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:

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:

$$\begin{align} & \hat{\beta }=5.76 \\ & \hat{\eta }=44.68 \\ \end{align}$$

using RRX or rank regression on X:

$$\begin{align} & \hat{\beta }=5.70 \\ & \hat{\eta }=44.54 \\ \end{align}$$

and using RRY or rank regression on Y:

$$\begin{align} & \hat{\beta }=5.41 \\ & \hat{\eta }=44.76 \\ \end{align}$$

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