Stochastic Analysis of a Priority Standby System under Preventive Maintenance

Abstract

In this paper, we propose a system of two dissimilar units: one unit prioritizes operation (priority unit), and the other unit is kept as a cold standby (ordinary unit). In this system, we assume that the failures, repairs, and preventive maintenance (PM) times follow arbitrary distributions for both units, except for the fact that the repair time of the ordinary unit follows an exponential distribution. The priority unit has normal, partial failure or total failure modes, while the ordinary unit has normal or total failure modes. The PM of the system can be started after time t when (i) the priority unit is in the normal or partial failure modes up to time t and (ii) the standby unit is available up to time t. PM can be achieved in two types: the costlier type with probability p and the cheaper type with probability (1−p). Under these assumptions, we investigate the reliability measures of the system using the regenerative point technique. Finally, we show a numerical example to illustrate the theoretical findings and show the effect of preventive maintenance in the reliability measures of the proposed system.

An Analytical Study of Powder Plant System

“…By these transition probabilities it is also verified that • p 01 + p 02 = 1 • p 14 + p 15 + p 16 + p 17 = 1 • p 51 + p 58 + p 59 + p 5,10 = 1 • p 51 + p 54 (8) + p 57 (9) + p 56 (10) = 1 • p 23 = p 32 = p 41 = p 61 = p 71 = p 84 = p 97 = p 10,6 = 1 The unconditional meantime is taken by the system to transit for any regenerative state 'j' when t (time) is counted from the epoch of entrance into state 'i' is mathematically stated as: 8) + m 57 (9) + m 56 (10) = K where,…”

“…https://www.indjst.org/ N 1 = p 01 (µ 1 + µ 5 p 15 ) D 1 = µ 1 + µ 4 (p 14 + p 15 p 54 (8) ) + Kp 15 + µ 6 (p 16 + p 15 p 56 (10) ) + µ 7 (p 17 + p 15 p 57 (9) ) ... ( 1)…”

“…N 2 = W 4 p 01 (p 14 + p 15 p 54 (8) ) + W 5 p 01 p 15 + W 6 p 01 (p 16 + p 15 p 56 (10) ) + W 7 p 01 (p 17 + p 15 p 57 (9) ) D 1 is defined in equation 1. 8) + p 15 p 57 (9) + p 15 p 56 (10) ) D 1 is already defined in equation 1.…”

“…An analysis of the behavior of a washing unit in a paper mill has been undertaken by Kumar et al (2019) (7) . In (2021), Sultan et al (8) conducted stochasticallyderived modeling of a standby unit with priority functions. Batra and colleagues (2021) (9) scrutinized a PCB unit's availability and reliability analysis.…”

Reliability Modeling of a Food Industrial System with two Types of Repair Persons wherein Demand is Season Dependent

“…Much research on system reliability measures has been done using the semi-Markov process and regenerative point technique. Murari et al (1985), Goel et al (1985), Muralidhar (1991), Tuteja andTaneja (1993), Siwach et al (2001), El-Said andEl-Sherbeny (2006), Rizwan et al (2010), Batra and Taneja (2019), Sheetal et al (2019), Taj et al (2020), Sultan and Moshref (2021) and Bhatti and Kakkar (2022) have worked on the reliability analysis of the systems using regenerative point technique. Aggarwal and Malik (2020) have analyzed the profit of a repairable cold standby system, where the server is free to take a rest between repairs.…”