3P-Weibull Rank Regression: Difference between revisions

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


This example compares the 3-parameter Weibull with rank regression calculation.
This example validates the calculations for 3-parameter Weibull with rank regression in Weibull++ standard folios.




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{{Reference_Example_Heading3}}
{{Reference_Example_Heading3}}
In the book, the results are obtained by visually fitting a straight line to the median rank at each failure point. The reliability function for a 3P-Weibull distribution is:
In the book, the results are obtained by visually fitting a straight line to the median rank at each failure point. The reliability function for a 3P-Weibull distribution is:


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3P-Weibull Rank Regression

This example validates the calculations for 3-parameter Weibull with rank regression in Weibull++ standard folios.


Reference Case

Table 6.3 on page 292 in the book Reliability Engineering Handbook Vol 1 by Dr. Kececioglu, Prentice-Hall, 1991.


Data

Num. in State State F or S Time to Failure
1 F 46
1 F 64
1 F 83
1 F 105
1 F 123
1 F 150
4 S 200


Result

In the book, the results are obtained by visually fitting a straight line to the median rank at each failure point. The reliability function for a 3P-Weibull distribution is:

[math]\displaystyle{ R(t)=e^{-\left({\frac{t-\gamma }{\eta}}\right )^{\beta }}\,\! }[/math]


The results are [math]\displaystyle{ {\beta}\,\! }[/math] = 1.2, [math]\displaystyle{ {\eta}\,\! }[/math] = 144 and [math]\displaystyle{ {\gamma}\,\! }[/math] = 30


Results in Weibull++


3PW RR.png


3PW RR plot.png
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