Consider the following structure with component C1 with reli

Consider the following structure with component C_1 with reliability R_1 in series with component C_2 with reliability R_2 and the two are in parallel with component C_3 with reliability R_3. The system is in series with another system that consists of three parallel components C_4, C_5 and C_6 with reliabilities R_4, R_5 and R_6 respectively. What is the reliability of the composite system in terms of R_1, R_2, R_3, R_4. R_5 and R_6?

Solution

R = P( ((C1 and C2) or (C3)) and (C4 or C5 or C6) )

= P(((C1 and C2) or (C3)) P(C4 or C5 or C6)

= [P(C1)P(C2) + P(C3) - P(C1)P(C2)P(C3)] [P(C4) + P(C5) + P(C6) - P(C4)P(C5) - P(C5)P(C6) - P(C4)P(C6) + P(C4)P(C5)P(C6)]

= [R1 R2 + R3 - R1 R2 R3][R4 + R5 + R6 - R4 R5 - R5 R6 - R4 R6 + R4 R5 R6] [answer]