Figure 8.14 A functional
diagram of a power supply
to four electric motors: (A)
without redundancy and (B)
and m 2, and through the signal cable c 2, the temperature (pressure) reading will be
fed to comparator CD2.
The system will be operational whenever an st path through working compo-
nents exists in the reliability network shown in Figure 8.13B . The reliability
network shown in Figure 8.13B cannot be reduced to combinations of series, paral-
lel or series parallel arrangements. Telecommunication systems and electronic
control systems may also have very complex reliability networks, which cannot be
represented with series parallel arrangements.
Traditionally, reliability networks have been presented as networks with a single
start node s and a single terminal node t (Andrews and Moss, 2002; Billinton and
Allan, 1992; Blischke and Murthy, 2000; Ebeling, 1997; Hoyland and Rausand,
1994; Ramakumar, 1993). This traditional representation, however, is insufficient
to model the failure logic of some systems. There are systems for which the correct
representation of the logic of failure requires more than a single terminal node.
Consider for example the simple system with redundancy in Figure 8.14A , that
consists of a power supply PS, power cable (PC), block of four switches (S1, S2,
S3 and S4) and four electric motors M1, M2, M3 and M4.
Because the reliability of the switches and the reliability of the power cable is
often a problem (the power cable for example, can often be accidentally dam-
aged), these components can be duplicated. In other words, redundancy can be
introduced. In many safety critical applications, all electric motors must be oper-
ational on demand. Typical examples are fans or pumps cooling chemical reactors,
pumps dispensing water in the case of fire, life support systems, automatic shut-
down systems and control systems. The reliability on demand of the system shown
in Figure 8.14A can be improved significantly, by making cheap and low-reliability
components redundant (the power cable and the switches) ( Figure 8.14B ). For the
system shown in Figure 8.14B , the electric motor M 1 for example will still oper-
ate if the power cable PC or the switch S 1 fails because power supply will be
maintained through the alternative power cable PC 0 and the switch S 1 0 . The same