TY - JOUR
T1 - On the delayed worse-than-minimal repair model and its application to preventive replacement
AU - Cha, Ji Hwan
AU - Finkelstein, Maxim
AU - Levitin, Gregory
N1 - Funding Information:
The work of the first author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant Number: 2019R1A6A1A11051177).
Publisher Copyright:
© 2021 The Author(s).
PY - 2023/1/1
Y1 - 2023/1/1
N2 - Minimal repair and other imperfect repair models have been intensively studied in the literature. Much less attention has been payed to the 'worse than minimal' repair problem, although it often occurs in practice due to the adverse effects of previous repairs, environmental and internal shocks, etc. To model this type of repair, we define a new point process that behaves as the non-homogeneous Poisson process up to a certain event or time (minimal repairs) and then it becomes the generalized Polya process of repairs (worse than minimal repairs). The corresponding replacement policy is defined and the optimal solutions that minimize the long run expected cost rate are analyzed. The replacement can be executed univariately either after the given time T or the given number of repairs (on the k-th failure). Moreover, the system can be also replaced by implementing the bivariate strategy, that is, after the time T or on the k-th failure, whichever comes first. The detailed numerical examples illustrate our findings. It is shown that the k-strategy outperforms the T -strategy (lower cost rates), whereas the bivariate strategy is not worse than the best univariate strategy.
AB - Minimal repair and other imperfect repair models have been intensively studied in the literature. Much less attention has been payed to the 'worse than minimal' repair problem, although it often occurs in practice due to the adverse effects of previous repairs, environmental and internal shocks, etc. To model this type of repair, we define a new point process that behaves as the non-homogeneous Poisson process up to a certain event or time (minimal repairs) and then it becomes the generalized Polya process of repairs (worse than minimal repairs). The corresponding replacement policy is defined and the optimal solutions that minimize the long run expected cost rate are analyzed. The replacement can be executed univariately either after the given time T or the given number of repairs (on the k-th failure). Moreover, the system can be also replaced by implementing the bivariate strategy, that is, after the time T or on the k-th failure, whichever comes first. The detailed numerical examples illustrate our findings. It is shown that the k-strategy outperforms the T -strategy (lower cost rates), whereas the bivariate strategy is not worse than the best univariate strategy.
KW - generalized Polya process
KW - long-run expected cost rate
KW - minimal repair
KW - optimal replacement
KW - worse than minimal repair
UR - http://www.scopus.com/inward/record.url?scp=85158071208&partnerID=8YFLogxK
U2 - 10.1093/imaman/dpab036
DO - 10.1093/imaman/dpab036
M3 - Article
AN - SCOPUS:85158071208
SN - 1471-678X
VL - 34
SP - 101
EP - 122
JO - IMA Journal of Management Mathematics
JF - IMA Journal of Management Mathematics
IS - 1
ER -