Template:Exponential Distribution Definition

The exponential distribution is commonly used for components or systems exhibiting a constant failure rate. Due to its simplicity, it has been widely employed, even in cases where it doesn't apply. In its most general case, the 2-parameter exponential distribution is defined by:


 * $$\begin{align}

f(t)=\lambda e^{-\lambda (t-\gamma)} \end{align}$$

Where $$ \lambda\,\!$$ is the constant failure rate in failures per unit of measurement (e.g., failures per hour, per cycle, etc.) and $$\gamma\,\!$$ is the location parameter. In addition, $$\lambda =\tfrac{1}{m}\,\!$$, where $${m}$$ is the mean time between failures (or to failure).

If the location parameter, $$\gamma\,\!$$, is assumed to be zero, then the distribution becomes the 1-parameter exponential or:


 * $$\begin{align}

f(t)=\lambda e^{-\lambda t} \end{align}$$

For a detailed discussion of this distribution, see The Exponential Distribution.