Template:Alta exponential distribution: Difference between revisions

Latest revision as of 01:08, 16 August 2012

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-== The Exponential Distribution  ==
+#REDIRECT [[Distributions_Used_in_Accelerated_Testing]]
-The exponential distribution is a very commonly used distribution in reliability engineering. Due to its simplicity, it has been widely employed, even in cases where it doesn't apply. The exponential distribution is used to describe units that have a constant failure rate. The single-parameter exponential ''pdf ''is given by:
-<br>
-::<math>\begin{align}
-  & f(T)= \lambda {{e}^{-\lambda T}}=\frac{1}{m}{{e}^{-\tfrac{1}{m}T}} \\
- & T\ge  0,\lambda >0,m>0
-\end{align}</math>
-<br>
-where:
-::*<span class="texhtml">λ = </span> constant failure rate, in failures per unit of measurement (e.g. failures per hour, per cycle, etc.).
-::*<math>\lambda =\tfrac{1}{m}</math>.
-::*<span class="texhtml">''m'' = </span> mean time between failures, or to a failure.
-::*<span class="texhtml">''T'' = </span> operating time, life, or age, in hours, cycles, miles, actuations, etc. This distribution requires the estimation of only one parameter, <span class="texhtml">λ</span> , for its application.
-{{alta statistical properties summary}}
-{{characteristics of the exponential distribution alta}}