Stochastic Analysis of a Two-Unit Cold Standby System Wherein Both Units May Become Operative Depending upon the Demand

Abstract

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 * ( ))

A Reliability Model for a Two Dissimilar Units Series System with Repair Time-Dependent Standby

“…A standby system with general life and repair time distribution was studied by Bieth et al [3].Mahmoud and Mosherf [4] discussed different types of failure and preventive maintenance in their study. Malhotra and Taneja [5] stochastically analysed a system wherein operability of more than one unit depends upon requirement. Manocha and Taneja [6] took arbitrary distribution for all random variables.…”

Reliability modelling and analysis of a single machine subsystem of a cable plant

“…Sanjay and Suresh [3] performed stochastic analysis of a reliability model of one-unit system with post inspection, post repair, preventive maintenance and replacement. Reetu and Gulshan [4] wrote on stochastic analysis of a two unit cold standby system wherein both units may become operative depending upon the demand. Rizwan, Padmavathi and Taneja [5] carried out performance analysis of a desalination plant as a single unit with mandatory shutdown during winter.…”

A Reliability Model for a System With Wrong Diagnosis on Failure and Two Types of Repairman

“…Due to complexity of systems, the faults which occur therein are, sometimes, not properly diagnosed. A lot of work has been reported by various researchers including [1][2][3][4][5][6] in the literature of reliability but the aspect of wrong diagnosis has not been taken into account as far as the profitability of the systems is concerned. As the wrong diagnosis takes place in many situations, therefore it is inevitable to develop a reliability model for a system introducing this concept.…”