The object of this book is to present a systematic method for auxiliary signal design in fault detection and diagnosis. It covers systems that can be represented by linear or linearised multiple-input, multiple-output stochastic models. It is very illustrative since each new concept is demonstrated with simple examples and plots. Some fundamental problems in change detection have been investigated. A basic knowledge of probability theory, statistical inference, matrix and control theory is required. Postgraduates and researchers will find it an interesting reference to fault detection and test signal design. The book can also be used as a tutorial material for final year undergraduates, especially those who work on a project related to test signal designs, fault detection or modeling.