52 2. RELIABILITY OF A COMPONENT UNDER CYCLIC LOAD
erefore, the range of the reliability of the component with a 95% confidence level will be:
R D 1 F D 0:9464 ˙ 0:0004:
2.8.6 RELIABILITY OF A COMPONENT UNDER MODEL #4 CYCLIC
LOADING SPECTRUM
Model #4 cyclic loading spectrum is multiple constant cyclic stress levels with multiple constant
numbers of cycles, which has been discussed in Section 1.2. When a component is under the
model #4 cyclic loading spectrum, no direct limit state function can be established. However,
the equivalent fatigue damage concept [11, 15] proposed by Dr. Dimitri B. Kececioglu in 1977
can be used to estimate the reliability of the component under such cyclic loading spectrum. e
assumption in the approach is that the cyclic number at a cyclic stress level could be transferred
to another stress level with an equivalent cyclic number under the condition that the probability
of a safe status of the component at the original stress level is the same as that at the transferred
stress level with the equivalent cyclic number. In this approach, the reliability index of the com-
ponent under cyclic loading is used as an indirect index for measuring the fatigue damage of a
component.
Let us use two levels of the model #4 cyclic loading spectrum as listed in Table 2.20 to
demonstrate the equivalent fatigue damage concept and procedure. e corresponding fatigue
life distributions are also listed in Table 2.20. In Table 2.20,
ai
and
aj
are the fully reversed
cyclic stress amplitudes in the cyclic stress levels i and j . n
Li
and n
Lj
are the numbers of cycles in
the cyclic stress levels i and j . ey are all constants for the model #4 cyclic loading spectrum,
that is, deterministic values.
S
0
f
is material fatigue strength, which is equal to the cyclic stress
amplitude of the corresponding stress level, as shown in Table 2.20. e component fatigue life
N
C
at the given fatigue strength S
0
f
D
ai
is typically a lognormal distribution, which has been
discussed in Section 2.8.2. It can be obtained per Equation (2.34). Its distribution parameters
can be calculated per Equations (2.35) and (2.36). In Table 2.20,
ln N
Ci
and
ln N
Ci
are the mean
and the standard deviation of the component fatigue life N
Ci
at the cyclic stress level i.
ln N
Cj
and
ln N
Cj
are the mean and the standard deviation of the component fatigue life N
Cj
at the
cyclic stress level j .
e general procedure for transferring cyclic stress level from stress level i to the stress
level j is described as the following.
Step 1: Calculate the index of the fatigue damage of the component due to the cyclic stress
.
ai
; n
Li
/ in the stress level i.
e index of the fatigue damage of the component due to the cyclic stress .
ai
; n
Li
/ in the stress
level #i can be indirectly represented by the probability P
.
N
C
> n
Li
/
D P
Œ
ln
.
N
C
/
> ln
.
n
Li
/
,