Degradation Data Analysis with a Power Regression Model

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

Reference Case

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.

Data

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%.

Time	1	2	3	4	5
100	1.05	0.58	0.86	0.6	0.62
200	1.4	0.9	1.25	0.6	0.64
300	1.75	1.2	1.45	0.6	1.25
400	2.1	1.75	1.75	0.9	1.3
500	2.1	2.01	1.75	0.9	0.95
600	2.8	2	2	1.2	1.25
700	2.8	2	2	1.5	1.55
800	2.8	2	2	1.5	1.9
900	3.2	2	2.3	1.5	1.25
1000	3.4	2.3	2.3	1.7	1.55
1200	3.8	2.6	2.6	2.1	1.5
1400	4.2	2.9	2.8	2.1	1.55
1600	4.2	3.2	3.15	1.8	1.9
1800	4.5	3.6	3.2	2.1	1.85
2000	4.9	3.8	3.2	2.1	2.2
2500	5.6	4.2	3.8	2.4	2.2
3000	5.9	4.4	3.8	2.7	2.5
3500	6.3	4.8	4	2.7	2.2
4000	6.6	5	4.2	3	2.8
4500	7	5.6	4.4	3	2.8
5000	7.8	5.9	4.6	3	2.8
6000	8.6	6.2	4.9	3.6	3.1
7000	9.1	6.8	5.2	3.6	3.1
8000	9.5	7.4	5.8	4.2	3.1
9000	10.5	7.7	6.1	4.6	3.7
10000	11.1	8.4	6.3	4.2	4.4
12000	12.2	8.9	7	4.8	3.7
14000	13	9.5	7.2	5.1	4.4
16000	14	10	7.6	4.8	4.4
18000	15	10.4	7.7	5.3	4.1
20000	16	10.9	8.1	5.8	4.1
25000	18.5	12.6	8.9	5.7	4.7
30000	20.3	13.2	9.5	6.2	4.7
35000	22.1	15.4	11.2	8	6.4
40000	24.2	18.1	14	10.9	9.4

Note: The results provided here were done with the "Use unbiased Std on Normal data" option set to No.

Result

In the book, the following equation is used: . It in fact is a power equation with and . 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: