Background
A specific consumer product (e.g. a mouthwash, shampoo, etc.) is made up of three
main ingredients (ingredients A, B and C) that have a characteristic (e.g.
concentration) that may or may not change with time. A quantitative measure of a characteristic can be obtained,
and this measure must be within a specified range for
compliance. If any measure is outside its specified range, then the product is out of compliance and considered
failed. There is no known dependency among these ingredients,
and thus they are assumed to be statistically independent.
Objective
The product has a shelf life of 24 months. Determine the
probability that a given specimen will be out of compliance at/after
this time period.
Experiment and Data
For this study, 40 random products (specimens) are stored
at normal use conditions. At 3, 6, 9 and 12 months,
10 specimens are removed and measured. The measurement process is
a destructive test (i.e. once the specimen is opened for testing, the
required readings are taken and that specimen is then disposed of). Measurements for each ingredient, and at each time
period are given in Tables 1 through 4.
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Table 1
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| Table 2
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Table 3 |
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Table 4 |
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Table
5 shows the acceptable range for each ingredient.
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Table 5 |
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Acceptable
Range |
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A |
B |
C |
| Low |
142 |
155 |
110 |
| High |
156 |
185 |
135 |
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Analysis
If viewed from a "traditional reliability"
perspective, the test in this example is not an accelerated test. However, its analysis
will require that we employ the fundamental principles of ALT. The measured value of each characteristic (as measured after each
holding period) can be viewed as the random variable (the time value
in standard ALT) affected by the aging process (the stress value). In other words, the stress on each sample is the
time in the holding cell and the random variable (what we
traditionally think of as time-to-failure) is the value of the
measured characteristic. With this approach, the analysis can
be easily performed independently for each component in the ALTA
software. In
the analysis, the lognormal distribution is assumed, along with a
general log-linear model.
(See
discussion on model settings for more details, as well as for a data
entry example in ALTA 7 PRO.)
Analysis Step 1
The data
for ingredient A are entered in ALTA 7 PRO and the lognormal
distribution along with an untransformed generalized log-linear
life-stress relationship are used to calculate the parameters.
Figure
1 shows
the data and settings used in the ALTA 7 Standard Folio. Several plots from this analysis
follow.
Figure 2 shows the Life Characteristic vs. Age plot with 90% 2-sided
confidence intervals. As can be seen from this plot, no increase
or decrease in the characteristic is noted. In other words, age (at
least up to the 12 months of observation) does not affect the
characteristic for this ingredient.
| Figure
2: Life
Characteristic vs. Age for A, w/ 90% 2S Confidence Intervals |
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The
last step in the analysis for this data set is to determine the
probability that ingredient A will be outside the limits. This
is easily done in ALTA's QCP, as shown in Figure 3.
The probability of
ingredient A being below limit after 24 months is 0.02% and the
probability of ingredient A being above limit after 24 months is 0.03%. (Note that
although they have not been used here, confidence
intervals can easily be employed in the QCP.)
Analysis Step 2
The data for ingredient B are entered in ALTA 7 PRO, and the analysis
is repeated. Figure 4 shows
the data and settings used.
Figure 5 shows the Life Characteristic vs. Age plot with 90% 2-sided
confidence intervals. As can be seen from this plot, there is a noticeable
decrease in the characteristic.
| Figure
5: Life Characteristic
vs. Age for B, w/ 90% 2S Confidence Intervals |
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Using
the QCP, the
probability that ingredient B will be outside the limits is found to be:
Analysis Step 3
The data for ingredient C are entered in ALTA 7 PRO, and the analysis
is repeated. Figure 6 shows
the data and settings used.
Figure 7 shows the Life Characteristic vs. Age plot with 90% 2-sided
confidence intervals. As can be seen from this plot, there is a noticeable
increase in the characteristic.
| Figure
7: Life Characteristic vs. Age for C, w/ 90% 2S Confidence Intervals. |
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Using
the QCP, the probability that ingredient C will be outside the limits is found to be:
Conclusion
The probability of failure (i.e. the probability of the characteristic being outside the limits) can now be easily
computed from the individual probabilities [assuming independence
PS=1-{(1-PA)*(1-PB)...}]. In this case, the main contributing factor
will be the probability that ingredient C exceeds the limits, which is
significantly high. Having isolated the fact that ingredient C is the main
cause of failure, appropriate corrective actions may be required.
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ALTA
7 Case Studies
Version
7
