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Any physiochemical variable (Ym) is always determined from certain measuredvariables {Xi}. The uncertainties {ui} of measuring {Xi} are generally a prioriensured as acceptable. However, there is no general method for assessinguncertainty (em) in the desired Ym, i.e. irrespective of whatever might be itssystem-specific-relationship (SSR) with {Xi}, and/ or be the causes of {ui}. Wehere therefore study the behaviors of different typical SSRs. The study showsthat any SSR is characterized by a set of parameters, which govern em. That is,em is shown to represent a net SSR-driven (purely systematic) change in ui(s);and it cannot vary for whether ui(s) be caused by either or both statisticaland systematic reasons. We thus present the general relationship of em withui(s), and discuss how it can be used to predict a priori the requirements foran evaluated Ym to be representative, and hence to set the guidelines fordesigning experiments and also really appropriate evaluation models. Say: Y_m=f_m ({X_i}_(i=1)^N), then, although: e_m= g_m ({u_i}_(i=1)^N), "N" is not a keyfactor in governing em. However, simply for varying "fm", the em isdemonstrated to be either equaling a ui, or >ui, or even <ui. Further, thelimiting error (d_m^(Lim.)) in determining an Ym is also shown to be decided by"fm" (SSR). Thus, all SSRs are classified into two groups: (I) the SSRs thatcan never lead "d_m^(Lim.)" to be zero; and (II) the SSRs that enable"d_m^(Lim.)" to be zero. In fact, the theoretical-tool (SSR) is by pros andcons no different from any discrete experimental-means of a study, and hasresemblance with chemical reactions as well.

The Theory of Uncertainty for Derived Results: Properties of Equations Representing Physicochemical Evaluation Systems