System reliability estimation via shrinkage

Beidi Qiang; Edsel A Peña

doi:10.1088/3050-2454/ae123a

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System reliability estimation via shrinkage

Papers | 更新时间：2026-02-13

- System reliability estimation via shrinkage
- 基于收缩估计的系统可靠性评估
- Journal of Reliability Science and Engineering Issue 4, Pages: 1-13(2025)
- 作者机构：
  
  Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL 62026United States of America
  Department of Statistics, University of South Carolina, Columbia, SC 29208United States of America
- 作者简介：
  
  [ "ProfessorBeid Qiang is an Associate Professor in the Department of Mathematics and Statistics at the University of Southern Illinois Edwardsville. She had her PhD degree in Statistics in 2017 from the University of South Carolina (USC), with research areas in survival analysis, reliability, and simultaneous estimation." ]
  [ "ProfessorEdsel A Pena is Professor and Chair of the Department of Statistics at the University of South Carolina (USC). Prior to joining USC in 2000, he was a faculty member from 1986-2000 at the Department of Mathematics and Statistics at Bowling Green State University in Ohio. He was visiting professor at the University of Michigan at Ann Arbor (1995-1996, 1999-2000). He obtained his PhD degree in Statistics in 1986 from Florida State University. He is an Elected Fellow of the American Statistical Association (ASA), Elected Member of the International Statistical Institute (ISI), and Elected Fellow of the Institute of Mathematical Statistics (IMS). From 2017 to 2023 he served as Executive Secretary of the IMS. From 2020 to 2023, he served as Program Director of the Statistics Program in the Division of Mathematical Sciences of the US National Science Foundation. His main research areas are in survival and event-time analysis, reliability, mathematical statistics, goodness-of-fit testing, and multiple testing and decision-making." ]
- 基金信息：
- DOI：10.1088/3050-2454/ae123a
  CLC：
- Received：29 August 2025，
  
  Revised：2025-10-03，
  
  Accepted：10 October 2025，
  
  Online First：29 October 2025，
  
  Published：2025
- 稿件说明：
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Beidi Qiang, Edsel A Peña. System reliability estimation via shrinkage[J]. Journal of Reliability Science and Engineering, 2025, (4): 1-13.
DOI：

Beidi Qiang, Edsel A Peña. System reliability estimation via shrinkage[J]. Journal of Reliability Science and Engineering, 2025, (4): 1-13. DOI： 10.1088/3050-2454/ae123a.

摘要

在由多个部件按照特定结构函数构成的一致性可靠性系统中，系统失效时间分布（即系统寿命）通常是最为关注的研究对象。系统可靠性的准确估计在工程与工业应用中具有至关重要的意义，直接影响系统设计、维护策略制定及风险评估等关键决策。系统寿命分布可通过观测到的系统失效时间直接进行估计；然而，当部件层面的寿命数据可获得时，可进一步提升系统可靠性估计的精度。本文表明，在对部件失效时间分布作非参数假设的条件下，传统估计方法（如乘积极限估计）在特定损失函数下仍具有进一步改进的空间。为此，本文提出一种新的方法，通过对部件层面估计量施加收缩变换，实现对系统可靠性的非参数估计改进。结果表明，该收缩策略能够在系统可靠性估计中获得更优的风险效率。

Abstract

In a coherent reliability system composed of multiple components configured according to a specific structure function

the distribution of system time to failure

or system lifetime

is often of primary interest. Accurate estimation of system reliability is critical in a wide range of engineering and industrial applications

forming decisions in system design

maintenance planning

and risk assessment. The system lifetime distribution can be estimated directly using the observed system failure times. However

when component-level lifetime data is available

it can yield improved estimates of system reliability. In this work

we demonstrate that under nonparametric assumptions about the component time-to-failure distributions

traditional estimators such as the product-limit estimator can be further improved under specific loss functions. We propose a novel methodology that enhances the nonparametric system reliability estimation through a shrinkage transformation applied to component-level estimators. This shrinkage approach leads to improved risk-efficiency in estimating system reliability.

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references

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