Probabilit y of a valve falling in a time period

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SUMMARY

The discussion revolves around calculating the probability of valve failures for a population of "fail to close" control valves over a specified time period of 0 to 24 months. The failure rate is modeled by the equation N = 0.001 X t^1.26, where N represents the number of failures per month. The calculated probability of at least one valve failure in this time frame is 0.4414. Additionally, for an installation with three valves, the probability that none of the valves fail during the same period is determined to be 0.1743.

PREREQUISITES
  • Understanding of probability theory and statistical distributions
  • Familiarity with cumulative distribution functions (CDF)
  • Knowledge of failure rate modeling in engineering contexts
  • Basic calculus for evaluating integrals related to probability
NEXT STEPS
  • Study the Poisson distribution and its applications in failure analysis
  • Learn about the derivation and application of cumulative distribution functions
  • Explore reliability engineering concepts related to valve failure rates
  • Investigate the use of statistical software for modeling failure probabilities
USEFUL FOR

Engineers, reliability analysts, and students studying probability and statistics in engineering contexts will benefit from this discussion, particularly those focused on equipment failure analysis and reliability assessments.

estado3
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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)
 
Last edited:
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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?
 
edited
 

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