Template:Exponential Statistical Properties: Difference between revisions

Latest revision as of 08:08, 10 August 2012

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-==Exponential Statistical Properties==
+#REDIRECT [[Exponential Distribution Functions]]
-===The Mean or MTTF===
-The mean, <math>\overline{T},</math> or mean time to failure (MTTF) is given by:
-::<math>\begin{align}
-   \bar{T}= & \int_{\gamma }^{\infty }t\cdot f(t)dt \\
-  = & \int_{\gamma }^{\infty }t\cdot \lambda \cdot {{e}^{-\lambda t}}dt \\
-  = & \gamma +\frac{1}{\lambda }=m
-\end{align}</math>
-Note that when <math>\gamma =0</math>, the MTTF is the inverse of the exponential distribution's constant failure rate. This is only true for the exponential distribution. Most other distributions do not have a constant failure rate. Consequently, the inverse relationship between failure rate and MTTF does not hold for these other distributions.
-{{Median}}
-{{Mode}}
-{{Standard Deviation}}
-{{Exponential Reliability Function}}
-{{One-Parameter Exponential Reliability Function}}
-{{Exponential Conditional Reliability}}
-{{Exponential Reliable Life}}
-{{Exponential Failure Rate Function}}