Degradation Model Analysis in ALTA
Given the fact that products today are often designed
with high reliability, even accelerated life testing may
not yield enough failures to estimate product reliability
in a short period of time. Degradation analysis is an effective
reliability analysis tool for products that are associated with a measurable performance characteristic, such as the wear of brake pads, increase in vibration or the propagation of crack size. Many failure mechanisms can be directly
or indirectly linked to the degradation of products. Failure
occurs when the degradation value reaches a predefined critical
level. Degradation analysis allows users to extrapolate
failure times based on the measured degradation data during
the degradation test. To reduce testing time even further,
degradation tests can be conducted at elevated stresses.
Product reliability at the use stress level can then be
estimated using the accelerated degradation test data. In
this article, we will show an example of degradation model
analysis using ALTA.
ALTA allows users to perform a degradation analysis
using the linear, exponential, power, logarithmic, Gompertz
and Lloyd-Lipow models. The equations for these models are
- Linear: y = a·x+b
- Exponential: y = b·ea·x
- Power: y = b·xa
- Logarithmic: y = a·ln(x)+b
- Gompertz: y = a+bc·x
- Lloyd-Lipow: y = a-b/x
where y is the degradation measurement, x
is the inspection time and a, b and c
are model parameters.
These models can be used to predict when the degradation
of a given unit will reach the predefined failure level.
The predicted time can then be treated as the failure time.
Once the model parameters are estimated for each test sample,
xi can be extrapolated using the defined
critical value of y. The computed xis
from all the units can then be used as failure times
for subsequent accelerated life data analysis.
A medical company produces a chemical solution that degrades
with time. A quantitative measure of the quality of the
product can be obtained. This measure (which will be referred to as
"QM" for the sake of convenience in this article) is said to be
around 100 when the product is first manufactured and decreases
with time. The minimum acceptable value for QM is 50.
Units with QM equal to or lower than 50 are considered to be out
of compliance or failed. Engineering analysis has indicated
that the QM has a higher degradation
rate at higher temperatures. Assuming the product's normal use temperature is 20
degrees Celsius (or 293K), the goal is to determine the
shelf life of the product via an accelerated degradation
test. The shelf life is defined as the time by which 10%
of the units will have a QM that is out of compliance.
In this experiment, 15 samples of the product were tested,
with 5 samples in each of 3 accelerated stress environments:
323K, 373K and 383K. The QM for each sample was measured
and recorded every month for 7 months. Table 1 gives the data obtained from these measurements.
Table 1 - Accelerated degradation data
We can see that all the readings for 323K and 373K are
above the critical QM threshold of 50, except that the QM
reading for C5 dropped down to 50 during the 7th month (marked in red above).
Because of this, the reading will be treated as an observed
failure in the analysis.
All of the measurements were entered into ALTA's degradation analysis folio, and the critical degradation level was set to 50. Figure 2 shows the first 20 rows of data.
Figure 2 - First 30 rows of data in degradation analysis folio
In cases where the physical model of the
degradation is unclear, the Degradation Model Wizard may
be used to rank models according to the total SSE (sum
of squares error). Figure 3 shows that, according to the
Wizard, the linear model fits the data best. (For details on using the
Wizard, and how it performs its evaluation, see http://www.weibull.com/hotwire/issue112/relbasics112.htm.)
Figure 3 - The Degradation Model Wizard recommends the linear model
Click the Implement button on the Degradation
Model Wizard to return to the data sheet with the linear
model selected. To solve for the parameters a and b for
each sample, click the Calculate icon on the
degradation analysis folio. After we have solved for our
two parameters, we can view plots of
our data. Figure 4 shows the degradation
vs. time plot for samples at 383K.
Figure 4 - Degradation vs. time plot for units at 383K
Then we click the Transfer Life Data to New Folio icon, and the extrapolated failure times at different temperature levels are displayed in a new standard folio, as shown in Figure 5.
Figure 5 - Extrapolated failure times in standard folio
However, we noticed from Table 1 that unit C5 was at the critical
level on the 7th month. Therefore, instead of using the
predicted failure time, we should use the observed one. So
we create a duplicate folio and change the failure time
for C5 to 7, as shown in Figure 6.
Figure 6 - Modified failure times in standard folio
The use stress level is set to 293K. The Arrhenius life-stress model and the Weibull distribution are selected for this analysis. The estimated shelf life (i.e., the time at which 10% of the units will have reached a QM level that is out of compliance) can be calculated using the B(X) Life calculation in the QCP. Based on this analysis, the projected shelf life at 293K is about 12.4 months, as shown in Figure 7.
Figure 7 - QCP calculation of shelf life
In this article, we discussed how to use the degradation
analysis folio in ALTA to analyze data from an
accelerated degradation test. To help us select the model
that will best fit the data, we used the Degradation Model
Wizard. This article also illustrated how to treat failures
that occur during an accelerated degradation test. Because
one unit actually reached the critical degradation level,
we replaced that unit's predicted failure time with the
observed failure time before calculating our product's shelf