Abouzar Bazyari

Accelerated lifetime test is a widely used and effective approach in reliability analysis because of its shorter testing duration. In this study, we study the Gompertz distribution under constant stress accelerated lifetime testing and make two assumptions regarding the relationship between the scale parameter and stress levels; one assumption is the Simple Linear Model and the other is Inverse Power-Law Model. The objective functions for the four estimation methods: maximum likelihood estimation (MLE), least squares estimation (LSE), maximum product spacing estimation (MPSE), and Cramervon Mises estimation (CVM) are obtained. We present a Monte Carlo simulation for two models by using four estimation methods under varying sample sizes. Additionally, we evaluate the performance of the scale parameter and reliability function under different scenarios. The comparison of mean squared error serves as a critical indicator for evaluating the performance of different methods and models. Furthermore, the scale parameter and reliability function are obtained based on the estimation results. Finally, a real dataset is analyzed to demonstrate the most suitable accelerated life model and calculate the Kolmogorov-Smirnov (K-S) distance and p-values to judge the model's performance.