ALTA Example 8 - Multiple Time-Dependent Stresses
The cumulative damage model allows you to analyze accelerated life testing data with up to eight time-dependent stresses. In this example, we consider such a case and look at how to create stress profiles in which stress is a function of time.
Experiment and Data
18 units of an electronic component are subjected to temperature and voltage stresses. The temperature is initially set at 100 K (use stress level) and is then increased linearly to 200 K over a period of 20 hours. At 120 hours, the temperature is again increased to 300 K over a 20-hour period. The voltage is initially set at 4 V (use stress level) and is then increased linearly to 8 V over a period of 10 hours. At 110 hours, the voltage is again increased to 12 V over a 10-hour period. The following failure times (in hours) are observed in the test: 171, 174, 192, 195, 200, 210, 220, 231, 233, 240, 242, 244, 245, 245, 250, 270, 271 and 274.
The test objectives are to determine the B10 life of these components at the normal use stress levels of 100 K and 4 V, and to determine how the B10 life would change if the voltage use stress level were 2 V instead of 4 V.
Step 1: Using ALTA PRO, the analyst creates a new standard folio for ungrouped times-to-failure data with two stress columns: Temperature (100 K use level) and Voltage (4 V use level).
Step 2: To consider the time-dependent stresses applied during the test, the analyst adds two stress profiles to the project by choosing Insert > Tools > ALTA Stress Profile. The first stress profile is for the temperature and is renamed to "Temp Profile."
After entering the segment end times and stress levels, the temperature profile appears as shown next. Note that the segments during which the stress increases are represented as functions of time. The mathematical formulas for these lines are easily obtained using the starting and ending points for each segment.
The analyst then clicks the Validate Stress Profile icon to confirm that the segments are continuous, and then clicks the Plot icon to see the Stress vs. Time plot.
Next, the stress profile for voltage, called "Volt Profile," is validated using the same steps described above. The voltage stress profile and its plot are shown next.
Step 3: After returning to the standard folio, the analyst selects the cumulative damage (CD) life-stress model and the Weibull distribution in the Model drop-down list on the control panel. To specify that both temperature and voltage will be considered in the analysis, he selects the check boxes in the headers of the Temperature and Voltage columns. He then clicks the Stress Transformation link to specify the following transformations for each stress.
To calculate the data, each failure time is entered in the Time Failed column. To assign stress profiles to the stress columns for each data point, the analyst clicks the cell and chooses a profile from the drop-down list. Finally, he clicks the Calculate icon to analyze the data.
The calculated folio is shown next.
Step 4: The B10 life at the use stress level can be calculated using the Quick Calculation Pad (QCP). To open this tool, the analyst clicks the QCP icon.
The settings shown next are used to calculate the B10 life at 100 K and 4 V. The B10 life is found to be about 816 hours.
Step 5: To determine how the B10 life would change if the voltage use stress level were 2 V instead of 4 V, the analyst clicks inside the Stress field in the QCP and then changes the value of the voltage stress level to 2. Therefore, if the component is used at 100 K and 2 V, the B10 life is about 924 hours, as shown next.