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3. Consider the problem of computing reliability of so-called seriesparallel systems. A series system is one in which all components are so interrelated that the entire system will fail if any one of its components fails. On the other hand, a parallel system is one that will fail only if all of its components fail. Ifa system consists of n components, and for i = 1, 2, , n, we dene events Ai = \"component i is mctioning properly.\" Let the reliability, Ri, of component i be dened as the probability that the component is functioning properly; then Ri = P(Ai). Find the system reliability of: a. The Series System (Hint: Use of intersection of the independent events Ais). b. The Parallel System (Hint: First nd the failure of the system by using intersection of complements of the independent events Ais, as the parallel system fails if all 11 components will fail. Finally, subtract the result from 1 to get the reliability) 4. Consider a seriesparallel system of 11 serial stages where stage i consists of ni identical components in parallel. Let the reliability of each component at stage i be Ri. Assuming that all components are independent, show that the system reliability Rspis givenby! R3}? = H[1(1 RI: ) 111'] TI. i=1 Moreover, nd the reliability of the system shown in Figure, consisting of ve stages, with nl = n2 = n5 =1, and n3 = 3 and n4 = 2. Also, R1 = 0.95, R2 = 0.99, R3 = 0.70, R4 = 0.75, and R5 = 0.9 H (Hint: Apply the results of Problem (3) to prove the given Eqn \"MHEE