Prediction of New Lifetimes of a Step-Stress Test Using Cumulative Exposure Model with Censored Gompertz Data

In this paper, we address the problem of predicting the time until failure for censored units, following a Gompertz distribution. This prediction is carried out within a simple step-stress strategy operating under a cumulative exposure model. We explore various prediction techniques, including the maximum likelihood predictor, conditional median predictor, and best unbiased predictor. Additionally, we delve into the prediction interval estimation for the future lifetimes of these censored units. We discuss methods such as the pivotal quantity, highest conditional density, and shortest-length approaches to achieve this. To assess the performance of the proposed prediction methods, we conduct Monte Carlo simulations. Furthermore, we utilize a real dataset for illustrative purposes and comparative analysis.