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 repair systems play a major role in many industrial organisations, such as communication, manufacturing systems, power plants, and other areas.

Research Goals and Hypotheses:

  • We focus on developing a mathematical stochastic model using a queuing approach for performance evaluation of machine-repairing systems in which the units are subjected to failure and repair.
  • Untimely breakdown caused by failed equipment results in a negative impact on any organisation. To restore the functioning of failed units, a repair facility must be available. In the present study, we consider two heterogeneous repairmen where repairmen render essential repair and optional repairs. The first repairman is present all the time to repair the failed components. In contrast, 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. In contrast, 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 be 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 system's steady-state probabilities is presented, and a successive-over-relaxation technique to evaluate the probabilities is employed.

Results and Discoveries:

We provide explicit expressions to obtain the system’s queuing and reliability measures, such as the expected number of failed units, standby units, probability that the 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 always available in the system, the system's performance and availability increase. Still, on the other hand, it would be a more costly affair for the system. So, for this sake, the repairmen's vacation policy is beneficial for system analysers if cost optimality is evaluated.

Citation to the base paper:

Gupta, R. & Aravind, A.A. (2024) ‘Threshold N-policy machine repair problem with multiple spares and switching failure”, International Journal of Industrial and Systems Engineering, Vol. 45, No. 4, pp. 515-544.

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

2024

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