Template:Example: Published 2P Weibull Distribution Suspension Data MLE Example: Difference between revisions

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'''Published 2P Weibull Distribution Suspension Data MLE Example '''
#REDIRECT [[Weibull Distribution Examples]]
 
From Wayne Nelson, Fan Example, Applied Life Data Analysis, page 317 [[Appendix: Weibull References|[30]]].
 
Seventy diesel engine fans accumulated 344,440 hours in service and twelve of them failed. A table of their life data is shown next (+ denotes non-failed units or suspensions, using Dr. Nelson's nomenclature). Evaluate the parameters with their two-sided 95% confidence bounds, using MLE for the two-parameter Weibull distribution.
 
[[Image:example18table.png|center]]
 
'''Published Results:'''
 
Weibull parameters (2P-Weibull, MLE):
 
[[Image:example18formula.png]]
 
 
Published 95% FM confidence limits on the parameters:
 
[[Image:example18formula2.png]]
 
Published variance/covariance matrix:
 
[[Image:example18formula3.png]]
 
Note that Nelson expresses the results as multiples of 1000 (or = 26.297, etc.). The published results were adjusted by this factor to correlate with Weibull++ results.
 
'''Computed Results in Weibull++'''
 
This same data set can be entered into Weibull++ by selecting the data sheet Times to Failure, with Right Censored Data (Suspensions) and I want to enter data in groups (in order to group identical values) options, and using two-parameter Weibull and MLE to calculate the parameter estimates.
 
You can also enter the data as given in Table without grouping them by opening a Data Sheet with Times to Failure and the with Right Censored Data (Suspensions) options. Then click the Group Data icon and chose Group exactly identical values.
 
[[Image:groupdataicon.png|center]]
 
[[Image:Weibull Distribution Example 18 Group Data.png|thumb|center|450px]]
 
The data will be automatically grouped and put into a new grouped data sheet.
 
Weibull++ computed parameters for maximum likelihood are:
 
[[Image:compexample18formula.png]]
 
Weibull++ computed 95% FM confidence limits on the parameters:
 
[[Image:compexample18formula2.png]]
 
Weibull++ computed/variance covariance matrix:
 
[[Image:compexample18formula3.png]]
 
The two-sided 95% bounds on the parameters can be determined from the QCP, in the Parameter Bounds tab.
 
[[Image:Weibull Distribution Example 18 QCP.png|center|thumb|450px]]
 
[[Image: Weibull Distribution Example 18 QCP Parameter Bounds.png|thumb|center|550px]]

Latest revision as of 02:16, 14 August 2012

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