Page 278 - Handbook of Materials Failure Analysis

274 CHAPTER 11 The reliability design of mechanical system

If the estimated characteristic life of p-value α, η α , in Equation 11.11,is
substituted into Equation 11.13, we obtain the B X life equation:

n
β 2 1 X β
¼ ln (11.14)
L 2 t
χ 2r +2ð Þ 1 x i¼1
BX i
α
Most lifetime testing has insufficient samples. The allowed number of failures would
not have as much as that of the sample size.
β
β β β β
n
X X
ð
ð
t ¼ t + n rÞh n rÞh (11.15)
i i
i¼1 i¼1
After Equation 11.15 inserts into Equation 11.14, B X life equation may be modified
as follows:
β 2 1 β β
ln ð (11.16)
L 2 n rÞh L
χ 2r +2ð Þ 1 x
BX BX
α
Then, sample size equation with the number of failure will be modified as:
2 β
χ 2r +2Þ 1 L
ð
α
n BX + r (11.17)
2 1 h
ln
1 x
2
ð
For a 60% confidence level, the first term χ α 2r +2Þ in Equation 11.17 can be approx-
2
imated to (r+1) [13]. And if the cumulative failure rate, x, is below about 20%, the
denominator of the second term ln 1 approximates to x by Taylor expansion. Then,
1 X
the general sample size equation can be approximated as follows:
β

1 L

ð
n r +1Þ BX + r (11.18)
x h
If the accelerated factors in Equation 11.5 are added into the planned testing time,
Equation 11.18 will be modified as:
β

1 L
n r +1Þ BX + r (11.19)
ð
a
x AF h
a
where h a is actual testing time and AF is accelerated factor.
7 CONCLUSION
As those discussed above since 2000, about 800 specifications have been established,
each of which has RQ as well as RM and performance test specifications (UP/SP),
and have been applied to establishing these standards. Yet RQ test specifications
would be not easy to be found in any specifications. And they can find the missing
design parameters from the failure mechanism [14–21].
Product design consists of performance/reliability design itself and verifies their
designs. For this, the verification groups as an independent party is separated from