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| '''Weibull Distribution Interval Data Example'''
| | #REDIRECT [[Weibull Distribution Examples]] |
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| 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:
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| {| border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
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| | align="center" style="background:#f0f0f0;"|'''Data Point Index'''
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| | align="center" style="background:#f0f0f0;"|'''Last Inspection'''
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| | align="center" style="background:#f0f0f0;"|'''Time to Failure'''
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| |-
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| | 1||30||32
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| |-
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| | 2||32||35
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| |-
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| | 3||35||37
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| |-
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| | 4||37||40
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| |-
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| | 5||42||42
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| |-
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| | 6||45||45
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| |-
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| | 7||50||50
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| |-
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| | 8||55||55
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| |-
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| |}
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| Analyze the data using several different parameter estimation techniques and compare the results.
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| '''Solution'''
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| 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'''.
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| [[Image: Data Type.png|center|550px]] | |
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| The data is entered as follows,
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| [[Image: Data Folio.png|center|550px]]
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| The computed parameters using maximum likelihood are:
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| ::<math>\begin{align}
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| & \hat{\beta }=5.76 \\
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| & \hat{\eta }=44.68 \\
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| \end{align}</math>
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| using RRX or rank regression on X:
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| ::<math>\begin{align}
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| & \hat{\beta }=5.70 \\
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| & \hat{\eta }=44.54 \\
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| \end{align}</math>
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| and using RRY or rank regression on Y:
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| ::<math>\begin{align}
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| & \hat{\beta }=5.41 \\
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| & \hat{\eta }=44.76 \\
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| \end{align}</math>
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| The plot of the MLE solution with the two-sided 90% confidence bounds is:
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| [[Image: MLE Plot.png|center|550px]]
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