1.An offshore platform consists of three large main power generators (MPGs), two operating and one spare (standby mode). The lifetime of each MPG follows the Weibull distribution with beta = 2.3 and theta = 40 years. In a given time, two MPGs are used, while third one can be used to replace a failed unit in 12 days with a cost of $ 5 million. The failure of each additional unit (beyond the one spare) requires the procurement and installation of a brand new transformer with a cost of $ 280 million. Estimate the failure probability of the system

and associated risk with the MPGs over the next 20 years of operation considering two scenarios: (i) spare MPG is available as good as new, and (ii) spare MPG is in failed state.