A system consists of two subsystems connected in series,

Chapter 4, Problem 10E

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

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(1), B: Exp(0.1), 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.

Questions & Answers

QUESTION:

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(1), B: Exp(0.1), 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.

ANSWER:

Step 1 of 4

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

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

Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back