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
N1 - Publisher Copyright:
© IMechE 2025.
PY - 2025
Y1 - 2025
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 - minimal repair
KW - optimal age replacement
KW - worse-than-minimal repair
UR - http://www.scopus.com/inward/record.url?scp=85215078573&partnerID=8YFLogxK
U2 - 10.1177/1748006X241306853
DO - 10.1177/1748006X241306853
M3 - Article
AN - SCOPUS:85215078573
SN - 1748-006X
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
ER -