View source for 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.

{| {| border="1" class="wikitable" style="margin: 1em auto 1em auto"
  |+ '''The Test Data'''
| align="center" style="background:#f0f0f0;"|'''Data Point Index'''
| align="center" style="background:#f0f0f0;"|'''Number in State'''
| align="center" style="background:#f0f0f0;"|'''Last Inspection'''
| align="center" style="background:#f0f0f0;"|'''State (S or F)'''
| align="center" style="background:#f0f0f0;"|'''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'''.

[[Image: Data Type for Example 14.png|center|550px]]

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:

[[Image: Data Folio for Example 14.png|center|550px]]

The computed parameters using MLE are:

<center><math>\hat{\beta }=0.748;\text{  }\hat{\eta }=44.38</math></center>

using RRX:

<center><math>\hat{\beta }=1.057;\text{  }\hat{\eta }=36.29</math></center>

and using RRY:
<center><math>\hat{\beta }=0.998;\text{  }\hat{\eta }=37.16</math></center>

The plot with the two-sided 90% confidence bounds for the rank regression on X solution is:
[[Image: RRX Plot  for Example 14.png|center|550px]]