A bathtub pattern for repairable systems: from better-than-minimal to minimal and worse-than-minimal repairs

Amy Langston; Maxim Finkelstein; Ji Hwan Cha

doi:10.1177/1748006X241306853

A bathtub pattern for repairable systems: from better-than-minimal to minimal and worse-than-minimal repairs

Amy Langston, Maxim Finkelstein, Ji Hwan Cha^*

^*Corresponding author for this work

Management Science

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

2 Citations (Scopus)

13 Downloads (Pure)

Abstract

We introduce a new combined repair process to describe repairs that are initially better-than-minimal, then become minimal, before finally becoming worse-than-minimal. The extended generalized Polya process (EGPP), non-homogeneous Poisson process (NHPP), and generalized Polya process (GPP) are used to describe this repair pattern, respectively. Several useful properties are derived for the combined process under two settings: change in repair type after a specified time and change in repair type after a specified number of failures/repairs. As an application, the optimal age replacement problem is defined and its optimal solution is analyzed. Detailed numerical examples support our findings.

Original language	English
Pages (from-to)	1000-1015
Number of pages	16
Journal	Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability
Volume	239
Issue number	5
Early online date	16 Jan 2025
DOIs	https://doi.org/10.1177/1748006X241306853
Publication status	Published - 1 Oct 2025

Funding

The work of the third author was supported by the 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
minimal repair
worse-than-minimal repair
optimal age replacement

Access to Document

10.1177/1748006X241306853

Langston-etal-A-bathtub-pattern-for-repairable-systems-from-better-than-minimal-to-minimal-and-worse-than-minimal-repairs
For the purposes of open access, a CC BY 4.0 licence has been applied to the accepted manuscript
Accepted author manuscript, 508 KBLicence: CC BY 4.0

Cite this

@article{31297253dae040fe9f85847053161ba4,

title = "A bathtub pattern for repairable systems: from better-than-minimal to minimal and worse-than-minimal repairs",

abstract = "We introduce a new combined repair process to describe repairs that are initially better-than-minimal, then become minimal, before finally becoming worse-than-minimal. The extended generalized Polya process (EGPP), non-homogeneous Poisson process (NHPP), and generalized Polya process (GPP) are used to describe this repair pattern, respectively. Several useful properties are derived for the combined process under two settings: change in repair type after a specified time and change in repair type after a specified number of failures/repairs. As an application, the optimal age replacement problem is defined and its optimal solution is analyzed. Detailed numerical examples support our findings.",

keywords = "better-than-minimal repair, minimal repair, worse-than-minimal repair, optimal age replacement",

author = "Amy Langston and Maxim Finkelstein and Cha, \{Ji Hwan\}",

year = "2025",

month = oct,

day = "1",

doi = "10.1177/1748006X241306853",

language = "English",

volume = "239",

pages = "1000--1015",

journal = "Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability ",

issn = "1748-006X",

publisher = "SAGE Publications Ltd",

number = "5",

}

A bathtub pattern for repairable systems: from better-than-minimal to minimal and worse-than-minimal repairs. / Langston, Amy; Finkelstein, Maxim; Cha, Ji Hwan.
In: Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability , Vol. 239, No. 5, 01.10.2025, p. 1000-1015.

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

TY - JOUR

T1 - A bathtub pattern for repairable systems

T2 - from better-than-minimal to minimal and worse-than-minimal repairs

AU - Langston, Amy

AU - Finkelstein, Maxim

AU - Cha, Ji Hwan

PY - 2025/10/1

Y1 - 2025/10/1

N2 - We introduce a new combined repair process to describe repairs that are initially better-than-minimal, then become minimal, before finally becoming worse-than-minimal. The extended generalized Polya process (EGPP), non-homogeneous Poisson process (NHPP), and generalized Polya process (GPP) are used to describe this repair pattern, respectively. Several useful properties are derived for the combined process under two settings: change in repair type after a specified time and change in repair type after a specified number of failures/repairs. As an application, the optimal age replacement problem is defined and its optimal solution is analyzed. Detailed numerical examples support our findings.

AB - We introduce a new combined repair process to describe repairs that are initially better-than-minimal, then become minimal, before finally becoming worse-than-minimal. The extended generalized Polya process (EGPP), non-homogeneous Poisson process (NHPP), and generalized Polya process (GPP) are used to describe this repair pattern, respectively. Several useful properties are derived for the combined process under two settings: change in repair type after a specified time and change in repair type after a specified number of failures/repairs. As an application, the optimal age replacement problem is defined and its optimal solution is analyzed. Detailed numerical examples support our findings.

KW - better-than-minimal repair

KW - minimal repair

KW - worse-than-minimal repair

KW - optimal age replacement

UR - https://www.scopus.com/pages/publications/85215078573

U2 - 10.1177/1748006X241306853

DO - 10.1177/1748006X241306853

M3 - Article

SN - 1748-006X

VL - 239

SP - 1000

EP - 1015

JO - Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability

JF - Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability

IS - 5

ER -

A bathtub pattern for repairable systems: from better-than-minimal to minimal and worse-than-minimal repairs

Abstract

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this