Degradation Data Analysis with a Linear Regression Model

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Degradation Data Analysis with a Linear Regression Model

This example validates the results for a degradation analysis with a linear regression model in Weibull++ degradation folios.


Reference Case

The data set is from Example 13.10 on page 338 in the book Statistical Methods for Reliability Data by Dr. Meeker and Dr. Escobar, John Wiley & Sons, 1998.


Data

The test is for the current (i.e., amperage) of a laser device. Failure is defined as a 10% increases in amperage.

Time Unit Number
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
250 0.47 0.71 0.71 0.36 0.27 0.36 0.36 0.46 0.51 0.41 0.44 0.4 0.3 0.44 0.51
500 0.93 1.22 1.17 0.62 0.61 1.39 0.92 1.07 0.93 1.79 1 0.8 0.74 0.7 0.83
750 2.11 1.9 1.73 1.36 1.11 1.95 1.21 1.42 1.57 2.38 1.57 1.4 1.52 1.05 1.29
1000 2.72 2.3 1.99 1.95 1.77 2.86 1.46 1.77 1.96 3 1.96 1.7 1.85 1.35 1.52
1250 3.51 2.87 2.53 2.3 2.06 3.46 1.93 2.11 2.59 3.84 2.51 3 2.39 1.8 1.91
1500 4.34 3.75 2.97 2.95 2.58 3.81 2.39 2.4 3.29 4.5 2.84 3.6 2.95 2.55 2.27
1750 4.91 4.42 3.3 3.39 2.99 4.53 2.68 2.78 3.61 5.25 3.47 4 3.51 2.83 2.78
2000 5.48 4.99 3.94 3.79 3.38 5.35 2.94 3.02 4.11 6.26 4.01 4.4 3.92 3.39 3.42
2250 5.99 5.51 4.16 4.11 4.05 5.92 3.42 3.29 4.6 7.05 4.51 4.8 5.03 3.72 3.78
2500 6.72 6.07 4.45 4.5 4.63 6.17 4.09 3.75 4.91 7.8 4.8 5.2 5.47 4.09 4.11
2750 7.13 6.64 4.89 4.72 5.24 7.7 4.58 4.16 5.34 8.32 5.2 5.5 5.84 4.83 4.38
3000 8 7.16 5.27 4.98 5.62 8.61 4.84 4.76 5.84 8.93 5.66 6 6.5 5.41 4.63
3250 8.92 7.78 5.69 5.28 6.04 9.15 5.11 5.16 6.4 9.55 6.2 6.2 6.94 5.76 5.38
3500 9.49 8.42 6.02 5.61 6.32 9.95 5.57 5.46 6.84 10.5 6.54 7 7.39 6.14 5.84
3750 9.87 8.91 6.45 5.95 7.1 10.49 6.11 5.81 7.2 11.3 6.96 7.4 7.85 6.51 6.16
4000 10.94 9.28 6.88 6.14 7.59 11.01 7.17 6.24 7.88 12.2 7.42 7.9 8.09 6.88 6.62


Result

The book provides a linear regression model, [math]y=b+at\,\![/math], but the parameters of the model are not provided. Only the predicted failure times are given. These are: 3702, 4194, 5847, 6172, 5301, 3592, 6051, 6538, 5110, 3306, 5326, 4995, 4721, 5689, and 6102. A Weibull distribution is used to fit the data; however, the model parameters are not provided. Only a probability plot is given.


Results in Weibull++

  • The following picture shows the parameters of the linear regression model for each unit.
DA linear model.png


  • The predicted pseudo failure times are shown next.
DA linear extrapolated.png


The predicted failure times in Weibull++ are slightly different from the values given in the book. Since the book does not provide the model parameters, we couldn’t compare the Weibulll++ results with the results in the book.


  • The next picture shows the parameters of the fitted Weibull distribution.
DA linear plot.png