Background
The cumulative damage model allows you to analyze accelerated life testing data with up to eight time-varying 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
A sample of 18 units of an electronic component is subjected to temperature and voltage stresses. The temperature is initially set at 100K (use stress level) and is then increased linearly to 200K over a period of 20 hr. At 120 hr, the temperature is again increased to 300K over a 20-hr period. The voltage is initially set at 4V (use stress level) and is then increased linearly to 8V over a period of 10 hr. At 110 hr, the voltage is again increased to 12V over a 10-hr period. The following times-to-failure are observed in the test, in hours: 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 B(10) life of these components at the normal use stress levels of 100K and 4V and to determine how the B(10) life would change if the voltage use stress level were 2V instead of 4V.

Analysis
Step 1: Using ALTA 7 PRO, the analyst creates a Standard Folio for ungrouped times-to-failure data with temperature and voltage as the stress types, with the temperature use stress level set to 100K and the voltage use stress level set to 4V.

Step 2: The analyst adds two new Stress Profiles to the project. The Temp Profile is shown in Figure 1. The Volt Stress Profile is shown in Figure 2. Note that the periods during which the stress is being increased are represented as functions of time. The mathematical formulas for these lines are easily obtained, as the starting and ending points for each line are given.

Step 3: In the Standard Folio, the analyst selects the cumulative damage life-stress model and the Weibull distribution, then uses the Stress Transformation window to specify the Reciprocal (Arrhenius LSR) transformation to be applied to the temperature stress and the Logarithmic (Power LSR) transformation to be applied to the voltage stress. Figure 3 displays the Standard Folio with the times-to-failure data entered, the Temp Profile assigned to each data point in the Temperature column, the Volt Stress Profile assigned to each data point in the Voltage column and the parameters estimated.

Step 4: The B(10) life can be calculated using the QCP, as shown in Figure 4. The B(10) life at the use stress levels of 100K and 4V is found to be 814.07 hr.

Step 5: To determine how the B(10) life would change if the voltage use stress level were 2V instead of 4V, the analyst simply changes the voltage stress level in the QCP, as shown in Figure 5. If the component is used at 100K and 2V instead of 4V, the B(10) life is found to be 919.97 hr.