58
Chapter 2
Again with a range from minus infinity to plus infinity. The probability of
Eq. (2.34) being valid or the reliability ~>0 is Eq. (2.38) integrated
zero to
infinity
R(~)
~v/~ a exp
(2.39)
0
which is the integration of a normal or Gaussian distribution. Using a math
handbook for evaluation, let
t -
(2.40)
when ~ = zero
when ( = ee
t - ~ - #~ - infinity
then from a math handbook
1
-~R(~) = R(0
exp
dt
(2.41)
Now the coupling equation is
t = - ~ = - /~A - #u
(2.42)
Z~
[(~A) 2 -~- (~a)2]
1/2
The R(t) from zero to infinity is 0.5 and from 0 to -t the value added after
say t=3.5 add 0.4998 to 0.5 or R(t)=0.998
R(t) + P(t) = I
(2.43)
Then
2
P(t)- 104
which is not accurate enough for a failure rate of one per 10 6 items or more.
Table 2.3 shows the value of minus t and the P(t) for more accurate calculations using Eq. (2.42).