ETL 1110-2-560
30 Jun 01
Appendix G: Non-Series-Parallel System Analysis
A complex system that is neither in series nor parallel is shown in Figure G-1. The reliability is evaluated
using the theorem on total probability:
RS(t) = RS(if X is working) RX(t) + RS(if X fails) (1 - RX(t))
(G-1)
B1
C1
A
B2
C2
Figure G-1. A non-series-parallel system
Select a critical component. In this case, select component A. The system can function with or without
it, and in each case the system resolves into a simpler system that is easily analyzed. If A works, it does
not matter if B1 or B2 is working. The system can then be represented by the reliability block diagram in
Figure G-2.
C1
C2
Figure G-2. Reduction of system with component A working
If component A does not work, the system can be reduced to Figure G-3.
B1
C1
B2
C2
Figure G-3. Reduction of system with component A not working
Figure G-2 is evaluated as follows:
RS(if A is working) = 1 {[1 - RC1(t)][1 - RC2(t)]}
(G-2)
G-1
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