Exact inference for two exponential populations with competing risks data

In a reliability comparative test, the joint censoring model is usually adopted to evaluate the performances of units with the same facility. However, most researchers ignore the possibility that there is more than one factor for the failure when a test unit fails. To solve this problem, we consider a joint Type-II hybrid censoring model for the analysis of exponential competing failure data. Based on the maximum likelihood theory, we compute the maximum likelihood estimators (MLEs) of parameters and then obtain the condition ensuring MLEs existence for every unknown parameter. Then we derive the conditional exact distributions and corresponding moment properties for parameters by the moment generating function (MGF). A Monte-Carlo simulation is conducted to compare the performances of different ways. And finally, we conduct a numerical example to illustrate the proposed method.