System Reliability

Exercise $6$

Consider a two engine plane in a one$-$out$-$of$-$two logic configuration. When both engines A and $B$ are fully energized they share the total load and the failure time densities are $f_A(t)$ and $f_B(t).$ If either one fails, the survivor must carry the full load and its failure density becomes $g_A(t)$ or $g_D(t).$

Derive an expression for the reliability of the system $R(t).$

Find the reliability if

$f_A(t)=f_B(t)=e^{-t}$

$g_A(t)=g_B(t)=k{e}^{-\text{k}\text{i}\text{t}},k>1$