Template:Example: Weibull Distribution Suspension and Interval Data Example - Revision history

Chris Kahn: Redirected page to Weibull Distribution Examples

2012-08-14T02:14:46Z

Redirected page to Weibull Distribution Examples

← Older revision		Revision as of 02:14, 14 August 2012
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	~~'''Published 3P Weibull Distribution Probability Plot Example'''~~		#REDIRECT [[Weibull Distribution Examples]]

	~~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" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"~~
	~~\|+ '''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\|650px]]~~

	~~The computed parameters using MLE are:~~

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

	~~using RRX:~~

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

	~~and using RRY:~~

	~~::<math>\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:~~
	~~[[Image: RRX Plot for Example 14.png\|center\|550px~~]]

Richard House at 02:18, 8 August 2012

2012-08-08T02:18:48Z

← Older revision		Revision as of 02:18, 8 August 2012
Line 62:		Line 62:
	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:		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~~]]		[[Image: Data Folio for Example 14.png\|center\|650px]]

	The computed parameters using MLE are:		The computed parameters using MLE are:

Richard House at 02:18, 8 August 2012

2012-08-08T02:18:00Z

← Older revision		Revision as of 02:18, 8 August 2012
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	\| 20\|\|48\|\|0\|\|F\|\|102		\| 20\|\|48\|\|0\|\|F\|\|102
	\|-		\|-
	\|
	\|}		\|}

Richard House at 02:17, 8 August 2012

2012-08-08T02:17:46Z

← Older revision		Revision as of 02:17, 8 August 2012
Line 3:		Line 3:
	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.		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~~"		{\| {\| border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
	\|+ '''The Test Data'''		\|+ '''The Test Data'''
	\| align="center" style="background:#f0f0f0;"\|'''Data Point Index'''		\| align="center" style="background:#f0f0f0;"\|'''Data Point Index'''

Richard House at 05:36, 6 August 2012

2012-08-06T05:36:02Z

← Older revision		Revision as of 05:36, 6 August 2012
Line 67:		Line 67:
	The computed parameters using MLE are:		The computed parameters using MLE are:

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

	using RRX:		using RRX:

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

	and using RRY:		and using RRY:
	~~<center>~~<math>\hat{\beta }=0.998;\text{ }\hat{\eta }=37.16</math~~></center~~>
			::<math>\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:		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]]		[[Image: RRX Plot for Example 14.png\|center\|550px]]

Richard House at 05:18, 6 August 2012

2012-08-06T05:18:03Z

← Older revision		Revision as of 05:18, 6 August 2012
Line 59:		Line 59:
	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'''.		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~~\|thumb~~\|center\|~~250px~~]]		[[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:		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~~\|thumb~~\|center\|~~250px~~]]		[[Image: Data Folio for Example 14.png\|center\|550px]]

	The computed parameters using MLE are:		The computed parameters using MLE are:
Line 77:		Line 77:

	The plot with the two-sided 90% confidence bounds for the rank regression on X solution is:		The plot with the two-sided 90% confidence bounds for the rank regression on X solution is:
	[[Image: RRX Plot for Example 14.png~~\|thumb~~\|center\|~~250px~~]]		[[Image: RRX Plot for Example 14.png\|center\|550px]]

Nicolette Young at 18:34, 25 April 2012

2012-04-25T18:34:15Z

← Older revision		Revision as of 18:34, 25 April 2012
Line 59:		Line 59:
	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'''.		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\|thumb\|center\|~~400px~~]]		[[Image: Data Type for Example 14.png\|thumb\|center\|250px]]

	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:		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\|thumb\|center\|~~400px~~]]		[[Image: Data Folio for Example 14.png\|thumb\|center\|250px]]

	The computed parameters using MLE are:		The computed parameters using MLE are:
Line 77:		Line 77:

	The plot with the two-sided 90% confidence bounds for the rank regression on X solution is:		The plot with the two-sided 90% confidence bounds for the rank regression on X solution is:
	[[Image: RRX Plot for Example 14.png\|thumb\|center\|~~400px~~]]		[[Image: RRX Plot for Example 14.png\|thumb\|center\|250px]]

Harry Guo at 23:15, 29 February 2012

2012-02-29T23:15:56Z

← Older revision		Revision as of 23:15, 29 February 2012
Line 4:		Line 4:

	{\| {\| border="1" class="wikitable" style="margin: 1em auto 1em auto"		{\| {\| border="1" class="wikitable" style="margin: 1em auto 1em auto"
	\|+ The Test Data'''		\|+ '''The Test Data'''
	\| align="center" style="background:#f0f0f0;"\|'''Data Point Index'''		\| align="center" style="background:#f0f0f0;"\|'''Data Point Index'''
	\| align="center" style="background:#f0f0f0;"\|'''Number in State'''		\| align="center" style="background:#f0f0f0;"\|'''Number in State'''
Line 59:		Line 59:
	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'''.		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\|thumb\|center\|400px]]

	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.		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\|thumb\|center\|400px]]

	The computed parameters using MLE are:		The computed parameters using MLE are:

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

	using RRX:		using RRX:

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

	and using RRY:		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:		The plot with the two-sided 90% confidence bounds for the rank regression on X solution is:
			[[Image: RRX Plot for Example 14.png\|thumb\|center\|400px]]

Harry Guo at 23:10, 29 February 2012

2012-02-29T23:10:13Z

Show changes

Harry Guo: Created page with '==Weibull Distribution Example 14== Suppose we want to model a left censored, right censored, interval, and complete data set, consisting of 274 units under test of which 185 un…'

2012-02-29T21:12:27Z

Created page with '==Weibull Distribution Example 14== Suppose we want to model a left censored, right censored, interval, and complete data set, consisting of 274 units under test of which 185 un…'

New page

==Weibull Distribution Example 14==

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. Table 6.8 contains the data.

Table 6.8 - The test data for Example 13

Data point index
Number in State
Last Inspection
State
(F or S)
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 to Weibull Distribution Example 14===

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 computed parameters using MLE are:

using RRX:

and using RRY:

The plot with the two-sided 90% confidence bounds for the rank regression on X solution is: