Does the operating point of a series-parallel network of monotone resistors satisfy all resistor ratings?

An important issue in circuit design is whether every element operates within its rated values. For the particular case of a series-parallel network of monotone resistors (i.e., one ports) whose characteristic curves are continuous and monotonically increasing, at least within the ranges between their rated values, we present a rapid procedure for resolving this question. If at least one resistor operates outside of its ratings, our procedure will reveal this fact without having to determine the operating point of the entire network, or even of that resistor alone. On the other hand, if all elements operate within their ratings, our procedure ascertains that as well, while again avoiding a computation of the operating point of the entire network. This procedure can also be applied to series-parallel subnetworks N_SP of an arbitrary network N_SP but now it can only reveal whether N cannot have a within-ratings operating point because N_SP does not have one