Optimal designs of accelerated degradation tests with random shock failures and measurement errors

IF 1.3 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Applied Stochastic Models in Business and Industry Pub Date : 2024-06-18 DOI:10.1002/asmb.2878
Lin Wu, Xiao-Dong Zhou, Rong-Xian Yue
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Abstract

Accelerated degradation tests (ADTs) are widely used for assessing the reliability of long-life products. During an ADT, accelerated stresses not only expedite the degradation of test products but also increase the likelihood of encountering traumatic shocks. Moreover, it is important to acknowledge that measurement errors can be inevitable during the observation process of an ADT. Unfortunately, these errors are often overlooked in the optimal design of the ADT, especially when multiple competing failure modes are present. In this article, we propose a new approach to design ADTs when measurement errors exist and test products suffer from degradation failures and random shock failures. We utilize the Wiener process to model the degradation path, incorporating normally distributed measurement errors, and an exponential distribution to fit the time between random shock failures. Given the number of test products and the termination time, we optimize the ADT plans under three common design criteria. The equivalence theorem is used to verify the optimality of the optimal ADT plans. A real-life example and sensitivity analysis are provided to illustrate our proposed method. The results demonstrate that when competing failure modes are present, the optimal ADT plans, which account for measurement errors, differ significantly from those that do not consider such errors.

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具有随机冲击故障和测量误差的加速降解试验的优化设计
加速降解试验(ADT)被广泛用于评估长寿命产品的可靠性。在 ADT 过程中,加速应力不仅会加速测试产品的降解,还会增加遭遇创伤性冲击的可能性。此外,必须承认的是,在 ADT 观察过程中,测量误差是不可避免的。遗憾的是,这些误差往往在 ADT 的优化设计中被忽视,尤其是在存在多种竞争失效模式的情况下。在本文中,我们提出了一种新方法,用于在存在测量误差、测试产品遭受降级故障和随机冲击故障时设计 ADT。我们利用维纳过程对降解路径进行建模,其中包含正态分布的测量误差,并利用指数分布来拟合随机冲击故障之间的时间间隔。考虑到测试产品的数量和终止时间,我们根据三种常见的设计标准优化 ADT 计划。等价定理被用来验证最佳 ADT 计划的最优性。我们提供了一个实际案例和敏感性分析来说明我们提出的方法。结果表明,当存在相互竞争的故障模式时,考虑测量误差的最佳 ADT 计划与不考虑测量误差的最佳 ADT 计划差别很大。
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来源期刊
CiteScore
2.70
自引率
0.00%
发文量
67
审稿时长
>12 weeks
期刊介绍: ASMBI - Applied Stochastic Models in Business and Industry (formerly Applied Stochastic Models and Data Analysis) was first published in 1985, publishing contributions in the interface between stochastic modelling, data analysis and their applications in business, finance, insurance, management and production. In 2007 ASMBI became the official journal of the International Society for Business and Industrial Statistics (www.isbis.org). The main objective is to publish papers, both technical and practical, presenting new results which solve real-life problems or have great potential in doing so. Mathematical rigour, innovative stochastic modelling and sound applications are the key ingredients of papers to be published, after a very selective review process. The journal is very open to new ideas, like Data Science and Big Data stemming from problems in business and industry or uncertainty quantification in engineering, as well as more traditional ones, like reliability, quality control, design of experiments, managerial processes, supply chains and inventories, insurance, econometrics, financial modelling (provided the papers are related to real problems). The journal is interested also in papers addressing the effects of business and industrial decisions on the environment, healthcare, social life. State-of-the art computational methods are very welcome as well, when combined with sound applications and innovative models.
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