The second reduction requires combining components 1,2 and 6 in series to give equivalent component 7.Using Equations 11.11 give
The final reduction requires combining components 5 and 7 in parallel to give equivalent component 8 which then represents the system indices. Using Equations 11.15 to 11.18 gives
This example shows that a series/parallel system can be evaluated by sequential application of the series and parallel equations. This method however cannot be used directly if the system is more complex, i.e. a non-series/parallel configuration such as the bridge network shown in Figure 5.1. Some authors [32,33] have suggested that such a network can be transformed into one containing only series/parallel branches using a method known as the star-delta transformation. This method can become quite tedious and the minimal cut set technique is eliminates the need for complicated transformation, and it directly indicate the predominant failure modes of the system. The importance of retaining a physical appreciation of the system and its failure modes is a fundamental requirement in overall system reliability evaluation.
11.5 Minimal cut set/failure modes approach
The minimal cut set method was described in detail in Chapter 5 and will not be discussed at length here. However, it should be recalled that it enables a reliability network, expressed in terms of minimal cut sets, to be deduced from the system operational logic and/or system network diagram. This reliability network consists of a number of minimal cut sets connected in series and each cut set consists of a number of components connected in parallel.