  McDiarmid's inequality has recently been proposed as a tool for setting
margin requirements for complex systems. If $F$ is the bounded output of a
complex system, depending on a vector of $n$ bounded inputs, this inequality
provides a bound $B_F(\epsilon)$, such that the probability of a deviation
exceeding $B_F(\epsilon)$ is less than $\epsilon$. I compare this bound with
the absolute bound, based on the range of $F$. I show that when $n_{eff}$, the
effective number of independent variates, is small, and when $\epsilon$ is
small, the absolute bound is smaller than $B_F(\epsilon)$, while also providing
a smaller probability of exceeding the bound, i.e., zero instead of $\epsilon$.
Thus, for $B_F(\epsilon)$ to be useful, the number of inputs must be large,
with a small dependence on any single input, which is consistent with the usual
guidance for application of concentration-of-measure results. When the number
of inputs is small, or when a small number of inputs account for much of the
uncertainty, the absolute bounds will provide better results. The use of
absolute bounds is equivalent to the original formulation of the method of
Quantification of Margins and Uncertainties (QMU).
