The k-out-of-n reliability configuration is a form of parallel reliability. The k-out-of-n system requires that at least k components succeed out of the total n parallel components for the system to succeed. For example, if an airplane has four engines and the design of the aircraft is such that at least two engines are required to function for the aircraft to remain airborne, then the engines are a k-out-of-n configuration, where k = 2 and n = 4. If k = 1 then we have the usual parallel structure. Using Monte Carlo simulation and/or explicit analytic calculations, show that as the number of units required to keep the system functioning approaches the total number of units in the system, the system's behavior tends towards that of a series system. And if the number of units required is equal to the number of units in the system, it is a series system. In other words, show (a) that a series system of statistically independent components is an n-out-of-n system and (b) that a parallel system of statistically independent components is a 1-out-of-n system. Use the following component reliabilities for your demonstration. Parallel System Component 1 0.85 Component 2 0.9 Component 3 0.75 Component 4 0.95 Component 5 0.8 Component 6 0.7 Series System Component 1 Component 2 Component 3 0.85 0.9 0.75 uires that at least k mple, if an airplane has tion for the aircraft to then we have the usual units required to keep the ends towards that of a m, it is a series system. In of-n system and (b) that a Series System Component 4 Component 5 Component 6 0.95 0.8 0.7