Modeling physical and natural phenomenon/process has been a necessity for the human beings. Initially mathematical models were used for modelling various natural phenomenon. Later, after realising the presence of uncontrollable errors, they tried to model it using the concept of probability. Modelling problems became complicated when there is dependence between these errors. Markov chains are being used widely to model various problems where there is dependence between the observations. In this monograph, some applications of the Markov chains in reliability modelling, quality assurance and distribution theory are considered. Here stochastic ageing is modeled using the Cox regression model and the Phase-Type distributions. This book can inspire those who have a basic knowledge about Markov Chains.