# Journal of Mathematics and Statistics

## Analysis of a Two Unit Standby Oil Delivering System with a Provision of Switching Over to another System at Need to Increase the Availability

Upasana Sharma, Rekha and Gulshan Taneja

DOI : 10.3844/jmssp.2011.57.60

Journal of Mathematics and Statistics

Volume 7, Issue 1

Pages 57-60

### Abstract

Problem statement: The study deals with a standby system consisting of two units. Initially one unit is operative and the other is standby. When both the units are failed then there is a provision of switching over to the other similar system. This practical situation may be observed in an oil refinery plant. Real data on failure and repair rates of such units collected from oil refinery plant, Pani pat, India have been used for present study. Approach: The system is analyzed by making use of semi-Markov processes and regenerative point technique. Results: Expression for the expected profit is obtained after obtaining various measures of system effectiveness. Graphical analysis is also done for a particular case and various interpretations are made. Conclusion: Upper/lower limits for various rates/costs/probabilities can be obtained to get the positive profit for the system and to decide about the least value of the price of the product to be produced.