The Probability of an “Excessive Nonfunctioning Interval”

Abstract

A “component” is defined as a zero-one function of time. The probability that this function is not continuously equal to “one” for longer than a stated value (the “excessive nonfunctioning interval”) anywhere in a given time period is derived assuming a common type of Markov process. This probability is found as the probability of “first passage” of a derived stochastic process.