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| ===IPL-Exponential Statistical Properties Summary===
| | #REDIRECT [[Inverse_Power_Law_(IPL)_Relationship#IPL-Exponential]] |
| <br>
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| ====Mean or MTTF====
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| 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}
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| & \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 \\
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| & = & \frac{1}{K{{V}^{n}}}
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| \end{align}</math>
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| <br>
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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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| <br>
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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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| <br>
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