Robust Rao-Type Tests for Non-destructive One-Shot Device Testing Under Step-Stress Model with Exponential Lifetimes

Abstract

One-shot devices analysis involves an extreme case of interval censoring, wherein one can only know whether the failure time is before the test time. Some kind of one-shot units do not get destroyed when tested, and then survival units can continue within the test providing extra information for inference. This not-destructiveness is a great advantage when the number of units under test are few. On the other hand, one-shot devices may last for long times under normal operating conditions and so accelerated life tests (ALTs), which increases the stress levels at which units are tested, may be needed. ALTs relate the lifetime distribution of an unit with the stress level at which it is tested via log-linear relationship, so inference results can be easily extrapolated to normal operating conditions. In particular, the step-stress model, which allows the experimenter to increase the stress level at pre-fixed times gradually during the life-testing experiment is specially advantageous for non-destructive one-shot devices. In this paper, we develop robust Rao-type test statistics based on the density power divergence (DPD) for testing linear null hypothesis for non-destructive one-shot devices under the step-stress ALTs with exponential lifetime distributions. We theoretically study their asymptotic and robustness properties, and empirically illustrates such properties through a simulation study.