6.4.4.2.3 __Logic Diagram Modeling
Method__

Logic diagrams may also be used to prepare a reliability
mathematical model from a reliability block diagram. This method is applicable
to single functioned and multifunctioned systems. This method is more tedious
than the conventional probability method but is a short cut method for the
Boolean truth table approach in combining terms to simplify the reliability
equation.

The logic diagram procedure for a single function system is to
translate the reliability block diagram into a switching network. A closed
contact represents equipment success, an open contact equipment failure. Each
complete path of contacts represents an alternate mode of operation. Each
equipment that is required for each alternative mode of operation is
identified by a contact along a path. All paths terminate at the same point
(success). The logic diagram is developed so that all paths are mutually
exclusive; by use of a few simple manipulations, the amount of effort involved
over the Boolean truth table method can be shortened.

Logic diagrams for series, parallel, and series-parallel
diagrams are easy to draw as shown in Table 6.4-4.

For complex configurations the procedure is to reduce the
reliability diagram to a series-parallel configuration by successively
splitting the diagram into subdiagrams by removing one equipment and replacing
it with a short circuit and an open circuit. An example will clarify the
procedure.