On the stochastic analysis of a master slave system having one master unit, one slave unit and one working unit

The purpose of the present paper is to study the stochastic analysis of a master slave system having one master unit, one slave unit and one working unit. Initially all the units are operating. Whenever master unit fails system fails completely but if slave unit fails it operates partially. The failure time distribution of all the operating units are assumed to be negative exponential while as repair time distributions are taken to be arbitrary. There is a single repair facility which repairs the unit on first come first serve basis but priority in repair is given to master unit. Various reliability characteristics are obtained in order to analyze the expected profit earned by the system. Also, a consistent asymptotically normal (CAN) estimator, a 100(1-a)% asymptotic confidence interval for the steady state availability of the system and the maximum likelihood estimator (MLE) of the system availability are obtained. Lastly a numerical example is discussed to highlight the important results.