We consider a replacement model for an additive damage process with linear restoration as outlined in a previous paper by M.J.M. Posner and D. Zuckerman. It was shown there that under certain assumptions a control limit policy is optimal for both discounted and undiscounted cost cases. However, they were only able to find the control limit by binary search. In this paper, we extend that analysis to determine the control limit analytically through a novel application of the martingale stopping theorem, and discuss its usefulness in cost minimization.
Bibliographical noteFunding Information:
The financial support of the Natural Sciences and Engineering Research Council of Canada under grant A4374 is gratefully acknowledged.
- additive damage
- control limit policy
- linear restoration rate
- martingale stopping theorem
- replacement model
ASJC Scopus subject areas
- Management Science and Operations Research
- Industrial and Manufacturing Engineering
- Applied Mathematics