On a new point process approach to reliability improvement modeling for repairable systems

Maxim Finkelstein; Ji Hwan Cha

doi:10.1002/asmb.2906

On a new point process approach to reliability improvement modeling for repairable systems

Maxim Finkelstein
, Ji Hwan Cha^*

^*Corresponding author for this work

Management Science

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this paper, we are the first to consider the combination of the minimal repair with the defined better than minimal repair. With a given probability, each failure of a repairable system is minimally repaired and with complementary probability it is better than minimally repaired. The latter can be interpreted in terms of a reliability growth model when a defect of a system is eliminated on each failure. It turns out that the better than minimal repair can be even better than a perfect one if a perfect repair is understood as a replacement of the whole system or stochastically equivalent operation. We provide stochastic description of the failure/repair process by introducing and describing the corresponding bivariate point process via the concept of stochastic intensity. Distributions for the number of failures for the pooled and marginal processes are derived along with their expected values. The latter can describe the process of reliability growth in applications. Some meaningful special cases are discussed.

Original language	English
Article number	e2906
Journal	Applied Stochastic Models in Business and Industry
Volume	41
Issue number	3
Early online date	24 Nov 2024
DOIs	https://doi.org/10.1002/asmb.2906
Publication status	Published - 6 May 2025

Funding

This work was supported by National Research Foundation of Korea, (Grant Number: 2019R1A6A1A11051177). Funding: The authors thank the reviewers for their helpful comments and suggestions. The work of the second author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant Number: 2019R1A6A1A11051177).

Keywords

better than minimal repair
point process minimal repair
reliability
stochastic intensity bivariate

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10.1002/asmb.2906

Finkelstein-and-Cha-On-a-new-point-process-approach-to-reliability-improvement-modeling-for-repairable-systems
Copyright © 2024 John Wiley & Sons Ltd. This is the peer reviewed version of the following article: Finkelstein, M. and Cha, J.H. (2024), On a New Point Process Approach to Reliability Improvement Modeling for Repairable Systems. Appl Stochastic Models Bus Ind. which has been published in final form at https://doi.org/10.1002/asmb.2906. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.
Accepted author manuscript, 356 KB

Cite this

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On a new point process approach to reliability improvement modeling for repairable systems

Abstract

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Keywords

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