This invention teaches further improvements in methods for forewarning of critical events via phase-space dissimilarity analysis of data from biomedical equipment, mechanical devices, and other physical processes. One improvement involves objective determination of a forewarning threshold (UFW), together with a failure-onset threshold (UFAIL) corresponding to a normalized value of a composite measure (C) of dissimilarity; and providing a visual or audible indication to a human observer of failure forewarning and/or failure onset. Another improvement relates to symbolization of the data according the binary numbers representing the slope between adjacent data points. Another improvement relates to adding measures of dissimilarity based on state-to-state dynamical changes of the system. And still another improvement relates to using a Shannon entropy as the measure of condition change in lieu of a connected or unconnected phase space.