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

Huixia Huo ()
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Huixia Huo: School of Science, Tianjin University of Commerce, Tianjin 300134, China

Mathematics, 2024, vol. 12, issue 5, 1-14

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.

Keywords: corrective maintenance; availability; cost; bilinear software systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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