Template:Example: Normal General Example All Data Type
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Normal Distribution General Example All Data Type
Suppose our data set includes left and right censored, interval censored and complete data as shown in the following table.
Grouped Data Times-to-Failure with Suspensions and Intervals (Interval, Left and Right Censored) | ||||
---|---|---|---|---|
Data point index | Number in State | Last Inspection | State (S or F) | State End Time |
1 | 1 | 10 | F | 10 |
2 | 1 | 20 | S | 20 |
3 | 2 | 0 | F | 30 |
4 | 2 | 40 | F | 40 |
5 | 1 | 50 | F | 50 |
6 | 1 | 60 | S | 60 |
7 | 1 | 70 | F | 70 |
8 | 2 | 20 | F | 80 |
9 | 1 | 10 | F | 85 |
10 | 1 | 100 | F | 100 |
Solution
This data set can be entered into Weibull++ by selecting the data type Times to Failure, with Right Censored Data (Suspensions), with Interval and Left Censored Data and with Grouped Observations.
The computed parameters using maximum likelihood are:
- [math]\displaystyle{ \begin{align} & \widehat{\mu }= & 48.11 \\ & {{{\hat{\sigma }}}_{T}}= & 26.42 \end{align} }[/math]
For rank regression on x:
- [math]\displaystyle{ \begin{align} & \widehat{\mu }= & 49.99 \\ & {{{\hat{\sigma }}}_{T}}= & 30.17 \end{align} }[/math]
For rank regression on y:
- [math]\displaystyle{ \begin{align} & \widehat{\mu }= & 51.61 \\ & {{{\hat{\sigma }}}_{T}}= & 33.07 \end{align} }[/math]