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<p>A predictor has been introduced for the matrix renewal function (MRF) of the finite state space semi-Markov processes (SMPs). Alongside the main outcome, it has also been tried to forecast the future sojourn times of the SMP for subsequent forthcoming states. As an application, the results have been employed for a repairable system, susceptible to both partial and catastrophic failures which has been considered as a three-state SMP. By using the established techniques and formulas, some important reliability measures have been predicted for specified leading times, e.g., the number of subsequent failures, the future downtime duration of the system and finally the future costs. Ultimately, a simulation study has been performed to compare the predicted values with the true ones.</p>

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Prediction in Semi-Markov Repairable Systems

  • 期刊论文

  • 发表日期：

    2025年2月17日

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  • M. Fathizadeh,
  • K. Khorshidian,
  • H. Mansoori

摘要

A predictor has been introduced for the matrix renewal function (MRF) of the finite state space semi-Markov processes (SMPs). Alongside the main outcome, it has also been tried to forecast the future sojourn times of the SMP for subsequent forthcoming states. As an application, the results have been employed for a repairable system, susceptible to both partial and catastrophic failures which has been considered as a three-state SMP. By using the established techniques and formulas, some important reliability measures have been predicted for specified leading times, e.g., the number of subsequent failures, the future downtime duration of the system and finally the future costs. Ultimately, a simulation study has been performed to compare the predicted values with the true ones.