Estimation in step-stress life tests with complementary risks from the exponentiated exponential distribution under time constraint and its applications to UAV data

In accelerated step-stress life tests, the stress levels are allowed to increase at some pre-determined time points such that information on the lifetime parameters can be obtained more quickly than under normal operating conditions. Because there are often multiple causes for the failure of a test unit, such as mechanical or electrical failures, in this article, a step-stress model under time constraint is studied when the lifetimes of different complementary risk factors are independent from exponentiated distributions. Although the baseline distributions can belong to a general class of distributions, including Weibull, Pareto, and Gompertz distributions, particular attention is paid to the case of an exponentiated exponential distribution. Under this setup, the maximum likelihood estimators of the unknown scale and shape parameters of the different causes are derived with the assumption of cumulative damage. Using the asymptotic distributions and the parametric bootstrap method, the confidence intervals for the parameters are then constructed. The precision of the estimates and the performance of the confidence intervals are also assessed through extensive Monte Carlo simulations, and finally, the inference methods discussed here are illustrated with motivating examples.