1P-Weibull with Zero Failure Data

This example compares the calculation for a 1-parameter Weibull with zero failure data.

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++: