More companies are using Reliability Engineering techniques to help engineers understand equipment failures modes and patterns of critical equipment and systems. The primary goal of these practices is to minimize down time and increase production rates.
One analytical tool which can be used to estimate the reliability of machines and systems is the Exponential Distribution technique, where the failure rates are constant as a function of time:
R(t) = e ^ (-FR *t)
Where:
R(t) = Estimated reliability for a period (i.e. hours, days, months, years, etc.)
e = Natural log base.
FR = 1/MTBF
MTBF = Mean time between failures (same units as the R(t))
For example:
In a plant with 100 motors from which 5% fail annually, you can calculate the projected reliability of the units running for 5 years as follows:
R(5)= e^-(0.05 * 5) = 0.778 or approx. 78%
This would mean that after 5-years, about 22% of the units can statistically be expected to fail.