Background
Consider a chemical solution (e.g. ink formulation, medicine, etc.) that
degrades with time. A quantitative measure of the quality of the
product can be obtained. This measure (QM) is said to be around 100
when the product is first manufactured and decreases with product
age. The minimum acceptable value for QM is 50. Products with
QM equal to or lower than 50 are considered to be "out of
compliance" or failed.
Engineering analysis has indicated that at higher temperatures the QM has a
higher rate of decrease. Assuming that the product's normal use temperature
is 20º C (or 293K), determine the shelf life of the product via an
accelerated degradation test.
For the purpose of this analysis, "shelf life" is defined as the time by which
10% of the products will have a QM that is out of compliance.
Experiment and Data
For this experiment, 15 samples of the product are tested, with 5 samples
in each of three environments: 323K, 373K and 383K. Once a
month, and for a period of seven months, the QM for each sample is
measured and recorded. The data obtained is given in Table 1.
| Table 1
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Analysis
Since all of the readings are above the critical QM threshold
of 50, none of the samples tested in this experiment have gone out of
compliance (or "failed") by the end of the test. However, there
is sufficient data for the degradation of each sample to
extrapolate a time-to-failure (i.e. the month at which we expect each
sample to be at QM=50).
Using ALTA's degradation analysis utility (shown in
Figure
1) the data for all samples are entered and individually fitted
to multiple exponential curves (Figure 1A shows
sample graphs). From each respective curve, a time-to-failure (i.e. the
time the product is expected to go out of
compliance) is automatically extrapolated and transferred to an ALTA Data Folio
(Figure 2).
Several plots can be obtained from the analysis. Specifically,
Figure 3A
shows a Weibull probability plot
at the use stress level, while Figure 3B shows a reliability curve for this
product, also at the use stress level. Figure
3C shows a life vs. stress plot where the blue line represents the time
by which 10% of the units are expected to be out of compliance (at a given
temperature). Figure 3D shows a
standardized residual plot of the data and fitted model to ascertain
adequacy.
Based on this analysis, the projected shelf life of this product is 15.6
months. The desired result can also be obtained from the QCP, as shown in
Figure 4.
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ALTA
7 Case Studies
Version
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