A Proportional Intensity Model with Frailty for Missing Recurrent Failure Data

IF 2.3 3区 工程技术 Q1 STATISTICS & PROBABILITY
Suk Joo Bae, Byeong Min Mun, Xiaoyan Zhu
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引用次数: 0

Abstract

AbstractIn some practical circumstances, data are recorded after the systems have begun operations, and data collection is stopped at a predetermined time or after a predetermined number of failures. In such circumstances, incompleteness of various types exists in the aspect of the missing number of failures and their occurrence times beyond the duration of the pilot study. Additionally, multiple repairable systems may present system-to-system variability caused by differences in the operating environments or working loads of individual systems. With respect to left-truncated and right-censored recurrent failure data from multiple repairable systems, we propose a reliability model based on a proportional intensity model with frailty. The frailty model explicitly models unobserved heterogeneity among systems. Covariates incorporated into the proportional intensity model additionally account for the heterogeneity between different operating conditions. To estimate the model parameters for the left-truncated and right-censored recurrent failure data, a Monte Carlo expectation maximization algorithm is proposed. Details of the estimation of the model parameters and the construction of their confidence intervals are examined. A real-world example and simulation studies under various scenarios show prominent applications of the proportional intensity model with frailty to left-truncated and right-censored multiple repairable systems for reliability prediction.1Index Terms: Monte Carlo expectation maximization (MCEM) algorithmnonhomogeneous Poisson processrecurrent failure dataproportional intensity modelrepairable systemDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also.
缺失经常性故障数据的具有脆弱性的比例强度模型
在某些实际情况下,在系统开始运行后记录数据,在预定的时间或预定的故障次数后停止数据收集。在这种情况下,各种类型的不完整性存在于缺失的故障数量和它们的发生时间超过了试点研究的持续时间。此外,多个可修复的系统可能呈现系统到系统的可变性,这是由单个系统的操作环境或工作负载的差异引起的。针对多可修系统的左截右截反复失效数据,提出了一种基于带脆弱性的比例强度模型的可靠性模型。脆弱性模型明确地模拟了系统间未观察到的异质性。纳入比例强度模型的协变量还考虑了不同操作条件之间的异质性。为了估计左截右截反复失效数据的模型参数,提出了一种蒙特卡罗期望最大化算法。详细介绍了模型参数的估计及其置信区间的构造。一个现实世界的例子和各种场景下的仿真研究表明,具有脆弱性的比例强度模型在左截短和右截短的多可修系统可靠性预测中的突出应用。1索引术语:蒙特卡罗期望最大化(MCEM)算法非齐次泊松过程反复失效数据比例强度模型可修复系统免责声明作为对作者和研究人员的服务,我们提供此版本的已接受手稿(AM)。在最终出版版本记录(VoR)之前,将对该手稿进行编辑、排版和审查。在制作和印前,可能会发现可能影响内容的错误,所有适用于期刊的法律免责声明也与这些版本有关。
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来源期刊
Technometrics
Technometrics 管理科学-统计学与概率论
CiteScore
4.50
自引率
16.00%
发文量
59
审稿时长
>12 weeks
期刊介绍: Technometrics is a Journal of Statistics for the Physical, Chemical, and Engineering Sciences, and is published Quarterly by the  American Society for Quality and the American Statistical Association.Since its inception in 1959, the mission of Technometrics has been to contribute to the development and use of statistical methods in the physical, chemical, and engineering sciences.
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