Statistical inference for masked interval data with Weibull distribution under simple step-stress test and tampered failure rate model

Abstract

In this article, we consider the planning of simple step-stress life test in the presence of competing risks with the possibility of masked causes of failure and interval censoring. It is assumed that the competing risks have independent Weibull distribution with the common shape parameter, but different scale parameters and a tampered failure rate model is hold. Maximum likelihood estimates of the model parameters are obtained for both cases, with and without masking. An expectation–maximization algorithm is used to estimate maximum likelihood estimates based on the masked data. For the case without masking, the Fisher information matrix is derived, and the problem of choosing the optimal test plan is considered using variance-optimality as well as determinant-optimality criteria. Through Monte Carlo simulations, the precision of the estimates is assessed and the optimal test plans are compared. Finally, the results are illustrated with an example.