$9$ Consider the system shown in Figure $7\mathrm{.}13.$ Assume that the signal can flow only in the directions shown.

$($a$)$ Develop an equation for the reliability of this system.

$($b$)$ Use your equation to calculate the system reliability if all components have a reliability of $0\mathrm{.}9.$

$($c$)$ Plot the system mission reliability as a function of time if

${}_1={}_3={}_5={}_7={}_9=0\mathrm{.}001\frac{f}{h}r$

${}_2={}_4={}_6={}_8={}_{10}=0\mathrm{.}002\frac{f}{h}r$