International Journal of Latest Research in Engineering and Technology (IJLRET) ISSN: 2454-5031 www.ijlret.com || Volume 03 - Issue 12 || December 2017 || PP. 98-103 www.ijlret.com 98 | Page Economic Analysis of a System Having Duplicate Cold Standby Unit with Priority to Repair of Original Unit Ajit Grewal 1 , Indu Rohilla and Jitender Kumar Assistant Director, Forensic Science Laboratory Mahuban Karnal Haryana School of Applied Science, Shinghania University, Pachari Beri Jhunjhunu (Raj.) Abstract: Identical unit in the system play very important role to increase the reliability of the system. But in this situation, the cost of the system becomes very high to hold redundant unit. Idea that the system, having the minimum cost that duplicate unit has taken as cold standby with different failure rate as the failure rate of original unit. Also, the idea of priority to one discipline over to other discipline can improve the system performance. Keeping the idea of such system a model is developed having different failure rate with priority to repair of the original unit over repair of the duplicate unit. There is a single server, who play dual role to repair of original as well as duplicate unit whenever required. It is assume that the time to take repair activity follows negative exponential distribution whereas the distributions of unit are taken as arbitrary with different probability density functions. The expressions of various economic measures are analyzed in steady state using semi-Markov process and regenerative point technique. The graphs are sketched for arbitrary values of the parameters to delineate the behavior of some important performance measures to check the efficacy of the system model under such situations. Key Words: Stochastic Analysis, Duplicate cold-standby, regenerative point, priority, steady state and semi- Markov process Introduction Redundancy is a common approach to enrich the reliability and availability of a system. In literature, the stochastic behavior of cold standby system has been widely discussed by many researchers, Osaki and Nakagawa [1971] discussed on a two-unit standby redundant system with standby failure. Nakagawa and Osaki [1975] analyzed stochastic behavior of a two-unit priority standby redundant system with repair. Subramanian et.al. [1976] highlighted reliability of a reparability system with standby failure. Gopalan and Nagarwalla [1985] analyzed cost-benefit of a one server two unit cold standby system with repair and age replacement. In a standby redundant system some additional paths are created for proper functioning of the system. Standby unit is the assistance to increase the reliability of the system. Singh and Sriniwas [1987] obtained stochastic analysis of a two unit cold standby system with preparation time for repair. In a cold standby redundant system as the operating unit fails, the standby unit takes its place and the failed unit goes under treatment. But it may be the possibility that the standby unit is already damaged owing to remain unused for a longer period of time or erosion etc. we may face a situation when the operating unit fails but the standby unit is already damaged. So far, the cold standby systems with the possibility of server failure have been discussed by the above researchers. Aggrawal et.al.[2010] highlighted the reliability characteristics of a cold-standby redundant system. Recently, Malik and Sudesh K. Barak [2013] analyzed profit of a system reliability model under preventing maintenance and repair. Bhardwaj and Singh [2014] discussed semi-Markov approach for asymptotic performance analysis of a Standby system with server failure. Bhardwaj and Singh [2014] obtained steady state behavior of a cold-standby system with server failure and arbitrary repair, replacement and treatment. Malik, Bhardwaj and Komaldeep Kaur [2015] analyzed performance of a stochastic system with standby failure and maintenance. But the concept of standby failure needs more attention due to its significant contribution during study. So keeping this aspect in view, we developed a stochastic model of redundant system with standby failure. The model consists of two non-identical units; original unit is in operative mode and duplicate unit is in cold standby mode. The cold standby unit becomes operative after failure of the original unit. There is single server for repair activity whenever required. The time to take repair activity follows negative exponential distribution whereas the distributions of unit are taken as arbitrary with different probability density functions. The expression for various reliability measures such as transition probabilities, mean sojourn times, mean time to system failure, steady state availability are deduced by using semi-Markov process and regenerative point technique. The graphs are delineated for arbitrary values of the parameters to highlight the behavior of some important performance measures to check the efficacy of the system model under such situations. The suggested model is applicable in the hospital in which generator system working as duplicate unit and electric supply is treated as original unit. Also, this model is backbone of the industries.