ON USE OF GAMMA DISTRIBUTION FOR EVALUATION OF RELIABILITY AND AVAILABILITY OF A SINGLE UNIT SYSTEM SUBJECT TO ARRIVAL TIME OF THE SERVER

Abstract

The preference to the use of single unit systems over the redundant systems has been given due to their intrinsic reliability and affordability. And, stochastic modeling of repairable systems of one or more unit has been done by assuming negative exponential distribution for failure and repair times. In fact, the repairable systems may or may not have constant failure and repair rates. In such situations some other distributions possessing monotonic nature of the random variables associated with different time points may be considered. Gamma distribution is one of the distributions that may offer a good fit to some set of failure data. Also, negative exponential distribution is a special case of this distribution. Hence, in this paper reliability and availability of a single unit system by considering Gamma distribution for the random variables associated with failure and repair times of the system have been evaluated. A single server is employed to carry out the repair activities. The server is allowed to take some time to arrive at the system (called arrival time). The system has all the transit points as regenerative and so regenerative point has been used to derive the expressions for reliability measures. The values of reliability and availability are obtained for particular situations of the parameters. The behavior of these measures has been observed for the arbitrary values of the parameters.