Looking at Thermal Cycling Data in Quantitative Accelerated Life Testing
[Editor's Note: This article has been updated for ALTA Version 8 since its original publication.]
In the growing field of accelerated testing, the ability to analyze data with a time-varying stress (e.g., step-stress) is becoming more and more popular. Analysis of such data used to be very difficult, if not impossible at times, but ReliaSoft's ALTA PRO software can analyze data from an accelerated life test where the applied stress is time-varying. The time-dependent stress profile can be any continuous function, such as a step-stress or ramp stress. Thermal cycling is another type of time-dependent profile. At first glance, it would seem that to conduct the analysis for data from this type of test you would obviously treat the thermal cycling as a time-varying stress in ALTA PRO. This seems logical, after all it is a time-varying stress, so why not treat it as such? To answer that question, we have to look at the underlying models utilized for time-varying stresses. These models assume that applied stress (or stimulus) has a single effect (i.e., the higher the stress, the greater the damage), whereas in the case of thermal cycling the stress may cause damage at both high and low stresses. In other words, blindly entering the stress as an equation describing the thermal cycle would generate erroneous results. To analyze this type of data properly, the stimuli in thermal cycling need to be identified and treated accordingly. One option is to treat a simple thermal cycle as two constant stresses.
Break the Cycle into its Constituent Stresses
To understand why it is necessary to break down thermal cycling into its constituent stresses instead of treating it as a single time-varying stress, we need to consider how the stress will be taken into account mathematically relative to how it is being applied physically. Consider the thermal cycling function shown in Figure 1.
Figure 1: Sinusoidal thermal cycling stress
Figure 1 illustrates a symmetric sinusoidal thermal cycling stress. During the cycling, the temperature will drop below the x-axis, but what does this actually imply? If the temperature along the x-axis is ambient, then as the temperature drops below the x-axis the component under test is being stressed by a temperature less than ambient (cold temperature). In general, less stress implies a longer life, but when considering a colder temperature this assumption may not be valid. It is very possible that a colder temperature stress may actually have a larger adverse effect on life than higher temperatures. So the thermal cycling needs to be represented in another manner. Once again, take a look at Figure 1 to identify some of the properties of the function that you might be concerned with. Amplitude, or more specifically, the difference between the high and low temperatures is one of those properties. The period, which represents the time it takes to complete one full cycle, is another. In particular, you would want to know the time it takes to go from high temperature to low temperature or vice versa. In other words, there are two stresses in this case that would impact the life of the product: the difference between high and low temperature and the time it takes to do that. An example of this is shown in Figure 2, where TH and TL are the high and low temperatures, respectively, ΔT is the difference between the high and low temperatures and Ct is the cycle time it takes for the temperature to go from high to low temperature.
Figure 2: Thermal cycling defined as two constant stresses
Therefore, as the cycle time increases, the frequency of the thermal cycle decreases. Defining the thermal cycling in this manner will correctly take into account the effect that the stress has on the life of the component by not implying that the component gets better as the stress decreases. Note that in this case both stresses are constant stresses. It should be pointed out that this could also be expanded if additional variables were present or the profile were different.
Example with Thermal Cycling and Voltage
Let's consider an accelerated life test with 72 units all tested to failure with time measured in hours. Thermal cycling (temperature measured in Kelvin) and voltage (V) are the applied stresses, where the thermal cycling stress is a sinusoidal function with constant amplitude and period. The 72 units are broken down into 4 groups of 18 with each group being placed in a different chamber with different stress conditions. The test conditions for each chamber are displayed in Table 1.
Table 1: Chamber test conditions
The failure data set is presented in Table 2.
Table 2: Accelerated test data
For the first stress level, the difference between the high and low temperatures is 40K and it takes 12 hours for the stress to cycle from the high temperature down to the low temperature. The second, third and fourth stress levels can be interpreted in the same way. The data set is entered into ALTA PRO and the parameters are estimated using the general log-linear life-stress relationship (with a logarithmic transformation on temperature and voltage, and no transformation on cycle time) and Weibull life distribution, as shown in Figure 3.
Figure 3: Accelerated test data entered into ALTA 8 PRO
As you can see, there are three stress columns in the data sheet, along with the time-to-failure column. The first two stresses define the thermal cycling and the last stress column represents the applied voltage. The life vs. stress plot can be used to determine which stress has the greatest impact on the life of the component. The life vs. stress plots for the three available stresses are shown in Figures 4-6.
After examining the plots you will notice that voltage has the greatest overall effect on the life of the component. However with regard to the thermal cycling stress, the difference between the high and low temperature basically has no effect at all. As the cycle time increases, the life of the component increases. But how can this be? Life increasing with stress? Or is the stress really increasing? An increased cycle time indicates a slower frequency which means that the temperature is changing at a much slower rate. Therefore, the slower the rate of change in temperature, the less of a shock it is to the component. So as the cycle time increases, the stress that the component is seeing actually decreases. Other results, including "use level" results, can also be easily obtained once the model has been fitted and its parameters estimated.
When it is all said and done, a data set from an accelerated test with thermal cycling has been analyzed by treating the thermal cycling as two constant stresses. Analyzing the data this way gives you detailed information as to how the component under test is being affected by the overall test conditions. The test conditions can then be improved to conduct a more efficient accelerated test and now you have specific information indicating what stress is causing the component to fail.
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