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

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  • Amy Langston
  • Maxim Finkelstein
  • Ji Hwan Cha

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.

Suggested Citation

  • Amy Langston & Maxim Finkelstein & Ji Hwan Cha, 2025. "A bathtub pattern for repairable systems: From better-than-minimal to minimal and worse-than-minimal repairs," Journal of Risk and Reliability, , vol. 239(5), pages 1000-1015, October.
    • Handle: RePEc:sae:risrel:v:239:y:2025:i:5:p:1000-1015
    DOI: 10.1177/1748006X241306853
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