  Accelerated life-tests (ALTs) are used for inferring lifetime characteristics
of highly reliable products. In particular, step-stress ALTs increase the
stress level at which units under test are subject at certain pre-fixed times,
thus accelerating the product's wear and inducing its failure. In some cases,
due to cost or product nature constraints, continuous monitoring of devices is
infeasible, and so the units are inspected for failures at particular
inspection time points. In a such setup, the ALT response is interval-censored.
Furthermore, when a test unit fails, there are often more than one fatal cause
for the failure, known as competing risks. In this paper, we assume that all
competing risks are independent and follow exponential distributions with scale
parameters depending on the stress level. Under this setup, we present a family
of robust estimators based on density power divergence, including the classical
maximum likelihood estimator (MLE) as a particular case. We derive asymptotic
and robustness properties of the Minimum Density Power Divergence Estimator
(MDPDE), showing its consistency for large samples. Based on these MDPDEs,
estimates of the lifetime characteristics of the product as well as estimates
of cause-specific lifetime characteristics are then developed. Direct
asymptotic, transformed and, bootstrap confidence intervals for the mean
lifetime to failure, reliability at a mission time and, distribution quantiles
are proposed, and their performance is then compared through Monte Carlo
simulations. Moreover, the performance of the MDPDE family has been examined
through an extensive numerical study and the methods of inference discussed
here are finally illustrated with a real-data example concerning electronic
devices.
