Biomedical Engineering Reference
In-Depth Information
(a)
(b)
(c)
(d)
(e)
FIGURE 6.30
(a) Failure illustration of femoral stem and acetabular cup, and photographs of retrieved cups with different fail-
ure modes resulted from (b) aseptic loosening with 20.5% residual HA, (c) septic loosening with 20.3% residual
HA, (d) osteolysis with 70.5% residual HA, and (e) polyethylene wear with 41.9% residual HA. Stable cups have
more residual HA-coated surface than loose cups.
engineering, which is combined with the statistics and the engineering, is a commonly
adopted statistical method for evaluating the most optimal design, processing, and manu-
facturing parameters. Reliability engineering is an engineering field that deals with the
study about the ability of a system or a component to perform its required functions under
stated conditions for a specified period of time. Not only it can evaluate the failure prob-
ability and failure modes of materials, but it can also predict the fracture possibility that
results from the stages of material design and manufacturing processes. A basic step in
many reliability engineering studies is choosing a probability density function. The rela-
tionships among the probability density function, the reliability function, and the hazard
function for determining failure behaviors are deduced and described in the following
section.
Statistical Significance of Data Distribution
Reliability projections are based on fitting models to life test data and both the choice of
the model and the analysis methodology used can have a major influence on the result.
The principal assumption underlying most statistical modeling is that a reasonably simple
population model or equation will generate the smooth population curve. In addition,
the larger amount of testing samples, the more closely it should resemble the population.
Figure 6.31 illustrates the relationships for the probability density function and hazard
function curves of the reliability engineering statistics. The model for the population curve
is called the probability density function (PDF), denoted by f ( x ). Suppose that the failure
probability of a material is P r ( x * ≤ x x * + Δ x ) within a limited stress increasing interval
[ x *, x * + Δ x ] while the fracture occurred, and the probability of x falling between these two
specified values is the integration under the probability density function from x * to x * +
Δ x , which is presented as:
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