1P-Weibull with Zero Failure Data

This example validates the calculations for a 1-parameter Weibull with zero failure data in Weibull++ standard folios.

The data set from Table 8.2 on page 196 of the book Statistical Methods for Reliability Data by Dr. Meeker and Dr. Escobar, John Wiley & Sons, 1998 is used.

The formulas for calculating the $$\eta \,\!$$ at a given confidence level of $$1 - \alpha\,\!$$ is on page 195.


 * $$\hat{\eta}_{L} = \left (\frac{2\sum_{i=1}^{n} t^{\beta}_{i}}{X^{2}_{(1-\alpha ;2)}}\right ) ^{\beta}$$

The 95% lower confidence bound on $$\eta \,\!$$ when $$\beta = 2\,\!$$ is:


 * $$\hat{\eta}_{L} = \left (\frac{2\sum_{i=1}^{n} t^{\beta}_{i}}{X^{2}_{(1-\alpha ;2)}} \right )^{\beta} = 10250\,\!$$

The following picture shows the result in Weibull++: