Template:Example: Normal General Example Interval Data: Difference between revisions

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|colspan="3" style="text-align:center"| Table 8.3 - Non-Grouped Data Times-to-Failure with intervals (lnterval and left censored)
|colspan="3" style="text-align:center"| Table - Non-Grouped Data Times-to-Failure with intervals (lnterval and left censored)
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Revision as of 23:30, 10 February 2012

Normal Distribution General Example Interval Data

Eight units are being reliability tested and the following is a table of their times-to-failure:


Table - Non-Grouped Data Times-to-Failure with intervals (lnterval and left censored)
Data point index Last Inspected State End Time
1 30 32
2 32 35
3 35 37
4 37 40
5 42 42
6 45 45
7 50 50
8 55 55

Solution

This is a sequence of interval times-to-failure. This data set can be entered into Weibull++ by creating a data sheet that can be used to analyze times-to-failure data with interval and left censored data.

[math]\displaystyle{ }[/math]

Lastinspected.png
Lastinspectedsheet.png

The computed parameters for maximum likelihood are:

[math]\displaystyle{ \begin{align} & \widehat{\mu }= & 41.40 \\ & {{{\hat{\sigma }}}_{T}}= & 7.740. \end{align} }[/math]

For rank regression on x:

[math]\displaystyle{ \begin{align} & \widehat{\mu }= & 41.40 \\ & {{{\hat{\sigma }}}_{T}}= & 9.03. \end{align} }[/math]

For rank regression on y:

[math]\displaystyle{ \begin{align} & \widehat{\mu }= & 41.39 \\ & {{{\hat{\sigma }}}_{T}}= & 9.25. \end{align} }[/math]


A plot of the MLE solution is shown next.

[math]\displaystyle{ }[/math]

Lastinspectedplot.png