Study of Two Unit Cold Standby Systems With Regenerative Point Technique

Abstract

The whole range of our work reported in this dissertation is covered into three chapters which are described as: Chapter I: A review of literature pertaining to the theory of reliability and modeling is given in this chapter. This also includes some basic concepts such as probability distributions, stochastic process, pro¯t function, etc. Chapter II: This chapter has been designed with a view to study a two-unit cold standby system with single server in which units are identical. Initially one unit is operative and the others as cold standby.The unit fails completely directly from normal mode. There is a single server who comes immediately at the complete failure of the unit for doing its repair. Various Reliability characteristic such as Reliability, Mean Time to System Failure(MTSF), Time Dependent Availability, Steady State Availability, Time-Dependent Busy Period, Steady State Busy Period Analysis, Time-Dependent Expected number of visits, Steady State Expected number of visits by server are obtained and ¯nally the pro¯t function is determine by using semi-Markov process and regenerative point technique. Chapter III: Here we study the extension of the work reported in previous chapter with the separate assumption that the repair process is divided into two stages. In the ¯rst stage, the re- pairing process of the unit is started but it does not get completed; instead the process is completed in the second stage. The elapsed time between two stages is called the waiting time. By using regenerative point technique some reliability characteristic of interest are also obtained.