Mathematical Model on Reliability with Three Units

The evolution of the new systems is directly or indirectly connected with betterment in the old systems and hence the efficiency. Thus assessment of reliability of equipment is of great importance in the context of rapidly growing technology and its further development. A large number of studies have been carried out to evaluate the reliability by taking two-unit set-up under different conditions. This paper presents the study of the execution of steam turbine running in electric power-station. Execution of any set-up can be computed with the help of its availability and reliability. In many combined cycle power plants, the turbine generator consists of steam turbines interconnected to each other. Here one steam turbine is considered as one unit. In this paper, a system is considered in which three indistinguishable units (steam turbine) are considered in which two units are functional and third is taken as an understudy. If two units do not perform, the working of third unit is discontinued till the availableness of the other functional unit. Here inspection before failure is conducted to check functional units in a regular and schedule time. Operating units are inspected before failure to analyse whether a functional units required normal maintenance or not, otherwise repair of the failed unit. Here a independent single server system is supposed which execute normal maintenance inspection and reparation. Inspection before failure and maintenance are taken in priority over repair of discontinued unit. Also supposed that unit is failed and under reparation, no pre-failure scheduled inspection is undertaken. In this paper, system will be analyzed to determine various reliability measures by using mathematical tools MTSF/MTBF, Markov chain, Markov process, renewal process etc.