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

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  • Huixia Huo

    (School of Science, Tianjin University of Commerce, Tianjin 300134, China)

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.

Suggested Citation

  • Huixia Huo, 2024. "Optimal Corrective Maintenance Policies via an Availability-Cost Hybrid Factor for Software Aging Systems," Mathematics, MDPI, vol. 12(5), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:694-:d:1347195
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    References listed on IDEAS

    as
    1. Huixia Huo & Houbao Xu & Zhuoqian Chen, 2021. "Modelling and dynamic behaviour analysis of the software rejuvenation system with periodic impulse," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 27(1), pages 522-542, January.
    2. Chen, Dongyan & Trivedi, Kishor S., 2005. "Optimization for condition-based maintenance with semi-Markov decision process," Reliability Engineering and System Safety, Elsevier, vol. 90(1), pages 25-29.
    3. Meng, Haining & Liu, Jianjun & Hei, Xinhong, 2015. "Modeling and optimizing periodically inspected software rejuvenation policy based on geometric sequences," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 184-191.
    4. Yi Ding & Anatoly Lisnianski & Ilia Frenkel & Lev Khvatskin, 2009. "Optimal corrective maintenance contract planning for aging multi‐state system," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(5), pages 612-631, September.
    5. Junjun Zheng & Hiroyuki Okamura & Tadashi Dohi, 2021. "Availability Analysis of Software Systems with Rejuvenation and Checkpointing," Mathematics, MDPI, vol. 9(8), pages 1-15, April.
    Full references (including those not matched with items on IDEAS)

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