Abstract
The concerned paper illustrates the comparison of two stochastic models of a cable manufacturing plant with varying demand. Here, it shows the comparison between a single unit system (Model 1) and a two-unit cold standby system (Model 2). In Model 1, the system is either in working state on some demand or put to shut down mode on no demand. In Model 2, at initial stage, one of the units is operative while the other is kept as cold standby. At times when the operative unit stops working due to some breakdown/failure, the standby unit instantaneously becomes operative while the repairman repairs the failed unit. In this working model, only one unit remains operative at a time. However, there may be a state when both the units fail. The comparison of systems is done by means of MTSF (mean time to system failure), steady state availability and profit function using Laplace transforms and software package Code-Blocks 13.12. Different graphs have been plotted to discover which model is superior to the other model under the given conditions. The system is analysed by making use of semi-Markov processes and regenerative point technique.
Highlights
The manufacturing of tools and special equipments is an inevitable part of our modern society
Vi Expected number of visits of repairman for each Model i where i = 1, 2 DTi Expected down time for each Model i where i = 1,2 P1 Profit incurred to the system for Model 1 NP2 Net profit [total profit incurred in Model 2—installation cost for addition unit (ICA)] μi Mean sojourn time in regenerative state i before transiting to any other state * Symbol for Laplace transforms ** Symbol for Laplace Stieltjes transforms qij(t), Qij(t), p.d.f and c.d.f of first passage time from a regenerative state i to a regenerative state j or to a failed state j without visiting any other regenerative state in (0, t] g(t), G(t) p.d.f. and c.d.f. of repair time for the unit
The semi-Markov process is applied to show the comparison of two stochastic models of a cable manufacturing plant with varying demand
Summary
The manufacturing of tools and special equipments is an inevitable part of our modern society. One has to keep tools/equipment available at all times, in order to run the systems. Since this can be expensive, availability and profit of an industrial system are becoming increasingly important. Though many researchers made meaningful contributions a lot in the field of system reliability modelling, fewer studies have reported the comparative analysis of different types of systems. Taneja and Naveen (2003), Ke and Chu (2007), Wang and Chen (2009) and Yusuf (2014) compared two models considering different situations such as expert repairman, redundant repairable system and switching failures. Though many researchers made meaningful contributions a lot in the field of system reliability modelling, fewer studies have reported the comparative analysis of different types of systems. Tuteja et al (1991), Alidrisi (1992), Mokaddis et al (1994), Pan (1997), Chandrasekhar et al (2004) and Xu et al (2005) analysed the reliability and availability of standby systems by studying various parameter viz. partial failures, Malhotra and Taneja SpringerPlus (2015)4:705 perfect or imperfect switching, Erlangian repair time and three types of repair facilities. Taneja and Naveen (2003), Ke and Chu (2007), Wang and Chen (2009) and Yusuf (2014) compared two models considering different situations such as expert repairman, redundant repairable system and switching failures. Zhang et al (2012) and Dessie (2014) studied the modeling of diesel system in locomotives and HIV/AIDS dynamic evolution
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