Probabilit y of a valve falling in a time period

AI Thread Summary
The discussion focuses on calculating the probability of valve failures over a specified time period using the equation N = 0.001 X t^1.26. Participants are attempting to derive the probability of a valve failing within 24 months, with an expected answer of 0.4414, but are struggling to reach this conclusion using density and cumulative distribution functions. Additionally, the second part of the problem involves determining the likelihood that an installation with three unrelated valves remains free of failures during the same period, with the answer being 0.1743. There is confusion regarding the specific time period referenced in the calculations. The thread highlights challenges in applying statistical methods to real-world failure rates.
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)
 
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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
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
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Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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