Probabilit y of a valve falling in a time period

In summary, the given equation N = 0.001 X t^1.26 can be used to calculate the probability of a valve failing within a time period of 0 to 24 months. This can be done using either the density function or the cumulative distribution function, with N being represented as lambda. The answer to the first part of the question is 0.4414. For the second part, if the installation contains 3 valves in unrelated parts of the plant, the probability of the installation being free of valve failure over the same time period is 0.1743.
  • #1
estado3
13
0

Homework Statement



A large population of nominally identical "fail to close" control valves are put into service on the same day on similar installations. The number of valve failures per month N was recorded over time and shown to be given approximately by the following equation

Calculate the probability that the valve fails in the time period (0,24) months

Homework Equations



N = 0.001 X t^1.26 (failures/month)

The Attempt at a Solution



have tried it with the density function and the cumulative distribution function with N being lambda but still far away from the ans of 0.4414

The second part of the question also has be stumped as it states if the installation contains 3 valves in unrelated parts of the plant, calculate the probability that the installation is free of valve failure over the same time period (ans is 0.1743)
 
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  • #2
estado3 said:

Homework Statement



A large population of nominally identical "fail to close" control valves are put into service on the same day on similar installations. The number of valve failures per month N was recorded over time and shown to be given approximately by the following equation

Homework Equations



N = 0.001 X t^1.26 (failures/month)

The Attempt at a Solution



have tried it with the density function and the cumulative distribution function with N being lambda but still far away from the ans of 0.4414
What was the question that 0.4414 is the answer to? I see no question given here!

The second part of the question also has be stumped as it states if the installation contains 3 valves in unrelated parts of the plant, calculate the probability that the installation is free of valve failure over the same time period (ans is 0.1743)
What time period?
 
  • #3
edited
 

1. What is the probability of a valve falling within a specific time period?

The probability of a valve falling within a specific time period depends on several factors such as the condition of the valve, the environment it is in, and the frequency of use. These factors can affect the likelihood of a valve falling and should be considered when calculating the probability.

2. How do you calculate the probability of a valve falling?

The probability of a valve falling can be calculated using the formula P = (n/N) x 100, where P is the probability, n is the number of times the valve has fallen in the past, and N is the total number of times the valve has been used. This formula assumes that the probability of a valve falling is independent of previous occurrences.

3. Can you predict when a valve will fall based on probability?

No, probability can only give an estimate of the likelihood of a valve falling. It cannot predict when a valve will fall with certainty. Other factors such as wear and tear, environmental conditions, and maintenance can also affect the likelihood of a valve falling and should be taken into account.

4. How can probability be used to prevent valve failure?

By calculating the probability of a valve falling, engineers and maintenance professionals can identify high-risk valves and prioritize them for inspections and maintenance. This can help prevent valve failure and ensure the safe operation of systems.

5. Is the probability of a valve falling the same for all valves?

No, the probability of a valve falling can vary depending on the type of valve, its condition, and its intended use. Some valves may have a higher likelihood of falling due to their design or the environment they are in. It is important to consider these factors when calculating the probability of a valve falling.

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