The present paper analyzes a two-unit cold standby system wherein both units may become operative depending upon the demand. Initially, one of the units is operative while the other is kept as cold standby. If the operative unit fails or the demand increases to the extent that one operative unit is not capable of meeting the demand, the standby unit becomes operative instantaneously. Thus, both units may become operative simultaneously to meet the increased demand. Availability in three types of upstates is as follows: (i) when the demand is less than or equal to production manufactured by one unit; (ii) when the demand is greater than whatever produced by one unit but less than or equal to production made by two units; and (iii) when the demand is greater than the produces by two units. Other measures of the system effectiveness have also been obtained in general case as well as for a particular case. Techniques of semi-Markov processes and regenerative processes have been used to obtain various measures of the system effectiveness. 1 ( ) = ((1 − 3 22 * ( )) − 02 * ( ) 20 * ( )) × [ (1 − 9 66 * ( )) × (1 − 10 77 * ( ) − 57 * ( ) 75 * ( )) − 15 * ( ) 51 * ( ) (1 − 10 77 * ( )) Journal of Quality and Reliability Engineering 7 + (1 − 10 77 * ( )) × (− 16 * ( ) ( 51 * ( ) 8 65 * ( ) + 16 * ( ))) − 75 * ( ) 16 * ( ) × ( (8,10) 67 * ( ) + (9,10) 67 * ( )) + 61 * ( ) 57 * ( )] + 10 * ( ) × [(1 − 9 66 * ( )) × ((1 − 10 77 * ( )) − 57 * ( ) 75 * ( )) × ( 01 * ( ) (1 − 3 22 * ( )) + 02 * ( ) 4 21 * ( )) + 02 * ( ) (1 − 10 77 * ( )) × ( ( 51 * ( ) 8 65 * ( ) + 61 * ( )) + ( (3,9) 26 * ( ) + (4,9) 26 * ( )) + (1 − 9 66 * ( )) (4,8) 25 * ( ) 51 * ( )) − 51 * ( ) 75 * ( ) ( (8,10) 67 * ( ) + (9,10) 67 * ( )) × ( (3,9) 26 * ( ) + (4,9) 26 * ( )) − 51 * ( ) 75 * ( ) × (1 − 9 66 * ( ))
This paper presents a real case analysis of a single machine subsystem of a cable plant using reliability modelling. Real maintenance data of a cable plant are collected for this purpose. Three types of maintenance are noted for the subsystem: repair, preventive maintenance random (PMR) and preventive maintenance scheduled (PMS). The subsystem is repaired upon failure, while preventive maintenance (PM) is carried out at random and scheduled basis. Optimum reliability indices such as mean time to subsystem failure (MTSF), availability of the subsystem, expected busy period of the repairman and expected number of subsystem repairs are obtained. Analysis is done using semi Markov processes and regenerative point techniques.
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.
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