Consider a component that is activated and functioning at time $t=0.$ Whenever the

component fails it is repaired. Let $T_1,T_2,$dots denote the successive lifetimes of the

component, and $D_1,D_2,$dots be the corresponding repair times $..$Let renewal be the event

when a repair is completed. Let $T_1$ follows exponential distribution with mean $\frac{1}{{}_1},$ and

successive failure times be independent following exponential distribution with mean $\frac{1}{{}_2}.$

Further let repair times be independent and identically distributed as exponential

distribution with mean $\frac{1}{}.$ Find point availability and limiting availability of the

component.