ALTA Example 5 - Indicator Variables
Software Used: ALTA 7 PRO
[Download ALTA 7 Example File (*.ralp)]
Background
In many cases, the life of a product is a function of stress and some other engineering variable, like materials, vendors or operation type. For this type of product, ALTA 7 PRO provides the general log-linear life-stress relationship, which allows you to analyze up to eight stress types and specify an underlying relationship for each stress.
Experiment and Data
A sample of electronic components are subjected to a quantitative accelerated life test in which three stress types are applied to the units. The stress types include temperature, voltage and a third indicator variable to describe whether the units are operated continuously or turned on and off. The stress profile for this test is presented in Table 1 and the time-to-failure and time-to-suspension data are presented in Table 2. The normal use stress levels are 328K for temperature and 10V for voltage.
| Table 1 Stress Profile Summary |
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| Table 2 Failure and Suspension Data |
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Analysis
The analysis is performed in an ALTA Standard Folio for grouped times-to-failure with suspensions data with three stress columns for temperature, voltage and operation type and a subset ID column. The operation type is treated as an indicator variable, with the discrete values of 0 and 1 to represent on/off and continuous operation, respectively. The stress profile identifier is entered in ALTA's multi-purpose Subset ID column, which is renamed to Stress Profile.
The general log-linear life-stress model is used and the Weibull distribution is used as the underlying life distribution for the data set. In the Stress Tranformation window, the transformation relationship is specified for each stress type. Temperature follows an Arrhenius model, voltage follows a power model and no transformation is performed on the operation type.
Figure 1 shows the ALTA Data Folio with data entered and parameters calculated.
Figure 1: The calculated results for the general log-linear life-stress model and Weibull life distribution.
Once the parameters are estimated, a variety of plots and results can be obtained.
The Weibull probability plot for the data is presented in Figure 2. This plot can be used to examine the choice of an underlying life distribution and the assumption of a common slope (shape parameter) at all stress levels. The linearity of the data and the fact that the data for each stress level appears parallel reinforce the assumptions made.
Figure 2: The Weibull probability plot for the analysis.
Life vs. stress plots can be very useful in assessing the effect of each stress on a product's failure. In this case, since the life is a function of three stresses, three different life vs. stress plots are available. These plots are created by holding two of the stresses constant at the desired use level and varying the remaining stress. Figure 3 displays the life vs. stress plot for temperature.
Figure 3: The effects of temperature on life. The life vs. stress plot with voltage and operation type held constant.
Figure 4 displays the life vs. stress plot for voltage.
Figure 4: The effects of voltage on life. The life vs. stress plot with temperature and operation type held constant.
The effects of the two different operation types on life can be observed in Figure 5. It can be seen that the on/off cycling has a greater effect on the life of the product in terms of accelerating failure than the continuous operation. In other words, a higher reliability can be achieved by running the product continuously.
Figure 5: The effects of operation type (on/off or continuous) on life. The life vs. stress plot with temperature and voltage held constant.
