Using ALTA to Model Destructive Degradation Data
In degradation testing and analysis (which can be performed under normal or accelerated conditions), the repeated measurements of a certain product characteristic (e.g., wear of brake pads or tread depth of tires) are analyzed in order to predict when a critical threshold will be reached and failure will occur (e.g., tread depth reaches a certain level). Since we don’t need to test all the units until they have reached that critical threshold, degradation data can be obtained with less testing time than times-to-failure data.
However, there are cases where traditional degradation testing will not be feasible because multiple measurements of each test unit are not possible (e.g., the act of measuring the degradation destroys the test unit, or the data is obtained from the field). This article will use an example to illustrate how you can use ReliaSoft's ALTA software to analyze this type of data and calculate metrics of interest.
Consider a mechanical component that wears down as it is being cycled during operation. Its wear is measured in millimeters (mm) of thickness loss, and the component is considered failed when the wear is greater than 1.5 mm. 24 such components undergo operational testing. Due to testing constraints, only one measurement is possible for each component. The following table shows the measured wear for each of the 24 components, along with the number of cycles at which each measurement was taken.
|Cycles||Wear (mm)||Cycles||Wear (mm)|
Given that the wear of each component is measured only once, traditional degradation analysis cannot be performed. This data, however, can still be analyzed using ALTA's standard folio. The folio with the data entered is shown next.
Note that the first column (which corresponds to the failure time in traditional ALTA) records the wear measurement. The second column (which corresponds to the applied stress in traditional ALTA) records the cycles at which the measurement was taken. The wear vs. cycles model selected in this case is the inverse power law model (IPL), which is commonly used to model degradation due to wear. The distribution of wear is modeled using the Weibull distribution, which is a flexible distribution that is also commonly used to model wear.
While traditional ALTA is used to generate a life distribution at different stress levels, this analysis generates a distribution of wear at different cycles of operation. As an example, consider the distribution of wear at 2,000 cycles of operation, as shown next.
Given that wear greater than 1.5 mm is considered to be a failure, the reliability of our component at 2,000 cycles is the probability that wear is less than 1.5 mm, which corresponds to the red colored area of the pdf.
If we were modeling times-to-failure data instead of wear data, this area would represent the unreliability of our component (i.e., the probability that the failure time would be less than a desired time value). Therefore, when obtaining results from this analysis, we need to keep in mind that all metrics are the reverse of the traditional reliability analysis.
For example, the probability plot at 2,000 cycles provides us with the reliability of the component at 2,000 cycles instead of the unreliability that is shown in traditional reliability analysis (again, because it gives us the probability that the wear at 2,000 cycles is less than the critical value of 1.5 mm). The plot is shown next.
We can use the Quick Calculation Pad (QCP) to calculate the exact reliability at 2,000 cycles. Note that since the labels in ALTA will correspond to the traditional reliability analysis, and the metrics for our analysis are reversed as discussed above, we need to select the metric that is the opposite of what we want to calculate. Therefore, since we want to calculate the reliability at 2,000 cycles, we will select Probability of Failure in the QCP. The stress value will be 2,000 cycles (recall that we entered cycles of measurement in the folio's stress column), and the mission end time will be the critical wear value of 1.5 mm.
The median estimate of the reliability at 2,000 cycles is 88.27%, and the lower one-sided 90% confidence bound is 80.09%.
Finally, we can calculate the B20 life of our component (in this case, the cycles by which 20% of our components will show a wear greater than 1.5 mm). The B20 can be calculated using the life vs. stress plot in ALTA (in our case, life is wear while stress is cycles of operation). Again, keeping in mind that everything is reversed in our analysis, the 80% unreliability line (which in our case is 80% reliability) is displayed in the plot shown next. And then we look for the x-value that corresponds to a y-value of 1.5 mm.
The B20 life of our component is about 2,111 cycles.
In this article we have shown how one can use ALTA to model destructive degradation data and data from other situations where only a single degradation measurement is available for each test unit. It should be noted that the analysis was possible even though each measurement was obtained at different cycles of operation. If such a testing scheme is selected, ideally one would want to have measurements from a wide range of operating times, or cycles, as was the case in the provided example.
Finally, because the degradation measurement (wear) increased with time (cycles) in this example, the metrics used in ALTA were reversed from the traditional reliability analysis. However, if the degradation measurement were decreasing with time (as would occur with the tread depth of a tire), this reversal of metrics would not be needed.