Problem 10E

A system consists of two subsystems connected in series, as shown in the following schematic illustration. Each subsystem consists of two components connected in parallel. The AB subsystem fails when both A and B have failed. The CD subsystem fails when both C and D have failed. The system fails as soon as one of the two subsystems fails. Assume that the lifetimes of the components, in months, have the following distributions: A: Exp(l), B: Exp(0.l), C: Exp(0.2), D: Exp(0.2).

a. Generate, by simulation, a large number (at least 1000) of system lifetimes.

b. Estimate the mean system lifetime.

c. Estimate the median system lifetime.

d. Estimate the probability that the system functions for more than 6 months.

e. Estimate the 90th percentile of system lifetimes.

f. Estimate the probability that the AB subsystem fails before the CD subsystem does.

Solution:

Step 1of 4:

A system consist of two subsystems connected in series. Each subsystem consist of two components connected in parallel. Subsystem 1 and 2 fails if both components of the system fails. The system fails if one of two subsystem fails. The lifetime of components in months have distributed as A: exp(1) , B: exp(0.1) ,C: exp(0.2), D: exp (0.2).

The system fails if one of two subsystem fails. Let X1 , X2 and Y1,Y2 denote the lifetime of components A,B, C, D respectively. And L1 and L2 are the lifetime of both subsystem. So the lifetime of the system can be represented as L= Min (L1,L2).