical estimation of the model parameters of component lifetime distribution based on system lifetime data with known system structure is discussed here. We propose the use of stochastic expectation-maximization (SEM) algorithm for obtaining the maximum likelihood estimates of model parameters based on complete and censored system lifetimes. Different ways of implementing the SEM algorithm are also studied. We have shown that the proposed methods are feasible and are easy to implement for various families of component lifetime distributions. The proposed methodologies are then illustrated with two popular lifetime models—the Weibull and Birnbaum-Saunders distributions. Monte Carlo simulation is then used to compare the performance of the proposed methods with the corresponding estimation by direct maximization. Finally, two illustrative examples are presented along with some concluding remarks.