$$

$($

$$

$)$

$=$

$$the break rate in breaks per mile per year and

$$

$=$

$$the age of the pipe in years.

An engineer wishes to design a new water distribution system as shown in Figure

$2$

$.$

$4$

$5$

$.$

$($

a

$)$

$$What is the reliability of the system after two years of service?

$($

Reliability is measured as the probability of successful water delivery from node

$1$

$$to node

$6$

$.$

$)$

$($

b

$)$

$$What is the mean time to failure?

$($

c

$)$

$$What do you suggest to ensure a reliability of

$0$

$.$

$9$

$8$

$$after

$2$

$$years of service?

FIGURE

$2$

$.$

$4$

$5$

$$A new water distribution system.