# 1P-Weibull with Zero Failure Data

 1P-Weibull with Zero Failure Data

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

Reference Case

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.

Data

Number in State State F or S Time to Failure
10 S 500
12 S 1000
8 S 1500
9 S 2000
7 S 2500
9 S 3000
6 S 3500
3 S 4000

Result

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:

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

Results in Weibull++

The following picture shows the result in Weibull++: