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This book intends to address the usual problem that arises when engineers' tries to draw conclusion base on the values obtained when an analysis is carried out. The principal components analysis (PCA) and Hotelling's T2 statistic are used in studying the clinker minerals of Portland Cement Company of Northern Nigeria (CCNN). The cement produced is considered to be a mixture of eight minerals, each being sensitive to the presence of fly ash. Effort was made in this book to show that the dependence on only one mineral in detecting fault or diagnosing noise was not effective but rather using the entire components such that each component's contribution to variation is being measured there by making a valid interpretation about fault. The book targets both the engineering and statistics students. To the Statistics students; it will intimate and equip them to know how relevance is the knowledge of statistics in other fields of human endeavor. To the Engineering students and likes, it will enlighten and educates them on how to draw a valid conclusion based on good decision making.