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'''Weibull Distribution Interval Data Example'''
#REDIRECT [[Weibull Distribution Examples]]
 
Suppose that we have run an experiment with eight units being tested and the following is a table of their last inspection times and times-to-failure:
 
{| border="1"
| align="center" style="background:#f0f0f0;"|'''Data Point Index'''
| align="center" style="background:#f0f0f0;"|'''Last Inspection'''
| align="center" style="background:#f0f0f0;"|'''Time to Failure'''
|-
| 1||30||32
|-
| 2||32||35
|-
| 3||35||37
|-
| 4||37||40
|-
| 5||42||42
|-
| 6||45||45
|-
| 7||50||50
|-
| 8||55||55
|-
|
|}
 
Analyze the data using several different parameter estimation techniques and compare the results.
 
'''Solution'''
 
This data set can be entered into Weibull++ by opening a new '''Data Folio''' and choosing '''Times-to-failure''' and '''My data set contains interval and/or left censored data'''.
 
[[Image: Data Type.png|thumb|center|400px]]
 
The data is entered as follows,
 
[[Image: Data Folio.png|thumb|center|400px]]
 
The computed parameters using maximum likelihood are:
 
<center><math>\begin{align}
  & \hat{\beta }=5.76 \\
& \hat{\eta }=44.68 \\
\end{align}</math></center>
 
using RRX or rank regression on X:
 
<center><math>\begin{align}
  & \hat{\beta }=5.70 \\
& \hat{\eta }=44.54 \\
\end{align}</math></center>
 
and using RRY or rank regression on Y:
 
<center><math>\begin{align}
  & \hat{\beta }=5.41 \\
& \hat{\eta }=44.76 \\
\end{align}</math></center>
 
The plot of the MLE solution with the two-sided 90% confidence bounds is:
[[Image: MLE Plot.png|thumb|center|400px]]

Latest revision as of 02:15, 14 August 2012

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