Fault detection and isolation in stochastic systems is typically model-based, meaning fault-indicating residuals are generated based on measurements and compared to equivalent mathematical system models. The residuals often exhibit Gaussian properties or can be transformed into a standard Gaussian framework by means of the asymptotic local approach. The e_ectiveness of the fault diagnosis depends on the model quality, but an increasing number of model parameters also leads to redundancies which, in turn, can distort the fault isolation. This occurs, for example, in structural engineering, where residuals are generated by comparing structural vibrations to the output of digital twins. This article proposes a framework to _nd the optimal parameter clusters for such problems. It explains how the optimal solution is a compromise, because with an increasing number of clusters, the fault isolation resolution increases, but the detectability in each cluster decreases, and the number of false alarms changes. To assess these factors during the clustering process, criteria for the minimum detectable change and the false-alarm susceptibility are introduced and evaluated in an optimization scheme.