Robust Rao-type tests for step-stress accelerated life-tests under interval-monitoring and Weibull lifetime distributions

Many products in engineering are highly reliable with large mean lifetimes to failure. Performing lifetests under normal operations conditions would thus require long experimentation times and high experimentation costs. Alternatively, accelerated lifetests shorten the experimentation time by running the tests at higher than normal stress conditions, thus inducing more failures. Additionally, a log-linear regression model can be used to relate the lifetime distribution of the product to the level of stress it experiences. After estimating the parameters of this relationship, results can be extrapolated to normal operating conditions. On the other hand, censored data is common in reliability analysis. Interval-censored data arise when continuous inspection is difficult or infeasible due to technical or budgetary constraints. In this paper, we develop robust restricted estimators based on the density power divergence for step-stress accelerated life-tests under Weibull distributions with interval-censored data. We present theoretical asymptotic properties of the estimators and develop robust Rao-type test statistics based on the proposed robust estimators for testing composite null hypothesis on the model parameters.