This chapter provides a formal decision software tool in the so-called dominant feature identification (DFI) framework, using matrix theory to extract the dominant features thereby enabling failure prediction and fault isolation. The DFI decision-making tool is based on a formal mathematical approach that selects dominant features using the singular value decomposition (SVD) of real-time measurements. The chapter utilizes SVD to decompose the inner product matrix of collected data from the sensors monitoring the wear of an industrial cutting tool. It reviews the theoretical preliminaries of principal component analysis using SVD. The chapter presents the usage of a dynamic auto-regressive moving average with exogenous model with extended least squares for tool wear prediction in the new DFI framework. DFI and neural networks are used in a two-stage framework for industrial fault detection and isolation applications. The chapter also provides detailed discussions on the improved experimental setup with the acoustic emission sensor and corresponding calculation of dominant features.