Summary of - Threshold N-policy machine repair problem with multiple spares and switching failure

Document Type

Article

Abstract

Study Background: This paper entitled “Threshold N-policy machine repair problem with multiple spares and switching failure” deals with the performance evaluation of a machine-repairing system. Machine repairing systems has a major role in many industrial organisations such as communication, manufacturing system, power plants and other areas.

Research Goals and Hypotheses:

  • We focus to develop a mathematical stochastic model using queuing approach for performance evaluation of machine repairing systems wherein the units are subjected to failure and repair.
  • Untimely breakdown caused by failed equipment results a negative impact on any organisation. In order to restore the functioning of failed units, repair facility must be available. In the present study, we consider two heterogeneous repairmen where repairmen render essential repair and optional repair. The first repairman is present all the time to repair the failed components whereas the second repairman takes a vacation of random extent whenever the number of failed components is fewer than N. The second repairman returns back and renders repair jobs when the number of failed units reaches N. Essential repair is provided to each failed unit, whereas few of them demand the second optional repair.
  • Multiple types of warm standby units are used to improve the reliability of any operating system. Due to the advancement of technology, failed units are automatically switched by standby units. Unfortunately, sometimes this switching may imperfect. The concept of standby switching failure is incorporated with degradation and common cause failure.

Methodological Approach:

The steady-state equations governing the system model are developed. A matrix technique to obtain the steady state probabilities of the system is presented and successive-over-relaxation technique to evaluate the probabilities is employed.

Results and Discoveries:

We provide explicit expressions to obtain system’s queuing and reliability measures such as the expected number of failed units, standby units, probability that repairman is busy, system reliability etc. We establish the cost function in order to quantify total cost per unit time by considering various cost factors. For validation purpose, sensitivity analysis is carried out by taking numerical illustrations. We observe that the cost of the system can be reduced to some extent by regular maintenance of the failed units. We also observed that if the server is available all the time in the system, it increases the good performance and availability of the system, but on the other hand it would be a more cost affair of the system. So, for this sake, vacation policy of repairman is benefited for system analysers if cost optimality is evaluated.

Citation to the base paper:

Jain, M. and Gupta, R. (2018) ‘N-policy for redundant repairable system with multiple types of warm standbys with switching failure and vacation’, International Journal of Mathematics in Operational Research, Vol. 13, No. 4, pp.419–449.

Publication Date: 05 January, 2024

Recommended Citation:

Gupta, R. & Aravind, A.A., “Summary of - Threshold N-policy machine repair problem with multiple spares and switching failure”, (2024). Open Access archive.

Publication Date

2023

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