{"title":"Optimal designs of accelerated degradation tests with random shock failures and measurement errors","authors":"Lin Wu, Xiao-Dong Zhou, Rong-Xian Yue","doi":"10.1002/asmb.2878","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"40 4","pages":"1125-1152"},"PeriodicalIF":1.3000,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Stochastic Models in Business and Industry","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/asmb.2878","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
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.
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.