,
or mean time to failure (MTTF) is given by:The mean, ,
or mean time to failure (MTTF) is given by:
Note that when γ = 0, 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.
The median, 
, is:
The mode, 
, is:
The standard deviation, σT, is:
The equation for the two-parameter exponential cumulative density function, or cdf is given by:
Recalling that the reliability function of a distribution is simply one minus the cdf, the reliability function of the two-parameter exponential distribution is given by:
The one-parameter exponential reliability function is given by:
The exponential conditional reliability equation gives the reliability for a mission of t duration, having already successfully accumulated T hours of operation up to the start of this new mission. The exponential conditional reliability function is:
which says that the reliability for a mission of t duration undertaken after the component or equipment has already accumulated T hours of operation from age zero is only a function of the mission duration, and not a function of the age at the beginning of the mission. This is referred to as the memoryless property.
The reliable life, or the mission duration for a desired reliability goal, tR, for the one-parameter exponential distribution is:
or:
The exponential failure rate function is:
Once again, note that the constant failure rate is a characteristic of the exponential distribution, and special cases of other distributions only. Most other distributions have failure rates that are functions of time.
See Also:
The Exponential Distribution
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