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. It is defined in its most general case by:

[math]\displaystyle{ \begin{align} f(t)=\lambda e^{-\lambda (t-\gamma)} \end{align} }[/math]

with two parameters, namely λ and γ (this form is also known as the 2-parameter exponential). [math]\displaystyle{ is the constant failure rate in failures per unit of measurement (e.g., failures per hour, per cycle, etc.). In addition, \lt math\gt \lambda =\tfrac{1}{m} }[/math], where [math]\displaystyle{ {m} }[/math] is the mean time between failures (or to failure).

If the location parameter, γ, is assumed to be zero, then the distribution becomes the 1-parameter exponential or:

[math]\displaystyle{ \begin{align} f(t)=\lambda e^{-\lambda t} \end{align} }[/math]

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