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Optimizing Costs in a Reliability System under Markovian Arrival of Failures and Reposition by K -Policy Inspection

Author

Listed:
  • Delia Montoro-Cazorla

    (Department of Statistics and Operational Research, University of Jaén, 23071 Jaén, Spain)

  • Rafael Pérez-Ocón

    (Department of Statistics and Operational Research, University of Granada, 18071 Granada, Spain)

Abstract

This paper presents an N warm standby system under shocks and inspections governed by Markovian arrival processes. The inspections detect the number of down units, and their replacement is carried out if there are a minimum K of failed units. This is a policy of the type ( K , N ) used in inventory theory. The study is performed via the up and down periods of the system (cycle); the distribution of these random times and the expected costs for each period comprising the cycle are determined on the basis of individual costs due to maintenance actions (per inspection and replacement of every unit) and others due to operation or inactivity of the system, per time unit. Intermediate addressed calculus are the distributions of the number of inspections by cycle and the expected cost involving every inspection, depending on the number of replaced units. The system is studied in transient and stationary regimes, and some reliability measures of interest and the cost rate are calculated. An optimization of these quantities is performed in terms of the number K in a numerical example. This general model extends to many others in the literature, and, by using the matrix-analytic method, compact and algorithmic expressions are achieved, facilitating its potential application.

Suggested Citation

  • Delia Montoro-Cazorla & Rafael Pérez-Ocón, 2022. "Optimizing Costs in a Reliability System under Markovian Arrival of Failures and Reposition by K -Policy Inspection," Mathematics, MDPI, vol. 10(11), pages 1-21, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1918-:d:831052
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    References listed on IDEAS

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    Cited by:

    1. María Luz Gámiz & Delia Montoro-Cazorla & María del Carmen Segovia-García & Rafael Pérez-Ocón, 2022. "MoMA Algorithm: A Bottom-Up Modeling Procedure for a Modular System under Environmental Conditions," Mathematics, MDPI, vol. 10(19), pages 1-19, September.

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