Accelerated Failure Time Models For Load Sharing Systems

We model the load sharing phenomenon in a k-out-of- m system through the accelerated failure time model. This model leads to multivariate families of distributions for ordered random variables, which are particular cases of the sequential order statistics. For illustrative purpose, we discuss the model, and the estimation problem for a two component parallel system under the setting of a linear failure rate distribution. In this set up, we discuss a test for the hypothesis that the failure times of components are statistically independent against the alternative that they show the load sharing phenomenon. We report simulation studies showing the performance of the estimators, and the test procedure. The test is also applied to two data sets for illustrative purpose.