This book grew out of an attempt to describe a variety of tools that were developed over a period of years in IBM to analyze Integrated Circuit fail data. The selection presented in this book focuses on those tools that have a significant statistical or datamining component. The danger of describing sta tistical analysis methods is the amount of non-trivial mathematics that is involved and that tends to obscure the usually straigthforward analysis ideas. This book is, therefore, divided into two roughly equal parts. The first part contains the description of the various analysis techniques and focuses on ideas and experimental results. The second part contains all the mathematical details that are necessary to prove the validity of the analysis techniques, the existence of solutions to the problems that those techniques engender, and the correctness of several properties that were assumed in the first part. Those who are interested only in using the analysis techniques themselves can skip the second part, but that part is important, if only to understand what is being done.