Determining the control limit policy in a replacement model with linear restoration

The authors 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, the authors 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.