International Journal of Research in Advent Technology, Vol.3, No.6, June 2015 E-ISSN: 2321-9637
Cost Analysis of a Two-Unit Standby Industrial System with Varying Demand Rachna Khurana1, A.K.lal2, S.S. Bhatia3, R.K.Tuteja4 School of Mathematics and Computer Applications, Deptt. Of Mathematics, Thapar University, Patiala, Punjab – 1470041,2,3, Mahrishi Dayanand University, Rohtak, Haryana, India4. Email: rkhuranaa@yahoo.com1, aklal@thapar.edu2, ssbhatia@thapar.edu3, rk_tuteja2006@yahoo.co.in4 Abstract: In this paper we develop a stochastic model for two-unit standby system by making one or both the units operative depending upon the load/demand. The system under consideration is assumed to have two shifts of working and whole system undergoes for scheduled preventive/corrective maintenance before starting the second shift. Mathematical formulation of the problem determining the transition probabilities of various states are developed considering two types of failure for each unit (Type -I which has no standby and the Type - II which has standby). Various reliability metrics such as MTSF, availability, busy period and profit have been discussed for measuring the system effectiveness by using semi-Markov process and regenerative point technique. The proposed model is finally applied to rice manufacturing plant as a case study. Index Terms: Availability, Busy Period, MTSF, Regenerative point technique, Semi-Markov Process Nakagawa, Kumar and Agarwal, Sridharan and Mohanavadivu [4,6,10] studied the stochastic behaviour of a 1. INTRODUCTION two-unit cold standby redundant system. Goel et al.[2] and The reliability of the system is an important Khaled et al.[3] also studied two unit standby systems. Goel parameter which measures the quality of its consistence performance over its expected life span. With the development of modern technology and the world economy, et al.[1] discussed the reliability analysis of a system with the reliability problem of a system attracts imperative preventive maintenance and two types of repair. Rander et attentions. As the systems are becoming more complex and al.[8] studied a system with two types of repairmen with the corrosion over a period of time is a natural phenomenon, imperfect assistant repairman and perfect master repairman. the maintenance of system in terms of periodic inspection, Taneja et al.[11] collected the real data on failure and repair repairs and replacements play an important role in keeping rates of 232 programmable logic controllers (PLC) and their performance satisfactory. The effectiveness of the discussed reliability and profit analysis of a system which system depends on its reliability indices, such as mean time consists of one main unit (used for manufacturing) and two to system failure (MTSF), availability and busy period of PLCs (used for controlling). Initially, one of the PLCs is repairman. The research as a result lacks a balance between operative and the other is hot standby. Tuteja et al.[12] modeling and its practical applications to industries. Since discussed the cost benefit analysis of two server two unit the reliability is the mathematical representation of failure warm standby system with different types of failure. The cost mechanism for the systems in terms of differential equations, analysis of a two-unit cold standby system subject to therefore the model embedded with real failures of the degradation, inspection and priority has been analyzed by industry is quite helpful from application point of view. Kumar et al [5]. Shakuntla et al.[9] discussed the availability Several research works on various types of systems of a rice industry. Wang Z et al.[13] analyzed the reliability such as standby, redundant etc. have been carried out in of systems with common cause failure under random load. literature but the standby systems have attracted the Recently, Wu and Wu [7] studied reliability analysis of twoimperative attention of many scholars and reliability unit cold standby repairable systems under poisson shocks. engineers for their applicability in their respective fields. In In the research mentioned above on standby systems, it the era of was found that their analysis for system reliability are based emerging new technologies, competition and complexity, the on the various hypothetical failure and repair situations and concept of reliability and availability significantly affect the assumed numerical values. However, no satisfactory work output that a manufacturer gets from his industry. One can has been carried out for varying demand of system in the easily achieve maximum reliability of the system by using field of reliability. There may be different situations standby component. For this purpose, one should have the depending upon demand/load. Incorporating this situation, knowledge which component of the system is more sensitive, we present a new contribution and motivation in the present depending on that one can mend the system or that particular paper to the reliability literature in terms of real case study of component. Modelling and analysis of these interesting areas an industry in which a two-unit stand by system with varying need to be explored further in terms of real industrial demand has been analyzed. We have proposed a model which applications. analyzes mean time to system failure (MTSF), availability of Standby systems have been widely studied in the system and cost benefit. This type of model can be literature of reliability due to their frequent use in modern applied to any industries where standby systems are used. business and industries. Several authors such as Osaki and
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