General Log-Linear (GLL)-Weibull Model

This example validates the results for the GLL life-stress relationship with a Weibull distribution in ALTA standard folios.

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.

The following table shows the data.

The model used in the book is:


 * $$\,\!ln\left ( \eta \right )=\alpha _{0}+\alpha _{1}\frac{1}{T}$$

The book has the following results:


 * The model parameters are: $$\,\!\alpha _{0}=-3.156$$, $$\,\!\alpha _{1}=4390$$ and $$\,\!\beta =2.27$$.


 * The variance of each parameter is: $$\,\!Var\left ( \alpha _{0} \right )=3.08$$, $$\,\!Var\left ( \alpha _{1} \right )=484819.5$$ and $$\,\!Var\left ( \beta\right )=0.1396$$.


 * The two-sided 90% confidence intervals for the model parameters are: $$\,\!\left [ \alpha _{0,L},\alpha _{0,U}  \right ]=\left [ -6.044, -0.269 \right ]$$ , $$\,\!\left [ \alpha _{1,L},\alpha _{1,U}  \right ]=\left [ 3244.8, 5535.3 \right ]$$ and $$\,\!\left [ \beta _{1,L},\beta _{1,U}  \right ]=\left [ 1.73, 2.97 \right ]$$.


 * 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 $$\,\!R\left ( 10000 \right )=0.9860$$ . The two-sided 90% confidence interval is [0.892, 0.998].

In ALTA, 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: