Monotonicity of likelihood support bounds for system failure rates

Simple expressions are derived for lower and upper support limits for the system failure probability of a series or parallel system based on binomial failure data. These limits are shown to be non-decreasing functions of the number of failures of any component for a fixed number of tests and non-increasing functions of the number of tests of any component for a fixed number of failures. This logically essential property, not shared by many other approximate upper limits, is critical to the efficient computation of Buehler bounds, using support limits as an ordering function.