This book, from the perspective of reliability science construction, proposes a new theory called BELIEF RELIABILITY theory on the basis of probability theory, uncertainty theory and chance theory. The main topics include the philosophical basis of reliability science, the principles of reliability science, the criteria of reasonable reliability metrics and the basic theoretical framework and methodology of belief reliability theory. In this book, the belief reliability metric, analysis, design and evaluation methods will provide readers with a brand-new perspective on reliability applications and uncertainty quantification.