Optimal Corrective Maintenance Policies via an Availability-Cost Hybrid Factor for Software Aging Systems

Abstract

Availability is an important index for the evaluation of the performance of software aging systems. Although the corrective maintenance increases the system availability, the associated cost may be very high; therefore, the balancing of availability and cost during the corrective maintenance phase is a critical issue. This paper investigates optimal corrective maintenance policies via an availability-cost hybrid factor for software aging systems. The system is described by a group of coupled differential equations, where the multiplier effect of the repair rate on a system variable is bilinear term. Our aim is to drive an optimal repair rate that ensures a balance between the maximal system availability and the minimal repair cost. In a finite time interval [0,T], we rigorously discuss the state space of the system and prove the existence of the optimal repair rate, and then derive the first-order necessary optimality conditions by applying a variational inequality with the adjoint variables.