5.6.2.4 __Exponential
Approximation__

In general, the repair time density function is lognormally
distributed. In practice, however, the standard deviation of the logarithms of
repair times (s*ln*Mct) is not usually known and must be estimated in order to
compute the probability of repair for any value of repair time. A value of
s = 0.55 has been
suggested by some prediction procedures, based on maintenance experience data
accumulated on equipment. In the absence of justifiable estimates of
s, it is
practicable to use the exponential distribution as an approximation of the
lognormal.

Figure 5.6-6 compares the
exponential function with several lognormal functions of different standard
deviations. All functions in the figure are normalized to a common
Mct at Mct i /Mct = 1.0. The
exponential approximation is, in general, conservative over the region shown.
Probability of repair in time t in the exponential case is given by

M(t) » 1 - e^{-t/ct} = 1 - e^{-mt}

where:

M(t) = probability of
repair in a specified time t

_{ct} = known mean
corrective maintenance time

This approximation will be used in the next section on
availability theory because it allows for a relatively simple description of
the basic concepts without becoming overwhelmed by the mathematics
involved.