Handbook of Civil Engineering Calculations

FIGURE 27. System with components in series.

components, C 1 and C 2 , and let the subscripts 1, 2, and S refer to C 1 , C 2 , and the sys-
tem, respectively. If the components are arranged in series, as shown in Fig. 27, the sys-
tem is operating only if both components are operating. Thus, the reliability of the sys-
tem is

Rs(t) = Rl(t)R 2 (t) (17)

If the components are arranged in parallel, as shown in Fig. 28, the system is operating if
either component is operating. To express it another way, the system fails if both compo-
nents fail, and

I-Rs(f) = [l-*i(0][l -* 2 (0]

or

Rs(f)=\-[\-Rl(tW-R2(f)] (18)

Equations 17 and 18 can be generalized to include any number of components. A system

having components in series has a reliability less than that of any component; a system

having components in parallel has a reliability greater than that of any component.

DEVICE WITH NEGATIVE-EXPONENTIAL

LIFE SPAN

A certain type of earth satellite has a negative-exponential life span with a mean value of

15 months. Four satellites of this type are launched simultaneously. If X denotes the num-

ber of satellites that remain in orbit at the expiration of 1 year, establish the probability

distribution of X.

FIGURE 28. System with components in parallel.