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Figure 4: Probability plot that compares the general log-linear model analysis with Arrhenius transform on temperature and IPL transform on humidity (shown in blue) against the field data analysis (shown in black)
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As technology evolves, however, it is becoming increasingly difficult to find an established relationship between life and stress for new failure mechanisms. If no model can be found, the most direct approach to determine the appropriate analysis model is to perform life tests at many different stress levels to empirically establish the mathematical form of the relationship. The drawback to this method is that it requires many tests and consequently can be very time-consuming and resource-intensive. This article uses a fictional example to present an alternative approach for choosing an accelerated testing data analysis model in the absence of an established physics-of-failure relationship between life and stress.
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Analysis of variance of primary data on plant growth analysis
The third candidate model for analyzing the accelerated testing data is the general log-linear (GLL) model. The life-stress relationship for the two-stress version of the general log-linear model is:
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The second candidate model for analyzing the accelerated testing data is the generalized Eyring model. The life-stress relationship for the generalized Eyring model is:
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Figure 3: Probability plot that compares the temperature-humidity model analysis extrapolated to use-level conditions (shown in blue) against the field data analysis (shown in black)
4.6 DATA SYNTHESIS - University of York
Figure 1 shows the effect of temperature on life, and Figure 2 shows the effect of humidity on life. As expected, increasing either of these stresses causes a decrease in life. However, Figure 3 shows a probability plot that superimposes the field data analysis against the analysis of the accelerated test data extrapolated to the use-level conditions (temperature = 313K and relative humidity = 50%). It can be seen that the temperature-humidity model predicts lifetimes that are much longer than observed in the field. For example, the B(10) life observed in the field is about 80,000 hours, while the B(10) life extrapolated to use conditions via the temperature-humidity model is around 1,400,000 hours. Therefore, XYZ Company concludes that there must be an interaction between the stresses and, therefore, the temperature-humidity model is not suitable for analysis.
4.6.2 Methods of data synthesis
where is the life of the device, is temperature, is relative humidity, and , and are model parameters. This model has no interaction term and therefore it assumes that the temperature and humidity stresses operate independently. Assuming a Weibull distribution, analysis of the accelerated testing data yields the parameters and 90% 2-sided confidence bounds on the parameters that are shown in Table 2.
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Figure 4 shows a probability plot that superimposes the field data analysis against the GLL analysis of the accelerated temperature/humidity data extrapolated to use-level conditions. The plot shows that the model provides fairly good correlation for unreliability values of about 25% and higher. However, since XYZ's device has very high reliability, the engineers are most concerned with very small unreliability values. For these values, the plot shows no overlap between the confidence bounds of the two analyses.