Robust inference for an interval-monitored step-stress experiment with competing risks for failure with an application to capacitor data

Accelerated life-tests (ALTs) are applied for inferring lifetime characteristics of highly reliable products. In some cases, due to cost or product nature constraints, continuous monitoring of devices is infeasible and so the units are inspected at particular inspection time points, resulting in interval-censored responses. Furthermore, when a test unit fails, there is often more than one competing risk. In this paper, we assume that all competing risks are independent and follow an exponential distribution depending on the stress level. Under this setup, we present a family of robust estimators based on the density power divergence (DPD), including the classical maximum likelihood estimator as a particular case. We then derive asymptotic and robustness properties of the minimum DPD estimators (MDPDEs). Based on these MDPDEs, estimates of some lifetime characteristics of the product as well as estimates of some cause-specific lifetime characteristics are developed. Direct, transformed and bootstrap confidence intervals are proposed, and their performance is empirically compared through Monte Carlo simulations. The methods of inference discussed in this work are finally illustrated with a real-data example regarding electronic devices.