5.6.2.2 Normal
Distribution
The normal distribution has been adequately treated in Section
5.3.2.1 in the discussion on reliability theory. The same procedures and
methodology apply for maintainability if one merely uses repair time for t,
mean repair time for m, and standard deviation of repair times for
s.
In maintainability, the normal
distribution applies to relatively straightforward maintenance tasks and
repair actions (e.g., simple removal and replacement tasks) which consistently
require a fixed amount of time to complete. Maintenance task times of this
nature are usually normally distributed, producing a probability density
function given by
where:
The mean time to repair (_{ct} ) is given by
The median time to repair
(_{ct})
is given by
which is equal to the mean
time to repair because of the symmetry of the normal distribution (see Fig.
5.31).
The maximum time to repair is given by

M_{maxct} = _{ct} + f S_{Mct} 
(5.97) 
where:
f 
= 
z(t_{1a}
) 

= 
value from normal distribution function
corresponding to the percentage point (1a) on the
maintainability function for which M_{maxct} is defined. Values of f as a function of
(1a)
are shown in Table 5.66. Note that this is the same as Table 5.62
with roundedoff values. 