# Degradation model analysis in Weibull++'s Accelerated Life Testing module  Weibull++'s Accelerated Life Testing module allows users to perform a degradation analysis using the linear, exponential, power, logarithmic, Gompertz and Lloyd-Lipow models. The equations for these models are listed below:

• Linear: = a·x+b
• Exponential: = 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 ab 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.

### Example

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 Weibull++'s Accelerated Life Testing module's degradation analysis folio, and the critical degradation level was set to 50. Figure 2 shows the first 21 rows of data. ##### Figure 2: First 21 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 https://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 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 choose Degradation > Transfer Life Data > Transfer Life Data to New Folio, and the extrapolated failure times at different temperature levels are displayed in a new life-stress data 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 12.27 months, as shown in Figure 7. ### Conclusion

In this article, we discussed how to use the degradation analysis folio in Weibull++'s Accelerated Life Testing model 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 life.