Here in this paper we have developed  the mathematical model of the library server using  Markov birth – death process assuming that library system server system is based on exponential distribution. The model so developed by victimisation Chapman Kolmogorov differential equation and is solved by using Mathematica. The solution so obtained is analysed for various rates of failures and repair. The finding so obtained are discussed with the concerned authorities of the library to boost the efficiency of the library.

The focal point of this manuscript is to address the reliability analysis of Boiler unit in the Thermal power plant driven from coal. It is made up of six subunits laid out in series and parallel manner, alongwith some standby units. The system under consideration is modelled in transient state aided by Markov birth-death process and CAS Mathematica is deployed to solve the resulting complicated system of probabilistic equations arising out of 8 working states.