Probability Series System Failure Rate Question

[rzn972]

Homework Statement

A circuit board has 20 integrated circuits(ic) with constant failure rate of 5 chips per million per hour (5FITs), 300 resistors(r) with a constant failure rate of 20 chips per million per 1000 hour (20 FIT), and 10 diodes(d) with a constant failure rate of 10 chips per million per 1000 hour (10 FIT). All of these components must work for the circuit to work. The circuit is connected in a series configuration. At some arbitrary time t, the circuit works properly. What is the probability that the circuit board will be working 5000 hours later?

Homework Equations

The Attempt at a Solution

So the probability of failures are P(ic failing)= 25/1000000 P(d fail)= 100/1000000 P(r fail)= 50/1000000. and the probability of a success is 1- (failure). In a series system, all components must succeed for the system to succeed. So just multiply the probability of successes? Does this look right? Or does the failure rate include exponential functions? (e^-lambda t). Thank you so much!

 

[Ray Vickson]

Homework Statement

A circuit board has 20 integrated circuits(ic) with constant failure rate of 5 chips per million per hour (5FITs), 300 resistors(r) with a constant failure rate of 20 chips per million per 1000 hour (20 FIT), and 10 diodes(d) with a constant failure rate of 10 chips per million per 1000 hour (10 FIT). All of these components must work for the circuit to work. The circuit is connected in a series configuration. At some arbitrary time t, the circuit works properly. What is the probability that the circuit board will be working 5000 hours later?

Homework Equations

The Attempt at a Solution

So the probability of failures are P(ic failing)= 25/1000000 P(d fail)= 100/1000000 P(r fail)= 50/1000000. and the probability of a success is 1- (failure). In a series system, all components must succeed for the system to succeed. So just multiply the probability of successes? Does this look right? Or does the failure rate include exponential functions? (e^-lambda t). Thank you so much!

What, exactly, do the symbols P(ic failing), P(d fail) and P(r fail) stand for? I could not get your numbers.

You need to start with the failure (or non-failure) probabilities of individual integrated circuits, resistors and diodes---being careful to choose common units for all three---then find out the failure (or non-failure) rates of 20 integrated circuits, 300 resistors and 10 diodes, over some fixed time period like 1 hour. Once you have that you can go on to look at the 5000-hour problem.