Consider the following structure with component C1 with reli

Consider the following structure with component C1 with reliability R1 in series with component C2 with reliability R2 and the two are in parallel with component C3 with reliability R3. The system is in series with another system that consists d three parallel components C4,C5 and C6 with reliabilities R4. R5and R6 respectively is the reliability of the composite system in terms of R1, R2, R3, R4, R5 and R6?

Solution

C1 and C2 are in series :

Therefore there Req = R1R2

Now R1R2 and C3 are in parallel.

Therefore, Req of left half of syatem = 1 - (1-R1R2)(1-R3)

Now,

C4,C5 and C6 are in parallel:

Therefore , their Req = 1 - (1-R4)(1-R5)(1-R6)

Since,

Left half and right half of system are in series:

Req (System) =  (1 - (1-R1R2)(1-R3)) * ( 1 - (1-R4)(1-R5)(1-R6))

= 1 - (1-R4)(1-R5)(1-R6) - (1-R1R2)(1-R3) + (1-R1R2)(1-R3)(1-R4)(1-R5)(1-R6) Answer