Template:Ipl ex stat prop sum: Difference between revisions

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(Created page with '===IPL-Exponential Statistical Properties Summary=== <br> ====Mean or MTTF==== The mean, <math>\overline{T},</math> or Mean Time To Failure (MTTF) for the IPL-exponential relat…')
 
 
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===IPL-Exponential Statistical Properties Summary===
#REDIRECT [[Inverse_Power_Law_(IPL)_Relationship#IPL-Exponential]]
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====Mean or MTTF====
The mean,  <math>\overline{T},</math>  or Mean Time To Failure (MTTF) for the IPL-exponential relationship is given by:
 
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::<math>\begin{align}
  & \overline{T}= & \mathop{}_{0}^{\infty }t\cdot f(t,V)dt=\mathop{}_{0}^{\infty }t\cdot K{{V}^{n}}{{e}^{-K{{V}^{n}}t}}dt \\
& = & \frac{1}{K{{V}^{n}}} 
\end{align}</math>
 
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Note that the MTTF is a function of stress only and is simply equal to the IPL relationship (which is the original assumption), when using the exponential distribution.
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====Median====
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The median,  <math>\breve{T},</math> for the IPL-exponential model is given by:
 
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::<math>\breve{T}=0.693\frac{1}{K{{V}^{n}}}</math>
 
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====Mode====
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The mode,  <math>\tilde{T},</math> for the IPL-exponential model is given by:
 
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::<math>\tilde{T}=0</math>
 
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====Standard Deviation====
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The standard deviation,  <math>{{\sigma }_{T}}</math> , for the IPL-exponential model is given by:
 
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::<math>{{\sigma }_{T}}=\frac{1}{K{{V}^{n}}}</math>
 
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Latest revision as of 23:02, 15 August 2012

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