5.6.2.3 Exponential
Distribution
In maintainability analysis, the exponential distribution
applies to maintenance tasks and maintenance actions whose completion times
are independent of previous maintenance experience (e.g., substitution methods
of failure isolation where several equally likely alternatives are available
and each alternative is exercised, one at a time, until the one which caused
the failure is isolated), producing a probability density function given
by
The method used in
evaluating the maintainability parameters is similar to that previously shown
in Section 5.3.4
for analyzing reliability with exponential timestofailure. The fundamental
maintainability parameter is repair rate, m(t), which is the reciprocal
of _{ct },
the meantimetorepair (MTTR). Thus, another expression for g(t) in terms of
m(t), the repair
rate, is
where m is the repair rate (which is constant for the
exponential case).
The maintainability function is given by
The
MTTR is given by
If the maintainability
function, M(t), is known, the MTTR can also be obtained from
The median time to repair _{ct} is
given by

_{ct} = 0.69 _{ct} 
(5.103) 
The maximum time to repair is given
by

M_{maxct}
= k_{e} _{ct} 
(5.104) 
where:
k_{e} 
= 
value of M_{cti} /_{ct} at the specified percentage point
a on the
exponential function at which M_{maxct} is defined. 
Values of ke are shown in
Table 5.67. 