The book Replacement Models in Reliability is mainly intended for researchers in Applied Statistics and also for those interested in Stochastic Replacement Models. The aim of this book is to present Reliabilistic Replacement Models in a simple but precise context. This book presents the state-of-the-art in replacement models in reliability. Topics in replacement models include burn-in, warranty and maintenance. Special focus is given, where the repair times are non-negligible. Two dimensional version of the geometric process and the quasi renewal process have been developed and their properties are presented in a systematic manner. Explicit expressions for the long run average cost are derived. Cost structures are determined for multistate degenerative systems. Replacement models with varying cost structures are also presented. This book provides comprehensive insights into replacement models. Numerical illustrations are included to strengthen the theoretical results. The book is helpful for researchers in manufacturing engineering, industrial engineering and engineering management programs, as well as for researchers and engineers in the quality and reliability engineering.