Robust Rao-type tests for step-stress accelerated lifetests with interval-censored data and Weibull lifetime distributions

Many engineering products are highly reliable in the present highly competitive market, often exhibiting long mean lifetimes to failure. This makes experimental testing both time-intensive and challenging. Accelerated life-tests are commonly used to induce early failures by subjecting products to higher-than-normal stress conditions, enabling enough failures to be observed for accurate statistical analysis. Additionally, censored data is a common challenge in reliability studies. Specifically, interval-censored data arises when continuous monitoring of devices is impractical or infeasible due to technical constraints or budget limitations. Statistical inference in such situations is often based on the likelihood function of the model. However, likelihood-based methods can be highly sensitive to outliers, which may result in biased or unreliable estimates. To address this issue, minimum density power divergence techniques can be used as a robust alternative. These methods extend traditional likelihood-based approach and have demonstrated appealing performance in reliability inference. 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 and use these restricted estimators to generalize the Rao Score test for testing composite null hypotheses, including testing the significance of stress factors contributing degradation of the devices. We present the theoretical asymptotic properties of the estimators and also associated test statistics, along with numerical analyses that support the robustness of the proposed estimators and tests of hypotheses.