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

Amy Langston, Maxim Finkelstein and Ji Hwan Cha

Journal of Risk and Reliability, 2025, vol. 239, issue 5, 1000-1015

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; minimal repair; optimal age replacement (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:sae:risrel:v:239:y:2025:i:5:p:1000-1015

DOI: 10.1177/1748006X241306853

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