Template:Example: Normal General Example All Data Type

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]