

MILHDBK338B: Electronic Reliability Design Handbook 
 

1. Probability Density Function of g(t)
1. Probability Density Function
of g(t)
To determine the lognormal pdf of the timestorepair given in
Table
5.63, the values of ’ and s_{t '}
should be
calculated from
where n_{j} is the number of identical observations
given in the third column of Table
5.63, N’ is the number of differentinvalue observed timestorepair, or
number of data groups, which for this problem is N’ = 29, given in the second
column of Table
5.63, and N is the total number of observed timestorepair,
which, for this example, is 46,
and
To facilitate the calculations, Table 5.64 was prepared. From
Table 5.64, ’ and s_{t '} , are obtained as follows:
TABLE 5.64: CALCULATIONS
TO DETERMINE ’ AND s_{T}FOR THE DATA IN
TABLE
5.63
and from Eq.
(5.89)
Consequently, the lognormal pdf representing the data in Table
5.63 is
or
where t’ = ln
t. The plot of this pdf is given in
Figure 5.63 in terms of the straight times in hours. See Table 5.65 for the
g(t) values used.
The pdf of the ln t or of the
t’ is
or
This pdf is that of a normal
distribution which is what one should expect since if t follows a lognormal
distribution, ln t should be normally distributed. This is shown plotted
in Figure 5.63, the values of g(t’) were obtained from Table
5.65.
FIGURE 5.63: PLOT OF THE
LOGNORMAL OF THE TIMESTORESTORE DATA GIVEN IN TABLE 5.65 IN TERMS OF THE
STRAIGHT t’s (Click image to enlarge)
TABLE 5.65: THE PROBABILITY DENSITY OF TIMETOREPAIR
DATA (FROM TABLE 5.6.2.1.11 BASED ON THE STRAIGHT TIMES TO REPAIR AND THE
NATURAL LOGARITHM OF THE TIMES TO REPAIR USED TO PLOT FIGURES 5.63 AND
5.64, RESPECTIVELY.*)
FIGURE 5.64: PLOT OF THE LOGNORMAL PDF OF THE
TIMESTORESTORE DATA GIVEN IN TABLE 5.65 IN TERMS OF THE LOGARITHMS OF
T, OR ln t’




 
 