208
Chapter 4
Four parallel components
Rp = 4 exp[-2t] - 6 exp[-22t] + 4 exp[-32t] - exp[-42t]
(4.35)
Five parallel components
Rp = 5 exp[-2t] - l0 exp[-22t] + 10 exp[-3J, t] - 5 exp[-42t]
+ exp[-52t]
(4.36)
F. Reliability of Standby Components [4.24]
The standby unit (Fig. 4.15) is in parallel with a primary unit, however, the
standby is switched on only when the primary unit fails. The 2 rates are
the same for both units and all standbys.
The Poissons distribution yields an identity which applies
I
2t (2t) 2 .
(20"] exp[-2t]
1
(4.37)
+...+
When n = 1 (one standby)
R = [1 + 2t] exp[-2t]
(4.38)
n = 2 (two standbys with a switch to primary)
R = 1 + ~ + ~-.~ J exp[-,lt]
(4.39)
for n units as standbys
~,t (2/) 2
+ (20"] exp[_2t
]
(4.40)
R=
+...
J
EXAMPLE 4.4. A water pump station Fig. 4.16 has been set up for
high reliability.
1. Calculator R(t) for the system
~ -~1 Standbyl
Figure 4.1ft. Standby systems.