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A delay time model with imperfect and failure-inducing inspections

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  • Flage, Roger

Abstract

This paper presents an inspection-based maintenance optimisation model where the inspections are imperfect and potentially failure-inducing. The model is based on the basic delay-time model in which a system has three states: perfectly functioning, defective and failed. The system is deteriorating through these states and to reveal defective systems, inspections are performed periodically using a procedure by which the system fails with a fixed state-dependent probability; otherwise, an inspection identifies a functioning system as defective (false positive) with a fixed probability and a defective system as functioning (false negative) with a fixed probability. The system is correctively replaced upon failure or preventively replaced either at the N'th inspection time or when an inspection reveals the system as defective, whichever occurs first. Replacement durations are assumed to be negligible and costs are associated with inspections, replacements and failures. The problem is to determine the optimal inspection interval T and preventive age replacement limit N that jointly minimise the long run expected cost per unit of time. The system may also be thought of as a passive two-state system subject to random demands; the three states of the model are then functioning, undetected failed and detected failed; and to ensure the renewal property of replacement cycles the demand process generating the ‘delay time’ is then restricted to the Poisson process. The inspiration for the presented model has been passive safety critical valves as used in (offshore) oil and gas production and transportation systems. In light of this the passive system interpretation is highlighted, as well as the possibility that inspection-induced failures are associated with accidents. Two numerical examples are included, and some potential extensions of the model are indicated.

Suggested Citation

  • Flage, Roger, 2014. "A delay time model with imperfect and failure-inducing inspections," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 1-12.
    • Handle: RePEc:eee:reensy:v:124:y:2014:i:c:p:1-12
    DOI: 10.1016/j.ress.2013.11.009
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    References listed on IDEAS

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    Cited by:

    1. Yang, Li & Ma, Xiaobing & Zhai, Qingqing & Zhao, Yu, 2016. "A delay time model for a mission-based system subject to periodic and random inspection and postponed replacement," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 96-104.
    2. de Jonge, Bram & Klingenberg, Warse & Teunter, Ruud & Tinga, Tiedo, 2016. "Reducing costs by clustering maintenance activities for multiple critical units," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 93-103.
    3. Alberti, Alexandre R. & Cavalcante, Cristiano A.V. & Scarf, Philip & Silva, André L.O., 2018. "Modelling inspection and replacement quality for a protection system," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 145-153.
    4. Alberti, Alexandre R. & Cavalcante, Cristiano A.V., 2020. "A two-scale maintenance policy for protection systems subject to shocks when meeting demands," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    5. Francisco Germán Badía & María Dolores Berrade, 2022. "On the Residual Lifetime and Inactivity Time in Mixtures," Mathematics, MDPI, vol. 10(15), pages 1-20, August.
    6. Zhang, Fengxia & Shen, Jingyuan & Liao, Haitao & Ma, Yizhong, 2021. "Optimal preventive maintenance policy for a system subject to two-phase imperfect inspections," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    7. Li Yang & Yu Zhao & Xiaobing Ma & Qingan Qiu, 2018. "An optimal inspection and replacement policy for a two-unit system," Journal of Risk and Reliability, , vol. 232(6), pages 766-776, December.
    8. de Jonge, Bram & Teunter, Ruud & Tinga, Tiedo, 2017. "The influence of practical factors on the benefits of condition-based maintenance over time-based maintenance," Reliability Engineering and System Safety, Elsevier, vol. 158(C), pages 21-30.
    9. Peng, Rui & Liu, Bin & Zhai, Qingqing & Wang, Wenbin, 2019. "Optimal maintenance strategy for systems with two failure modes," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 624-632.
    10. Ajith Tom James & O. P. Gandhi & S. G. Deshmukh, 2017. "Assessment of failures in automobiles due to maintenance errors," 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. 8(4), pages 719-739, December.
    11. Yang, Li & Ma, Xiaobing & Peng, Rui & Zhai, Qingqing & Zhao, Yu, 2017. "A preventive maintenance policy based on dependent two-stage deterioration and external shocks," Reliability Engineering and System Safety, Elsevier, vol. 160(C), pages 201-211.
    12. Zhao, Qian Qian & Yun, Won Young, 2019. "Storage availability of one-shot system under periodic inspection considering inspection error," Reliability Engineering and System Safety, Elsevier, vol. 186(C), pages 120-133.
    13. Akcay, Alp, 2022. "An alert-assisted inspection policy for a production process with imperfect condition signals," European Journal of Operational Research, Elsevier, vol. 298(2), pages 510-525.
    14. de Jonge, Bram & Scarf, Philip A., 2020. "A review on maintenance optimization," European Journal of Operational Research, Elsevier, vol. 285(3), pages 805-824.
    15. Wang, Jiantai & Ma, Xiaobing & Yang, Li & Qiu, Qingan & Shang, Lijun & Wang, Jingjing, 2024. "A hybrid inspection-replacement policy for multi-stage degradation considering imperfect inspection with variable probabilities," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    16. Zhang, Fengxia & Shen, Jingyuan & Ma, Yizhong, 2020. "Optimal maintenance policy considering imperfect repairs and non-constant probabilities of inspection errors," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    17. Sheu, Shey-Huei & Tsai, Hsin-Nan & Wang, Fu-Kwun & Zhang, Zhe George, 2015. "An extended optimal replacement model for a deteriorating system with inspections," Reliability Engineering and System Safety, Elsevier, vol. 139(C), pages 33-49.

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