Tolerance Limits for the Output of Systems of Cascaded Elements

A methodology is given for analyzing the cumulative effect of a cascaded system of transducers on an input signal, where the transducers themselves activate peripheral activities, and are designed to leave the input signal unchanged, except for random magnification perturbations. Relationships are developed which relate component tolerances with the system output tolerance, and hence with system reliability. Examples are given which illustrate the type of problems that are amenable to solution by the general methodology developed, in electronics applications and otherwise. They include the determination of system output tolerances from given component tolerances, a system reliability determination when the input represents a binary digit, and a determination of minimal component precisions that are required to achieve given system tolerances. Care has been given to present the basic methodology in a complete, detailed, and self-contained manner.