Almazah Mohammed M A, Alshahrani Mohammed A, Ramzan Qasim, Raza Irfan Ali, Tahir Muhammad, Ahmad Zahoor
Department of Mathematics, College of Sciences and Arts (Muhyil), King Khalid University, 61421, Muhyil, Saudi Arabia.
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, 11942, Al-Kharj, Saudi Arabia.
Sci Rep. 2025 Jul 11;15(1):25137. doi: 10.1038/s41598-025-95469-x.
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.
在工程领域，精确估计和可靠性分析对于确保系统的安全性和性能至关重要。本研究采用了几种先进的统计技术来实现这些目标。修正威布尔分布（MWD）是Lai等人（《IEEE可靠性快报》52(1):33 - 37，2003年）引入的II型威布尔模型的一个变体，因其在对浴盆形失效率数据建模方面的通用性而在工程和技术领域受到了广泛关注。其简单灵活的失效率函数（FRF）便于使用各种方法进行直接的参数估计。本文介绍了用于修正威布尔分布在步进应力部分加速寿命试验（SSPALT）中参数估计的新技术，这是预测部件在不同应力条件下寿命的一个关键方面。我们比较了最大似然估计器（MLE）和贝叶斯估计器，由于伽马先验适合捕捉失效率参数的正偏态性质，因此使用伽马先验，并在平方误差、广义熵和线性指数等平衡和非平衡损失函数下对这些估计器进行评估。通过仿真研究，我们评估了这些估计器的性能，并使用飞机挡风玻璃数据的失效时间验证了我们的方法。这项工作为可靠性工程师提供了实用工具，以改进维护计划、风险评估和工程系统的整体可靠性。
