Question

a system contains two components, C and D

9. A system contains two components, C and D, connected in parallel as shown in the diagram. Assume C and D function independently. For the system to function, either C or D must function.

Answer 1

a) P( System function) when any C and D functions

P( System Functions) = (1-0.08)+(1-0.12)-(1-0.08)*(1-0.12) = 0.9904

b)  (1-p)+(1-p)-(1-p)*(1-p) = 0.99

p = 0.1

c) Parrellel system function if all works

(1-p)(1-p)(1-p) = 0.99

p = 0.00334

Answer 2

P(CU D U THIRD) = P(C) + P(D) + P(THIRD) - P(C^ D) - P(D^T) - P(C^T) + P(C^D^THIRD)

 = (1-p)+(1-p)+(1-p)-(1-p)(1-p)-(1-p)(1-p)-(1-p)(1-p)+[(1-p)(1-p)(1-p)]