Biomedical Engineering Reference
In-Depth Information
mechanisms. The Weibull distribution most frequently provides the best fit of life data.
The primary advantage of Weibull statistical analysis is the ability to provide reasonable
accurate failure analysis and failure forecasts with extremely small amounts of testing
samples. Solutions are possible at the earliest indications of a problem without having
to crash a few more. If all the bearings are tested to failure, the cost and time required
is much greater. Therefore, a small amount of testing samples also allow cost-effective
component testing. Another advantage of the Weibull statistical analysis is that it provides
a sample and useful graphical plot. The data plot is extremely important to engineering
clinicians and managers.
With regard to clinical applications, plasma-sprayed HA-coated implants with a suf-
HA-coated implants with a suf-
ficient, reliable strength and reliability are indispensable due to their long-term stability.
However, many metallurgical variables affect the coating strength, including variables
associated with materials manufacturing, and result in a certain extent of data fluctuation.
To solve these problems and determine the reliability and failure modes of the coatings,
this statistical method of survival analysis has been accepted as an engineering design
method for such materials [239,248]. In the present subject, the variable
x
in Equation 6.33
can be defined as a certain mechanical strength (denoted by
σ
), such as the adhesive bond-
ing strength, shear strength, fracture strength, toughness, and so forth, resulting from a
mechanical testing. In order to evaluate the statistical significance for the data fluctuation
of the measured bonding strength as shown in Figure 6.23, therefore, the Weibull model
is applied to clarify the metallurgical effects on the failure mechanism of plasma-sprayed
HACs. Equation 6.34 shows the general form of the Weibull distribution function, where
σ
represents the bonding strength, and at least 20 specimens (
n
= 20) are tested for the pur-
pose of statistical significance of the Weibull analysis.
s, plasma-sprayed HA-coated implants with a suf-
, plasma-sprayed HA-coated implants with a suf-
plasma-sprayed HA-coated implants with a suf-
=
∫
σ σ
m
i
−
( )
σ σ
σ
F
(
)
=
f
d
= −
1
exp
−
i
o
(6.34)
σ
σ σ
i
c
=
0
σ
F
(
σ
i
) is the cumulative failure probability corresponding to a measured bonding strength
σ
i
(
i
is the ranking of specimens from the lowest value to the highest one,
i
= 1-20).
According to the definition of the Weibull statistics, the failure behavior of materials is
determined by three parameters:
m
,
σ
c
, and
σ
o
. The Weibull modulus (
m
), which controls
the shape of function curves, is a measure of the variability of the data. In addition, it
should be worth noting that the failure behaviors can also be determined by the value
distribution of the Weibull modulus (
m
) as shown in Figure 6.32, and can be interpreted
as follows:
• A value of
m
< 1 indicates that the failure is an “early failure” mode. The failure
probability and the failure rate are very high as shown in Figure 6.32a. However,
the decreasing of the failure rate (DFR) occurred over time when the significant
infant mortality or those defective items failing early are weeded out of the popu-
defective items failing early are weeded out of the popu-
lation. This situation is mostly resulted from the error of design and preexisted
defects in materials or systems during the manufacturing processes.
• A value of
m
= 1 indicates that the failure probability or the failure rate is constant
over time as shown in Figure 6.32b (constant failure rate, CFR), that is, a random
failure. This might suggest that random external events result in the mortality and
failures.
or those defective items failing early are weeded out of the popu-
those defective items failing early are weeded out of the popu-
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