Statistical inference of a step-stress model with competing risks under time censoring for alpha power exponential distribution

Accelerated life testing in a reliability experiment allows test units to be under more stress than normal (expected). Step-stress tests are a subset of accelerated life tests that raise the stress levels at specific predetermined time periods to gather data on lifetime parameters more quickly than they would under normal operating settings. Additionally, there are frequently a number of risk factors connected to the root cause of a test unit failure (mechanical, electrical, etc.). In this article, we discuss the statistical inference of a step-stress model in the presence of time censoring assuming independent alpha power exponential distribution. The point estimates of the unknown scale and shape parameters of the various causes are determined using the maximum likelihood technique under the assumption of cumulative damage. We also go through creating confidence intervals for the parameters using asymptotic distributions and the parametric bootstrap approach. Extensive Monte Carlo simulations are used to evaluate the accuracy of the estimates and the performance of the confidence intervals, and finally, an example is used to explain the methods of inference presented here.