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Fluctuating rate coefficients are necessary in the mass-action rate laws of kinetic processes with disorder. Measuring the fluctuations of rate coefficients is a challenge, particularly for nonlinear rate laws. Here we present a measure of the total disorder in the kinetics of irreversible decay $A^i\to \textrm{products}$, $i=1,2,3,\ldots n$ governed by (non)linear rate equations. We measure the inequality between the time-integrated square of the rate coefficient (multiplied by the time interval of interest) and the square of the time-integrated rate coefficient. We apply this measure of the rate coefficient history to empirical models for static and dynamically disordered kinetics with $i\geq 2$, which shows and show  this inequality measures the cumulative deviation in rate coefficients from a constant value. The equality is a necessary and sufficient condition for the traditional rate laws with ``rate constants'' to hold for irreversible kinetic processes.