Template:Example: Weibull Distribution Interval Data Example

Weibull Distribution Interval Data Example

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:

Data Point Index	Last Inspection	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.

The data is entered as follows,

The computed parameters using maximum likelihood are:

[math]\displaystyle{ \begin{align} & \hat{\beta }=5.76 \\ & \hat{\eta }=44.68 \\ \end{align} }[/math]

using RRX or rank regression on X:

[math]\displaystyle{ \begin{align} & \hat{\beta }=5.70 \\ & \hat{\eta }=44.54 \\ \end{align} }[/math]

and using RRY or rank regression on Y:

[math]\displaystyle{ \begin{align} & \hat{\beta }=5.41 \\ & \hat{\eta }=44.76 \\ \end{align} }[/math]

The plot of the MLE solution with the two-sided 90% confidence bounds is: