System failure-frequency analysis using a differential operator

A method for obtaining the failure frequency of any system whose structure function is coherent is introduced. The relationship of the availability to the failure frequency can be expressed as a unique differential operator. In this way, regardless of the form of expression, the failure frequency can be obtained by applying the differential operator to the availability expression. Some reduction techniques are shown to be useful in evaluating failure frequency by means of this differential operator. If the reduction formulas are approximate rather than exact, it is generally difficult to apply the operator. This operator is tested on a special type of approximate reduction (the quadrilateral-star transformation). A numerical example for this reduction is presented