Degradation Data Analysis with a Power Regression Model

This example compares the results for a degradation analysis with a power regression model.

The data set is from Example 8.1 on page 336 in the book Life Cycle Reliability Engineering by Dr. Guangbin Yang, John Wiley & Sons, 2007.

The following table shows the percent transconductance degradation data taken at different times for five units of a MOS field-effect transistor. The failure criterion is defined as a degradation greater than or equal to 15%.

In the book, the following equation is used: $$ln(y) = \beta_{1} + \beta_{2} ln(t)\,\!$$. It in fact is a power equation $$y = bt^{a}\,\!$$ with $$ln(b) = \beta_{1}\,\!$$ and $$a = \beta_{2}\,\!$$. This degradation equation is used for each test unit to predict the pseudo failure time, and then a lognormal distribution is used to model the pseudo failure times. The results are:


 * The parameters of the power regression model for each unit are:
 * For unit 1: $$\beta_{1}\,\!$$ = -2.413, $$\beta_{2}\,\!$$ = 0.524
 * For unit 2: $$\beta_{1}\,\!$$ = -2.735, $$\beta_{2}\,\!$$ = 0.525
 * For unit 3: $$\beta_{1}\,\!$$ = -2.056, $$\beta_{2}\,\!$$ = 0.424
 * For unit 4: $$\beta_{1}\,\!$$ = -2.796, $$\beta_{2}\,\!$$ = 0.465
 * For unit 5: $$\beta_{1}\,\!$$ = -2.217, $$\beta_{2}\,\!$$ = 0.383


 * The predicted pseudo failure times are: 17,553; 31,816; 75,809; 138,229.


 * The parameters of the fitted lognormal distribution are: Ln-Mean = 11.214, Ln-Std = 1.085.


 * The following picture shows the parameters of the power regression model for each unit.




 * The predicted pseudo failure times are shown next.




 * The next picture shows the parameters of the fitted lognormal distribution.