Estimation of parameters for the modified Weibull distribution under step-stress accelerated life testing with application to aircraft windshields data

In the field of engineering, precise estimation and reliability analysis are vital for ensuring the safety and performance of systems. This research employs several advanced statistical techniques to achieve these objectives. The Modified Weibull Distribution (MWD), a variant of the type-II Weibull model introduced by Lai et al. (IEEE Trans Reliab 52 (1):33–37, 2003), has gained significant attention in engineering and technology for its versatility in modeling bathtub-shaped failure rate data. Its simple and flexible failure rate function (FRF) facilitates straightforward parameter estimation using various methods. This paper introduces novel techniques for parameter estimation in step-stress partially accelerated life testing (SSPALT) for the MWD, a key aspect for predicting component lifespan under varying stress conditions. We compare Maximum Likelihood Estimators (MLE) and Bayesian estimators, utilizing gamma priors due to their suitability for capturing the positive, skewed nature of failure rate parameters, and evaluate these across balanced and unbalanced loss functions, such as Square Error, General Entropy, and Linear Exponential. Through simulation studies, we assess the performance of these estimators and validate our approach using failure times of aircraft windshield data. This work offers practical tools for reliability engineers to improve maintenance scheduling, risk assessment, and the overall reliability of engineering systems.