3-Unit System Comprising Two Types of Units with First Come First Served Repair Pattern Except When Both Types of Units are Waiting for Repair

Goyal Goyal

doi:10.3844/jmssp.2010.316.320

Abstract

Problem statement: In this study we investigated the probabilistic analysis of a three unit system working in a sugar Mill, wherein one unit is big and the other two units are small and identical, is examined. Upon failure of the big unit, both small units are made operative and failed unit is undertaken for repair immediately. Priority for operation is given to the big unit. Priority for repair is given to big unit if both types (i.e., big and small) of units are in queue to get the repair done. System is able to work with full capacity only if big unit or both small units are in good condition. If only one small unit is operable, the system works at reduced capacity. The system under consideration goes to rest during the non-seasonal period. Approach: System was analyzed by making use of semi-Markov processes and regenerative point technique and various measures of the system effectiveness are obtained including the profit incurred to the system. Results: Graphs had been plotted to depict the behavior of the profit with respect to failure rate for different values of repair rate and with respect to revenue per unit up time for which system is working at full capacity for different values of cost for PM/CM. Conclusion: The profit increases with the decrease in the values of the failure rate and with the increase in the values of revenue per unit up time. It has lower (higher) values on increasing the values of cost (repair rate). Cut-off points obtained for failure rate help decide about having the system with failure rate lesser than that the value at cut-off point. Also, the price of the product should be fixed in such a way so as to get the revenue greater than the value at cut-off point.

Highlights

Two/three-unit standby systems with two stages, that is, working or failed, have been widely discussed under various assumptions/situations by a large number of researchers including (Mokaddis et al, 1997; Tuteja et al, 2001; Goel et al, 1986; Taneja and Nanda, 2003; Li et al, 1998; Dhillon, 1992; Taneja, 2005; Rizwan, 2007; Murari and Maruthachalam, 1981)
There may be one more stage i.e., stage of Rest period of the system which exists in case of some seasonal systems like system working in a sugar mill
Goyal et al (2009) studied reliability and profit analysis of a two-unit standby system working in a sugar mill with operating and rest periods

Summary

Introduction

Two/three-unit standby systems with two stages, that is, working or failed, have been widely discussed under various assumptions/situations by a large number of researchers including (Mokaddis et al, 1997; Tuteja et al, 2001; Goel et al, 1986; Taneja and Nanda, 2003; Li et al, 1998; Dhillon, 1992; Taneja, 2005; Rizwan, 2007; Murari and Maruthachalam, 1981). Goyal et al (2009) studied reliability and profit analysis of a two-unit standby system working in a sugar mill with operating and rest periods. Thereafter, Goyal et al (2010) did reliability modeling and analysis of a sulphated juice pump system comprising three identical units with two types of working capacity and rest period on the basis of information gathered visiting some sugar mills in Haryana (India). When the Rest period is about to complete, the PM/CM is carried out to make the system ready for operation. They considered that the priority for repair as well as operation is given to the big unit. From the economic point of view, it may not be good all the times to give such priority

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Results

Discussion

Conclusion