General Log-Linear (GLL)-Weibull Model

This example validates the results for the GLL life-stress relationship with a Weibull distribution in Accelerated Life Testing (ALTA) life-stress data folios.

Reference Case

The data set is from Example 7.14 on page 297 in book Life Cycle Reliability Engineering by Dr. Guangbin Yang, John Wiley & Sons, 2007.

Data

The following table shows the data.

State F/S	Time to State (Hr)	Temperature (°C)	Group ID
F	1138	100	1
F	1944	100	1
F	2764	100	1
F	2846	100	1
F	3246	100	1
F	3803	100	1
F	5046	100	1
F	5139	100	1
S	5500	100	1
S	5500	100	1
S	5500	100	1
S	5500	100	1
F	1121	120	2
F	1572	120	2
F	2329	120	2
F	2573	120	2
F	2702	120	2
F	3702	120	2
F	4277	120	2
S	4500	120	2
F	420	150	3
F	650	150	3
F	703	150	3
F	838	150	3
F	1086	150	3
F	1125	150	3
F	1387	150	3
F	1673	150	3
F	1896	150	3
F	2037	150	3

Result

The model used in the book is:

The book has the following results:

• The model parameters are: , and .

• The variance of each parameter is: , and .

• The two-sided 90% confidence intervals for the model parameters are: , and .

• The estimated B10 life at temperature of 35°C is 24,286 hours. The two-sided 90% confidence interval is [10371, 56867].

• The estimated reliability at 35°C and 10,000 hours is . The two-sided 90% confidence interval is [0.892, 0.998].

Results in Weibull++

In Weibull++, the GLL model with Weibull distribution is used. Since temperature is the stress, the reciprocal transform is used. The results are:

• The model parameters are:

• The variances of the parameters are:

• The two-sided 90% confidence intervals for the model parameters are:

• The estimated B10 life and its two-sided 90% confidence intervals are:

• The estimated reliability with its two-sided 90% confidence interval at 35°C and 10,000 hours are: