{"title":"The step-stress tampered failure rate model under interval monitoring","authors":"Panayiotis Bobotas, Maria Kateri","doi":"10.1016/j.stamet.2015.06.002","DOIUrl":null,"url":null,"abstract":"<div><p>A step-stress accelerated life testing model is constructed that deals with type-I censored experiments for which a continuous monitoring of the tested items is infeasible and only their inspection at particular time points<span><span> is possible, producing thus grouped data. A general scale family of distributions is considered for the underlying lifetimes, which allows for flexible modeling by permitting different lifetime distributions for different stress levels. The maximum likelihood estimators of its parameters and their density functions are derived explicitly only when the inspection points coincide with the points of stress-level change. In case of additional inspection points, the estimates are obtained numerically. Asymptotic, exact (whenever possible) and </span>bootstrap confidence intervals (CIs) are considered. For the bootstrap CIs a smoothing-modification is introduced, accounting for the categorical nature of the data.</span></p></div>","PeriodicalId":48877,"journal":{"name":"Statistical Methodology","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2015-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.stamet.2015.06.002","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistical Methodology","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1572312715000490","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 6
Abstract
A step-stress accelerated life testing model is constructed that deals with type-I censored experiments for which a continuous monitoring of the tested items is infeasible and only their inspection at particular time points is possible, producing thus grouped data. A general scale family of distributions is considered for the underlying lifetimes, which allows for flexible modeling by permitting different lifetime distributions for different stress levels. The maximum likelihood estimators of its parameters and their density functions are derived explicitly only when the inspection points coincide with the points of stress-level change. In case of additional inspection points, the estimates are obtained numerically. Asymptotic, exact (whenever possible) and bootstrap confidence intervals (CIs) are considered. For the bootstrap CIs a smoothing-modification is introduced, accounting for the categorical nature of the data.
期刊介绍：
Statistical Methodology aims to publish articles of high quality reflecting the varied facets of contemporary statistical theory as well as of significant applications. In addition to helping to stimulate research, the journal intends to bring about interactions among statisticians and scientists in other disciplines broadly interested in statistical methodology. The journal focuses on traditional areas such as statistical inference, multivariate analysis, design of experiments, sampling theory, regression analysis, re-sampling methods, time series, nonparametric statistics, etc., and also gives special emphasis to established as well as emerging applied areas.
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