(3) *Complex system models. *Complex systems can be represented as a series-parallel combination or

a non-series-parallel configuration. A series-parallel RBD is shown in Figure 9. This type of system is

analyzed by breaking it down into its basic parallel and series modules and then determining the

reliability function for each module separately. The process can be continued until a reliability function

for the entire system is determined. The reliability function of Figure 9 would be evaluated as follows:

(19)

(20)

(21)

A non-series-parallel system is shown in Figure 10. One method of analyzing non-series-parallel systems

uses the following general theorem:

(22)

The method lies in selecting a critical component (X) and finding the conditional reliability of the system

with and without the component working. The theorem on total probability is then used to obtain the

systems reliability (see Appendix G).