in failure time distributions for systems modeled by finite chains. This introductory chapter attempts to provide an over- view of the material and ideas covered. The presentation is loose and fragmentary, and should be read lightly initially. Subsequent perusal from time to time may help tie the mat- erial together and provide a unity less readily obtainable otherwise. The detailed presentation begins in Chapter 1, and some readers may prefer to begin there directly. O.l. Time-Reversibility and Spectral Representation. Continuous time chains may be discussed in terms of discrete time chains...