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

Amy Langston, Maxim Finkelstein, Ji Hwan Cha

Research output: Contribution to journalArticlepeer-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.

Bibliographical note

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© IMechE 2025.

Keywords

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

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