1P-Weibull with Zero Failure Data: Difference between revisions
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Kate Racaza (talk | contribs) (Created page with '{{Reference Example}} This example compares the calculation for a 1-parameter Weibull with zero failure data. {{Reference_Example_Heading1}} The data from Table 8.2 on page 1…') |
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{{Reference Example}} | {{Reference Example}} | ||
This example | This example validates the calculations for a 1-parameter Weibull with zero failure data in Weibull++ standard folios. | ||
{{Reference_Example_Heading1}} | {{Reference_Example_Heading1}} | ||
The data 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 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. | ||
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The formulas for calculating the <math>\eta \,\!</math> at a given confidence level of <math>1 - \alpha\,\!</math> is on page 195. | The formulas for calculating the <math>\eta \,\!</math> at a given confidence level of <math>1 - \alpha\,\!</math> is on page 195. | ||
::<math>\hat{\eta}_{L} = \left (\frac{2\sum_{i=1}^{n} t^{\beta}_{i}}{ | ::<math>\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>\eta \,\!</math> when <math>\beta = 2\,\!</math> is: | The 95% lower confidence bound on <math>\eta \,\!</math> when <math>\beta = 2\,\!</math> is: | ||
::<math>\hat{\eta}_{L} = \left (\frac{2\sum_{i=1}^{n} t^{\beta}_{i}}{ | ::<math>\hat{\eta}_{L} = \left (\frac{2\sum_{i=1}^{n} t^{\beta}_{i}}{X^{2}_{(1-\alpha ;2)}} \right )^{\beta} = 10250\,\!</math> | ||
{{Reference_Example_Heading4}} | {{Reference_Example_Heading4}} | ||
The following picture shows the result in Weibull++: | |||
[[Image:1PW_no_failures.png|center]] | [[Image:1PW_no_failures.png|center]] |
Latest revision as of 16:14, 28 September 2015
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