Template:Example: Weibull Distribution Suspension and Interval Data Example
Published 3P Weibull Distribution Probability Plot Example
Suppose we want to model a left censored, right censored, interval, and complete data set, consisting of 274 units under test of which 185 units fail. The following Table contains the data.
| Data Point Index | Number in State | Last Inspection | State (S or F) | State End Time |
| 1 | 2 | 5 | F | 5 |
| 2 | 23 | 5 | S | 5 |
| 3 | 28 | 0 | F | 7 |
| 4 | 4 | 10 | F | 10 |
| 5 | 7 | 15 | F | 15 |
| 6 | 8 | 20 | F | 20 |
| 7 | 29 | 20 | S | 20 |
| 8 | 32 | 0 | F | 22 |
| 9 | 6 | 25 | F | 25 |
| 10 | 4 | 27 | F | 30 |
| 11 | 8 | 30 | F | 35 |
| 12 | 5 | 30 | F | 40 |
| 13 | 9 | 27 | F | 45 |
| 14 | 7 | 25 | F | 50 |
| 15 | 5 | 20 | F | 55 |
| 16 | 3 | 15 | F | 60 |
| 17 | 6 | 10 | F | 65 |
| 18 | 3 | 5 | F | 70 |
| 19 | 37 | 100 | S | 100 |
| 20 | 48 | 0 | F | 102 |
Solution
This data set can be entered into Weibull++ by selecting the Times-to-failure and My data set contains suspensions (right censored data), My data set contains interval and/or left censored data and I want to enter data in groups options.
Since standard ranking methods for dealing with these different data types are inadequate, we will want to use the ReliaSoft ranking method. This option is the default in Weibull++ when dealing with interval data. The Data Folio is given below:
The computed parameters using MLE are:
- [math]\displaystyle{ \hat{\beta }=0.748;\text{ }\hat{\eta }=44.38 }[/math]
using RRX:
- [math]\displaystyle{ \hat{\beta }=1.057;\text{ }\hat{\eta }=36.29 }[/math]
and using RRY:
- [math]\displaystyle{ \hat{\beta }=0.998;\text{ }\hat{\eta }=37.16 }[/math]
The plot with the two-sided 90% confidence bounds for the rank regression on X solution is:
