The lognormal is the most commonly used distribution in maintainability analysis because it is considered representative of the distribution of most repair times. 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:

(Equation 7)

where:

t = M_{cti} = repair time from each failure

_{t'} = standard deviation of repair times =

(Equation 8)

t' = ln M_{cti} = ln t

N = number of repair actions

The mean time to repair is given by:

The median time to repair is given by:

The maximum time to repair is given by:

where z(t' _{1-} ) = the value from the normal distribution function corresponding to the percentage point (1-)
on the maintainability function for which M_{Maxct} is defined. Most commonly used values of z(t' _{1-}) are shown in Table XIV.

**Table XIV - Values of z(t' 1-a ) Most Commonly Used in
Maintainability Analysis**
(1-) |
z(t' _{1-}
) |

0.80 0.85 0.90 0.95 0.99 |
0.8416 1.036 1.282 1.645 2.326 |