This book applies traditional reliability engineering methods to prognostics and health management (PHM), looking at remaining useful life (RUL) and its dynamics, to enable engineers to effectively and accurately predict machinery and systems useful lifespan. One of the key tools used in defining and implementing predictive maintenance policies is the RUL indicator. However, it is essential to account for the uncertainty inherent to the RUL, as otherwise predictive maintenance strategies can be incorrect. This can cause high costs or, alternatively, inappropriate decisions. Methods used to estimate RUL are numerous and diverse and, broadly speaking, fall into three categories: model-based, data-driven, or hybrid, which uses both. The author starts by building on established theory and looks at traditional reliability engineering methods through their relation to PHM requirements and presents the concept of RUL loss rate. Following on from this, the author presents an innovative general method for defining a nonlinear transformation enabling the mean residual life to become a linear function of time. He applies this method to frequently encountered time-to-failure distributions, such as Weibull and gamma, and degradation processes. Latest research results, including the author’s (some of which were previously unpublished), are drawn upon and combined with very classical work. Statistical estimation techniques are then presented to estimate RUL from field data, and risk-based methods for maintenance optimization are described, including the use of RUL dynamics for predictive maintenance. The book ends with suggestions for future research, including links with machine learning and deep learning. The theory is illustrated by industrial examples. Each chapter is followed by a series of exercises. FEATURES Provides both practical and theoretical background of RUL Describes how the uncertainty of RUL can be related to RUL loss rate Provides new insights into time-to-failure distributions Offers tools for predictive maintenance This book will be of interest to engineers, researchers and students in reliability engineering, prognostics and health management, and maintenance management.