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

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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.
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]]
[[Image:example18table.png|center]]


'''Published Results:'''
'''Published Results:'''
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Weibull parameters (2P-Weibull, MLE):
Weibull parameters (2P-Weibull, MLE):


[[Image:example18formula.png|center]]
[[Image:example18formula.png]]




Published 95% FM confidence limits on the parameters:
Published 95% FM confidence limits on the parameters:


[[Image:example18formula2.png|center]]
[[Image:example18formula2.png]]
 


Published variance/covariance matrix:
Published variance/covariance matrix:


[[Image:example18formula3.png|center]]
[[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.
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++'''
'''Computed Results in Weibull++'''
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[[Image:groupdataicon.png|center]]
[[Image:groupdataicon.png|center]]


[[Image:Weibull Distribution Example 18 Group Data.png|thumb|center|250px]]
[[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.
The data will be automatically grouped and put into a new grouped data sheet.
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Weibull++ computed parameters for maximum likelihood are:
Weibull++ computed parameters for maximum likelihood are:


[[Image:compexample18formula.png|center]]
[[Image:compexample18formula.png]]


Weibull++ computed 95% FM confidence limits on the parameters:
Weibull++ computed 95% FM confidence limits on the parameters:


[[Image:compexample18formula2.png|center]]
[[Image:compexample18formula2.png]]


Weibull++ computed/variance covariance matrix:
Weibull++ computed/variance covariance matrix:


[[Image:compexample18formula3.png|center]]
[[Image:compexample18formula3.png]]


The two-sided 95% bounds on the parameters can be determined from the QCP, in the Parameter Bounds tab.
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|250px]]
[[Image:Weibull Distribution Example 18 QCP.png|center|thumb|450px]]


[[Image: Weibull Distribution Example 18 QCP Parameter Bounds.png|thumb|center|250px]]
[[Image: Weibull Distribution Example 18 QCP Parameter Bounds.png|thumb|center|550px]]

Revision as of 05:24, 6 August 2012

Published 2P Weibull Distribution Suspension Data MLE Example

From Wayne Nelson, Fan Example, Applied Life Data Analysis, page 317 [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.

Example18table.png

Published Results:

Weibull parameters (2P-Weibull, MLE):

Example18formula.png


Published 95% FM confidence limits on the parameters:

Example18formula2.png

Published variance/covariance matrix:

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.

Groupdataicon.png
Weibull Distribution Example 18 Group Data.png

The data will be automatically grouped and put into a new grouped data sheet.

Weibull++ computed parameters for maximum likelihood are:

Compexample18formula.png

Weibull++ computed 95% FM confidence limits on the parameters:

Compexample18formula2.png

Weibull++ computed/variance covariance matrix:

Compexample18formula3.png

The two-sided 95% bounds on the parameters can be determined from the QCP, in the Parameter Bounds tab.

Weibull Distribution Example 18 QCP.png
Weibull Distribution Example 18 QCP Parameter Bounds.png
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