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

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==Weibull Distribution Example 18: 2-Parameter MLE with Right Censored Data==
#REDIRECT [[Weibull Distribution Examples]]
 
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.
 
Table 6.9 - Nelson's Fan Failure Data (hr), for Example 17 [30]
 
[[Image:example18table6.9.png|center]]
 
===Published Results for Weibull Distribution Example 18===
 
Weibull parameters (two-parameter Weibull, MLE):
 
[[Image:example18formula.png|center]]
 
Published 95% FM confidence limits on the parameters:
 
[[Image:example18formula2.png|center]]
 
Published variance/covariance matrix:
 
[[Image:example18formula3.png|center]]
 
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 for Weibull Distribution Example 18===
 
This same data set can be entered into Weibull++ 7 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 6.9 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:example18autogroupdata.png|center]]
 
The data will be automatically grouped and put into a new grouped data sheet.
 
Weibull++ computed parameters for maximum likelihood are:
 
[[Image:compexample18formula.png|center]]
 
Weibull++ computed 95% FM confidence limits on the parameters:
 
[[Image:compexample18formula2.png|center]]
 
Weibull++ computed/variance covariance matrix:
 
[[Image:compexample18formula3.png|center]]
 
The two-sided 95% bounds on the parameters can be determined from the QCP, in the Parameter Bounds tab.
 
[[Image:ex18folioparameterbounds.png|center]]

Latest revision as of 02:16, 14 August 2012

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