Template:Alta exponential distribution

The Exponential Distribution

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:

[math]\displaystyle{ \begin{align} & f(T)= \lambda {{e}^{-\lambda T}}=\frac{1}{m}{{e}^{-\tfrac{1}{m}T}} \\ & T\ge 0,\lambda \gt 0,m\gt 0 \end{align} }[/math]

where:

• λ = constant failure rate, in failures per unit of measurement (e.g. failures per hour, per cycle, etc.).
• [math]\displaystyle{ \lambda =\tfrac{1}{m} }[/math].
• m = mean time between failures, or to a failure.
• T = operating time, life, or age, in hours, cycles, miles, actuations, etc. This distribution requires the estimation of only one parameter, λ , for its application.