1P-Weibull with Zero Failure Data: Difference between revisions

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{{Reference Example}}
{{Reference Example}}


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


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{{Reference_Example_Heading4}}
{{Reference_Example_Heading4}}


The following picture shows the results in Weibull++:
The following picture shows the result in Weibull++:


[[Image:1PW_no_failures.png|center]]
[[Image:1PW_no_failures.png|center]]

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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 [math]\displaystyle{ \eta \,\! }[/math] at a given confidence level of [math]\displaystyle{ 1 - \alpha\,\! }[/math] is on page 195.

[math]\displaystyle{ \hat{\eta}_{L} = \left (\frac{2\sum_{i=1}^{n} t^{\beta}_{i}}{X^{2}_{(1-\alpha ;2)}}\right ) ^{\beta} }[/math]


The 95% lower confidence bound on [math]\displaystyle{ \eta \,\! }[/math] when [math]\displaystyle{ \beta = 2\,\! }[/math] is:

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


Results in Weibull++

The following picture shows the result in Weibull++:

1PW no failures.png
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