# Probability Series System Failure Rate Question

• rzn972
In summary, the probability of failure for an integrated circuit is 25 out of 1 million, for a diode it is 100 out of 1 million, and for a resistor it is 50 out of 1 million. Using the failure rates, the probability of success for each component can be calculated as 1 minus the failure rate. In a series configuration, all components must succeed for the circuit to work. Therefore, the overall probability of the circuit board working 5000 hours later can be found by multiplying the individual probabilities of success for each component. The failure rates may include exponential functions, such as e^-lambda t, which should be taken into account when calculating the probabilities.
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?

## 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!

Last edited:
rzn972 said:

## 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?

## 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.

## 1. What is a probability series system failure rate?

A probability series system failure rate is a measure of the likelihood or chance that a series of components in a system will fail within a given time frame. It takes into account the individual failure rates of each component as well as the probability of multiple failures occurring in sequence.

## 2. How is the probability series system failure rate calculated?

The probability series system failure rate is calculated by multiplying the individual failure rates of each component in the series. For example, if Component A has a failure rate of 0.1 and Component B has a failure rate of 0.2, the probability series system failure rate would be 0.1 x 0.2 = 0.02 or 2%.

## 3. How is the probability series system failure rate different from the individual component failure rates?

The probability series system failure rate takes into account the interaction between components in a system, while individual component failure rates only consider the probability of a single component failing. The probability series system failure rate gives a more accurate estimate of the overall system reliability.

## 4. Can the probability series system failure rate be used to predict the exact timing of system failures?

No, the probability series system failure rate is a statistical measure and cannot predict the exact timing of system failures. It provides an estimate of the likelihood of failure within a given time frame, but the actual timing of failures can vary.

## 5. How can the probability series system failure rate be used in decision making?

The probability series system failure rate can be used to inform decision making, especially in risk management. By understanding the likelihood of system failures, engineers and managers can make informed decisions about maintenance schedules, replacement plans, and system design improvements to improve overall reliability and reduce potential risks.

• Calculus and Beyond Homework Help
Replies
4
Views
3K
• Calculus and Beyond Homework Help
Replies
17
Views
1K
• Calculus and Beyond Homework Help
Replies
9
Views
1K
• Calculus and Beyond Homework Help
Replies
5
Views
2K
• Precalculus Mathematics Homework Help
Replies
4
Views
794
• Engineering and Comp Sci Homework Help
Replies
5
Views
1K
• Calculus and Beyond Homework Help
Replies
6
Views
2K
• Mechanical Engineering
Replies
8
Views
893
• Calculus and Beyond Homework Help
Replies
1
Views
2K
• Set Theory, Logic, Probability, Statistics
Replies
9
Views
2K