While Model-based Monitoring systems based on state observer theory have shown much promise in the laboratory, they have not been widely accepted by industry because, inpractice, these systems often have poor performance with respect to accuracy, band-width, reliability(false alarms), and robustness. In this paper, the linitations of the deterministic discrete-time state observer are investigated quantitatively from the machine monitoring viewpoint. The limitations in the transient and steady-state observer performance are quantified as estimation error bounds from which performance indices are selected. Each index represents the conditioning of the corresponding performance. By utilizing matrix norm theory, an unified main index is determined, that dominates all the indices. This index could from the basis for an observer design methodology that should improve the performance of model-based monitoring systems.