IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i5p694-d1347195.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/5/694/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/5/694/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jia, Heping & Ding, Yi & Peng, Rui & Liu, Hanlin & Song, Yonghua, 2020. "Reliability assessment and activation sequence optimization of non-repairable multi-state generation systems considering warm standby," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    2. Zhuoqian Chen & Houbao Xu & Huixia Huo, 2022. "Computational Scheme for the First-Order Linear Integro-Differential Equations Based on the Shifted Legendre Spectral Collocation Method," Mathematics, MDPI, vol. 10(21), pages 1-21, November.
    3. Zhao, Yunfei & Huang, Linan & Smidts, Carol & Zhu, Quanyan, 2020. "Finite-horizon semi-Markov game for time-sensitive attack response and probabilistic risk assessment in nuclear power plants," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    4. Zhou, Zhi-Jie & Hu, Chang-Hua & Xu, Dong-Ling & Chen, Mao-Yin & Zhou, Dong-Hua, 2010. "A model for real-time failure prognosis based on hidden Markov model and belief rule base," European Journal of Operational Research, Elsevier, vol. 207(1), pages 269-283, November.
    5. Panagiotidou, S. & Tagaras, G., 2012. "Optimal integrated process control and maintenance under general deterioration," Reliability Engineering and System Safety, Elsevier, vol. 104(C), pages 58-70.
    6. Alaswad, Suzan & Xiang, Yisha, 2017. "A review on condition-based maintenance optimization models for stochastically deteriorating system," Reliability Engineering and System Safety, Elsevier, vol. 157(C), pages 54-63.
    7. Alberto Reyes & L. Enrique Sucar & Pablo H. Ibargüengoytia & Eduardo F. Morales, 2020. "Planning Under Uncertainty Applications in Power Plants Using Factored Markov Decision Processes," Energies, MDPI, vol. 13(9), pages 1-17, May.
    8. Olde Keizer, Minou & Teunter, Ruud, 2014. "Opportunistic condition-based maintenance and aperiodic inspections for a two-unit series system," Research Report 14033-OPERA, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    9. Levitin, Gregory & Xing, Liudong & Huang, Hong-Zhong, 2019. "Optimization of partial software rejuvenation policy," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 289-296.
    10. Girish Kumar & Vipul Jain & Umang Soni, 2019. "Modelling and simulation of repairable mechanical systems reliability and availability," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(5), pages 1221-1233, October.
    11. 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.
    12. Peng, Hao & van Houtum, Geert-Jan, 2016. "Joint optimization of condition-based maintenance and production lot-sizing," European Journal of Operational Research, Elsevier, vol. 253(1), pages 94-107.
    13. Prasenjit Mondal, 2016. "On undiscounted semi-Markov decision processes with absorbing states," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(2), pages 161-177, April.
    14. Yen-Luan Chen & Chin-Chih Chang & Dwan-Fang Sheu, 2016. "Optimum random and age replacement policies for customer-demand multi-state system reliability under imperfect maintenance," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(5), pages 1130-1141, April.
    15. Zhang, Xueqing & Gao, Hui, 2012. "Road maintenance optimization through a discrete-time semi-Markov decision process," Reliability Engineering and System Safety, Elsevier, vol. 103(C), pages 110-119.
    16. Jackson, Canek & Pascual, Rodrigo & Mac Cawley, Alejandro & Godoy, Sergio, 2023. "Product–service system negotiation in aircraft lease contracts with option of disagreement," Journal of Air Transport Management, Elsevier, vol. 107(C).
    17. Ahmadi, Reza & Fouladirad, Mitra, 2017. "Maintenance planning for a deteriorating production process," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 108-118.
    18. Insua, David Rios & Ruggeri, Fabrizio & Soyer, Refik & Wilson, Simon, 2020. "Advances in Bayesian decision making in reliability," European Journal of Operational Research, Elsevier, vol. 282(1), pages 1-18.
    19. Tadashi Dohi & Hiroyuki Okamura & Cun-Hua Qian, 2022. "Computation algorithms for workload-dependent optimal checkpoint placement," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(2), pages 788-796, June.
    20. Rui Jiang & Michael Kim & Viliam Makis, 2012. "A Bayesian model and numerical algorithm for CBM availability maximization," Annals of Operations Research, Springer, vol. 196(1), pages 333-348, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:694-:d:1347195. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.