202
Chapter 4
1.0
0.5Figure 4.7. Gaussian reliability curve with time.
Figure 4.8.
20
,~0 40
REV5 ~ lO~
Gaussian failure of a bearing Example 4.2.
Censored observations [1.7,1.22,4.24] will drop extreme values from the
data set using statistical
methods so that better values for/~ and ~ may
be obtained with better confidence.
EXAMPLE 4.2. Estimate the reliability
of a bearing at 20 × 106 and
at 40 × l06 if the mean life is 30 × 106 revolutions and the standard deviation
is 5 × 106 Revs, in Fig. 4.8.
The simplest method of solution is to use tabulated values of the probability integral. Most tables are normalized with the argument given in
terms of the number of standard deviations (i.e. t/l~). In this case, there
is interest in computing the reliability of + 2 ~ either side of the mean life.
Graphically speaking, the area from 20 × 106 cycles to 40 × 106 cycles. Since
the area Eq. (4.2) under the normalized distribution curve ± 2 ~, is 0.9544
2~+#
1 f
1
[- 1 rx - ~t-12]
--exp
-~ dx
R(20x
106)
=0"5+~d
~ 2L Z J J
-2~+#