5.6.2.1 Lognormal
Distribution
This is the most commonly used distribution in maintainability
analysis. It applies to most maintenance tasks and repair actions comprised of
several subsidiary tasks of unequal frequency and time duration.
The probability density function is given by


(5.76) 
where:
t
= M_{cti} = repair time from each
failure

"1"> 
= standard deviation of ln of
repair times.


N = number of repair actions 
(5.79) 
The mean time to repair is given by
(also see Eq. (5.76))
The median time to repair is given by
The maximum time to repair is given
by
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.
Most commonly used values of
f or
z(t’_{1a}
) are shown in Table 5.62.