Chanseok Park

In this talk, we will consider parametric reliability estimation for load-sharing systems under a load-sharing rule. Consider a system of multiple components connected in parallel.  In this system, as components fail one by one, the total load or traffic applied to the system is re-distributed among the remaining working components. This is commonly referred to as load-sharing.  We will review the earlier work on load-sharing models and then discuss the problem of estimating load-sharing parameters. The earliest work on the load-sharing model can be traced back to the model by Daniels (1945). Since then, most statistical reliability research has focused on the characterization of system reliability under a known load-sharing rule. Yet, parametric inference under a known load-sharing rule has not yet been fully developed. Recently, Kim and Kvam (2004) provided an important first step in drawing parametric inference on load-sharing properties under the exponential lifetime distribution assumption by numerically solving the estimating equations associated with the system. In this talk, we introduce the closed-form MLE for the parametric model suggested by Kim and Kvam.  In addition, we also provide other closed-form MLEs under the Weibull distribution assumption. For log-normally distributed lifetimes, it seems to be impossible to obtain closed-form MLEs. Instead, we provide a methodology for the MLE using the EM algorithm. As far as future research work is concerned, we also discuss the proposed semi-parametric models and more complex load-sharing systems such as the k-out-of-n system.