EXAMPLE $9\mathrm{.}12.$ A system comprises four identical modules each having a time$-$to$-$ failure distribution that is Weibull with beta $=1\mathrm{.}4$ and theta $=200$ hr$.$ Repair time is lognormal with t med $=2\mathrm{.}5$ hr and s $=0\mathrm{.}87$ Assuming that a failure results in the failed unit's replacement with an identical unit $($renewal process$)$ and assuming that an equilibrium is achieved over a $5-$yr period, find the expected number of repairs $($failures$).$