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

Department of Statistics

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

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
DOIs	https://doi.org/10.1177/1748006X241306853
State	Published - Oct 2025

Bibliographical note

Publisher Copyright:
© IMechE 2025

Keywords

Better-than-minimal repair
minimal repair
minimal repair
optimal age replacement
worse-than-minimal repair

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10.1177/1748006X241306853

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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.",

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

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AU - Langston, Amy

AU - Finkelstein, Maxim

AU - Cha, Ji Hwan

N1 - Publisher Copyright: © IMechE 2025

PY - 2025/10

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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.

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

Abstract

Bibliographical note

Keywords

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