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Accelerated life-tests (ALTs) are applied for inferring lifetimecharacteristics of highly reliable products. In particular, step-stress ALTsincrease the stress level at which units under test are subject at certainpre-fixed times, thus accelerating product wear and inducing its failure. Insome cases, due to cost or product nature constraints, continuous monitoring ofdevices is infeasible but the units are inspected for failures at particularinspection time points. In such setups, the ALT response is interval-censored.Furthermore, when a test unit fails, there are often more than one fatal causefor the failure, known as competing risks. In this paper, we assume that allcompeting risks are independent and follow an exponential distribution withscale parameter depending on the stress level. Under this setup, we present afamily of robust estimators based on the density power divergence, includingthe classical maximum likelihood estimator as a particular case. We deriveasymptotic and robustness properties of the MDPDE, showing its consistency forlarge samples. Based on these MDPDEs, estimates of the lifetime characteristicsof the product as well as estimates of cause-specific lifetime characteristicshave been developed. Direct, transformed and bootstrap confidence intervals forthe mean lifetime to failure, reliability at a mission time, and distributionquantiles are proposed, and their performance is empirically compared throughsimulations. Besides, the performance of the MDPDE family has been examinedthrough an extensive numerical study and the methods of inference discussedhere are illustrated with a real-data example regarding electronic devices.

Robust inference for an interval-monitored step-stress model with competing risks