Assume that $m=0\mathrm{.}0002$ errors per hour, $n=0\mathrm{.}005$ failures per hour, $m=0\mathrm{.}05$ repairs per hour, and $n=0\mathrm{.}06$ repairs per hour. Calculate:

a$)$ The steady$-$state probability of system failure due to maintenance error?

b$)$ The system steady$-$state availability?

The system can fail due to preventive maintenance$-$related human error and nonhuman error. The values of human and nonhuman error rates are $0\mathrm{.}0006$ errors per hour and $0\mathrm{.}007$ failures per hour, respectively. Calculate the probability of $(1)$ the system normally? And $(2)$ failure due to maintenance error? And $(3)$ non$-$maintenance error? for a $200-$h mission?

Assume that $m=n=0.$ Develop an expression for the system mean time to failure