Degradation Analysis

Given that products are frequently being designed with higher reliabilities and developed in shorter amounts of time, even accelerated life testing is often not sufficient to yield reliability results in the desired timeframe. In some cases, it is possible to infer the reliability behavior of unfailed test samples with only the accumulated test time information and assumptions about the distribution. However, this generally leads to a great deal of uncertainty in the results. Another option in this situation is the use of degradation analysis. Degradation analysis involves the measurement and extrapolation of degradation or performance data that can be directly related to the presumed failure of the product in question. Many failure mechanisms can be directly linked to the degradation of part of the product and degradation analysis allows the user to extrapolate to an assumed failure time based on the measurements of degradation or performance over time. To reduce testing time even further, tests can be performed at elevated stresses and the degradation at these elevated stresses can be measured resulting in a type of analysis known as accelerated degradation.

In some cases, it is possible to directly measure the degradation over time, as with the wear of brake pads or with the propagation of crack size. In other cases, direct measurement of degradation might not be possible without invasive or destructive measurement techniques that would directly affect the subsequent performance of the product. In such cases, the degradation of the product can be estimated through the measurement of certain performance characteristics, such as using resistance to gauge the degradation of a dielectric material. In either case, however, it is necessary to be able to define a level of degradation or performance at which a failure is said to have occurred. With this failure level of performance defined, it is a relatively simple matter to use basic mathematical models to extrapolate the performance measurements over time to the point where the failure is said to occur. This is done at different stress levels and therefore each time-to-failure is also associated with a corresponding stress level. Once the times-to-failure at the corresponding stress levels have been determined, it is merely a matter of analyzing the extrapolated failure times in the same manner as you would analyze conventional accelerated time-to-failure data.

Once the level of failure (or the degradation level that would constitute a failure) is defined, the degradation for multiple units over time needs to be measured (with different groups of units being at different stress levels). As with conventional accelerated data, the amount of certainty in the results is directly related to the number of units being tested, the number of units at each stress level, as well as in the amount of overstressing with respect to the normal operating conditions. The performance or degradation of these units needs to be measured over time, either continuously or at predetermined intervals. Once this information has been recorded, the next task is to extrapolate the performance measurements to the defined failure level in order to estimate the failure time. ALTA allows the user to perform such analysis using a linear, exponential, power, logarithmic, Gompertz or Lloyd-Lipow model to perform this extrapolation. These models have the following forms:

13.3.1.gif

where y represents the performance, x represents time and a and b are model parameters to be solved for.

Once the model parameters ai and bi (and ci for Lloyd-Lipow) are estimated for each sample i, a time, xi, can be extrapolated that corresponds to the defined level of failure y. The computed xi can now be used as our times-to-failure for subsequent accelerated life data analysis. As with any sort of extrapolation, one must be careful not to extrapolate too far beyond the actual range of data in order to avoid large inaccuracies (modeling errors).

One may also define a censoring time past which no failure times are extrapolated. In practice, there is usually a rather narrow band in which this censoring time has any practical meaning. With a relatively low censoring time, no failure times will be extrapolated, which defeats the purpose of degradation analysis. A relatively high censoring time would occur after all of the theoretical failure times, thus being rendered meaningless. Nevertheless, certain situations may arise in which it is beneficial to be able to censor the accelerated degradation data

Example

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 20 degrees Celsius (or 293K), the goal is to 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.

For this experiment, 15 samples of the product were tested, with 5 samples in each of three accelerated stress environments: 323K, 373K and 383K. Once a month, and for a period of seven months, the QM for each sample was measured and recorded. The data obtained is given in Table 1.

Table 1: Accelerated Degradation

Since all of the readings are above the critical QM threshold of 50, none of the samples tested in this experiment had gone out of compliance (or failed) by the end of the test. However, there was 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).

Fig. 2: Data entered in ALTA's degradation analysis

Using ALTA's Degradation Analysis Folio (shown in Figure 2) the data for all samples were entered and individually fitted to multiple exponential curves (Figure 3 shows sample graphs). From each respective curve, a time-to-failure (i.e. the time the product is expected to go out of compliance) was automatically extrapolated and transferred to an ALTA Standard Folio (Figure 4).

Fig. 3: Sample degradation lines.

Fig. 4: Extrapolated time-to-failure data in the ALTA 7 PRO Data Folio.

Several plots can be obtained from the analysis. Specifically, Figure 5 shows a Weibull probability plot at the use stress level. Figure 6 shows a Life vs. Stress plot where the line represents the time by which 10% of the units are expected to be out of compliance (at a given temperature).

Fig. 5: Use level Weibull probability plot.

Fig. 6: Life vs. Stress plot.

Based on this analysis, the projected shelf life of this product is 15.6 months. The desired result could also have been obtained from the QCP, as shown next.