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We recently described the performance characteristics of the exponentially adjusted moving mean (EAMM), a patient-data, moving block mean procedure, which is a generalized algorithm that unifies Bull’s algorithm and the classic average of normals (AON) procedure. Herein we describe the trend EAMM (TEAMM), a continuous signal analog of the EAMM procedure related to classic trend analysis. Using computer simulation, we have compared EAMM and TEAMM over a range of biases for various sample sizes (N or equivalent smoothing factor α) and exponential parameters (P) under conditions of equivalent false rejection (fixed on a per patient sample basis). We found optimal pairs of N and P for each level of bias by determination of minimum mean patient samples to rejection. Overall optimal algorithms were determined through calculation of undetected lost medical utility (ULMU), a novel function that quantifies the medical damage due to analytic bias. The ULMU function was calculated based on lost test specificity in a normal population. We found that optimized TEAMM was superior to optimized EAMM for all levels of analytic bias. If these observations hold true for non-Gaussian populations, TEAMM procedures are the method of choice for detecting bias using patient samples or as an event gauge to trigger use of known-value control materials.