Template:Example: Weibull Distribution Suspension and Interval Data Example

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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.

The Test 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.

Data Type for Example 14.png

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:

Data Folio for Example 14.png

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:

RRX Plot for Example 14.png