Failure Probability: Solved 0.08643

In summary, the failure probability for the valves in Q5 during the useful life period is calculated using an exponential distribution function with specific values for lambda. The probability of a loss of flow from the manifold within the first 3 years is found to be 0.08643.
  • #1
abba02
11
0
[SOLVED] Failure probability

1. Homework Statement [/b
The performance of the valves in Q5 has been assessed in more detail under conditions
closer to those experienced in-service and the distribution functions of the random time
to failure have been quantified. The useful life period, prior to wear-out, occurs from
installtion to 5years. During this period, all of the distribution functions are modeled
using an exponential distribution function of the form:
FT (t) = 1 − exp[−_λit] where i=1,2,3,4,5
If _λ1 = λ_2 = _λ3 = 0.05; λ_4 = 0.267; λ_5 = 0.189 (all in years−1), calculate the probability
of a loss of flow from the manifold sometime in the period (0,3)years.
ANSWER[P[F]=0.08643]

Homework Equations


FT (t) = 1 − exp[−_λit] where i=1,2,3,4,5

The Attempt at a Solution


ATTEMPT
Have tried to substitute .05 for lambada and 3 for t in the given equation but my answer is still very different from the given answer of 0.08643
 
Last edited:
Physics news on Phys.org
  • #2
The attempt at a solution:

V1,V2 AND V3 ARE IN SERIES AND SS1 ARE IN PARALLEL TO V4 AND V5

(PV1 OR PV2 OR PV3) AND PV4 AND PV5

FT (t) = 1 − exp[−_λit] where i=1,2,3,4,5

If _λ1 = λ_2 = _λ3 = 0.05; λ_4 = 0.267; λ_5 = 0.189 (all in years−1),

For PSS FT (t) =1- exp [-λ1+λ2+λ3*3] where t=3 = .36237

For PV4, FT (t) =1- exp [-λ4*3]=.55112

For PV5,FT (t) =1- exp [-λ5*3]= .43278

Therefore the probability of loss of flow from the manifold at time 3 years is

PSS1 AND PV4 AND PV5= .36237*.55112*.43278= .08643
 
  • #3
.

I would first check the calculations and assumptions made in the attempt at solving this problem. It is important to ensure that all variables and values are correctly substituted and that the correct equation is used. If the calculations and assumptions are correct, I would suggest trying a different approach or method to solve the problem. It may also be helpful to consult with colleagues or experts in the field to get their insights and perspectives on the problem. Additionally, I would recommend thoroughly reviewing the given information and understanding the concept of exponential distribution functions to better approach and solve the problem.
 

What is failure probability?

Failure probability is a measure of the likelihood that a system or process will fail to meet its intended objectives or specifications.

How is failure probability calculated?

The calculation of failure probability involves analyzing various factors such as the design of the system, the materials used, the environment in which it operates, and any potential external factors that may contribute to failure. This is typically done using statistical methods and models.

What does a failure probability of 0.08643 mean?

A failure probability of 0.08643 means that there is a 8.643% chance that the system or process will fail to meet its intended objectives or specifications. This is considered a relatively low probability, but it is not zero, so there is still some risk of failure.

How can failure probability be reduced?

Failure probability can be reduced by identifying and addressing potential weaknesses or vulnerabilities in the system or process, implementing quality control measures, and continuously monitoring and improving the system. It is also important to regularly review and update the system or process to account for changing conditions or new information.

What are some examples of failure probability in real-world situations?

Failure probability can be applied to a wide range of situations, from the reliability of mechanical systems in cars and airplanes to the success rates of medical treatments. It is also relevant in fields such as finance, where the probability of a company or investment failing can be assessed. It can also be used in project management to estimate the likelihood of a project being completed on time and within budget.

Similar threads

  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
2K
Replies
1
Views
2K
Replies
1
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
9
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
4
Views
4K
  • Calculus and Beyond Homework Help
Replies
2
Views
3K
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
1K
  • Calculus and Beyond Homework Help
Replies
3
Views
6K
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
3K
Back
Top