Hypothesis Tests - Revision history

Lisa Hacker at 20:40, 18 September 2023

2023-09-18T20:40:53Z

← Older revision		Revision as of 20:40, 18 September 2023
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	{{Template:~~RGA_BOOK_SUB~~\|Appendix B\|Hypothesis Tests}}		{{Template:RGA_BOOK\|Appendix B\|Hypothesis Tests}}
	The RGA software provides two types of hypothesis tests: common beta hypothesis (CBH) and Laplace trend. Both tests are applicable to the following data types:		The RGA software provides two types of hypothesis tests: common beta hypothesis (CBH) and Laplace trend. Both tests are applicable to the following data types:

Beth Ann Paape at 22:30, 3 July 2014

2014-07-03T22:30:18Z

← Older revision		Revision as of 22:30, 3 July 2014
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	{{Template:RGA_BOOK_SUB\|Appendix B\|Hypothesis Tests}}		{{Template:RGA_BOOK_SUB\|Appendix B\|Hypothesis Tests}}

	The RGA software provides two types of hypothesis tests: common beta hypothesis (CBH) and Laplace trend. Both tests are applicable to the following data types:		The RGA software provides two types of hypothesis tests: common beta hypothesis (CBH) and Laplace trend. Both tests are applicable to the following data types:

Beth Ann Paape at 22:27, 3 July 2014

2014-07-03T22:27:48Z

← Older revision		Revision as of 22:27, 3 July 2014
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	{{Template:RGA_BOOK_SUB\|Appendix B\|Hypothesis Tests}}		{{Template:RGA_BOOK_SUB\|Appendix B\|Hypothesis Tests}}

	~~There are~~ two hypothesis tests ~~available~~: common beta hypothesis (CBH) and Laplace trend. Both tests are applicable to the following data types:		The RGA software provides two types of hypothesis tests: common beta hypothesis (CBH) and Laplace trend. Both tests are applicable to the following data types:

	*Times-to-failure data		*Times-to-failure data

Beth Ann Paape at 22:22, 3 July 2014

2014-07-03T22:22:24Z

← Older revision		Revision as of 22:22, 3 July 2014
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	{{Template:RGA_BOOK_SUB\|Appendix B\|Hypothesis Tests}}		{{Template:RGA_BOOK_SUB\|Appendix B\|Hypothesis Tests}}


	There are two hypothesis tests available: common beta hypothesis (CBH) and Laplace trend. Both tests are applicable to the following data types:		There are two hypothesis tests available: common beta hypothesis (CBH) and Laplace trend. Both tests are applicable to the following data types:
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	==Common Beta Hypothesis Test==		==Common Beta Hypothesis Test==
	The common beta hypothesis (CBH) ~~test indicates whether~~ all ~~the~~ systems in the data set have similar beta ~~values so you~~		The common beta hypothesis (CBH) tests the hypothesis that all systems in the data set have similar values of beta. As shown by Crow [[RGA_References\|[17]]], suppose that <math>K\,\!</math> number of systems are under test. Each system has an intensity function given by:
	~~can evaluate whether the systems should be combined into a single representative system~~. As shown by Crow [[RGA_References\|[17]]], suppose that <math>K\,\!</math> number of systems are under test. Each system has an intensity function given by:

	:<math>{{u}_{q}}(t)={{\lambda }_{q}}{{\beta }_{q}}{{t}^{{{\beta }_{q}}-1}}\,\!</math>		:<math>{{u}_{q}}(t)={{\lambda }_{q}}{{\beta }_{q}}{{t}^{{{\beta }_{q}}-1}}\,\!</math>

Beth Ann Paape at 22:19, 3 July 2014

2014-07-03T22:19:43Z

@@ Line 1: / Line 1: @@
 {{Template:RGA_BOOK_SUB|Appendix B|Hypothesis Tests}}
 ==Common Beta Hypothesis Test==
-The common beta hypothesis (CBH) test is applicable to the following data types: multiple systems-concurrent operating times, repairable and fleet. As shown by Crow [[RGA_References|[17]]], suppose that <math>K\,\!</math> number of systems are under test. Each system has an intensity function given by:
+The common beta hypothesis (CBH) test indicates whether all the systems in the data set have similar beta values so you
 :<math>{{u}_{q}}(t)={{\lambda }_{q}}{{\beta }_{q}}{{t}^{{{\beta }_{q}}-1}}\,\!</math>
@@ Line 110: / Line 123: @@
 ==Laplace Trend Test==
-The Laplace trend test evaluates the hypothesis that a trend does not exist within the data. The Laplace trend test is applicable to the following data types:
+The Laplace trend test evaluates the hypothesis that a trend does not exist within the data. The Laplace trend test can determine whether the system is deteriorating, improving, or if there is no trend at all. Calculate the test statistic, <math>U\,\!</math>, using the following equation:
 :<math>U=\frac{\tfrac{\underset{i=1}{\overset{N}{\mathop{\sum }}}\,{{X}_{i}}}{N}-\tfrac{T}{2}}{T\sqrt{\tfrac{1}{12N}}}\,\!</math>

Beth Ann Paape at 19:52, 1 July 2014

2014-07-01T19:52:57Z

← Older revision		Revision as of 19:52, 1 July 2014
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	**Multiple Systems - Concurrent Operating Times		**Multiple Systems - Concurrent Operating Times
	**Multiple Systems with Dates		**Multiple Systems with Dates
	**Multiple Systems with Event Codes		**Multiple Systems with Event Codes
	*Repairable Systems ~~data~~		*Fielded data
	*Fleet ~~data~~		**Repairable Systems
			**Fleet

	The Laplace trend test can determine whether the system is deteriorating, improving, or if there is no trend at all. Calculate the test statistic, <math>U\,\!</math>, using the following equation:		The Laplace trend test can determine whether the system is deteriorating, improving, or if there is no trend at all. Calculate the test statistic, <math>U\,\!</math>, using the following equation:

Beth Ann Paape at 17:54, 1 July 2014

2014-07-01T17:54:08Z

← Older revision		Revision as of 17:54, 1 July 2014
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	The Laplace trend test evaluates the hypothesis that a trend does not exist within the data. The Laplace trend test is applicable to the following data types:		The Laplace trend test evaluates the hypothesis that a trend does not exist within the data. The Laplace trend test is applicable to the following data types:

	*Times-to-failure		*Times-to-failure data
	**Multiple Systems - Concurrent Operating Times		**Multiple Systems - Concurrent Operating Times
	**Multiple Systems with Dates		**Multiple Systems with Dates
	**Multiple Systems with Event Codes		**Multiple Systems with Event Codes
	*Repairable Systems		*Repairable Systems data
	*Fleet		*Fleet data

	The Laplace trend test can determine whether the system is deteriorating, improving, or if there is no trend at all. Calculate the test statistic, <math>U\,\!</math>, using the following equation:		The Laplace trend test can determine whether the system is deteriorating, improving, or if there is no trend at all. Calculate the test statistic, <math>U\,\!</math>, using the following equation:

Beth Ann Paape at 16:35, 1 July 2014

2014-07-01T16:35:58Z

← Older revision		Revision as of 16:35, 1 July 2014
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	==Laplace Trend Test==		==Laplace Trend Test==
	The Laplace trend test evaluates the hypothesis that a trend does not exist within the data. The Laplace trend test is applicable to the following data types: ~~multiple systems~~-~~concurrent operating times, repairable and fleet.~~ The Laplace trend test can determine whether the system is deteriorating, improving, or if there is no trend at all. Calculate the test statistic, <math>U\,\!</math>, using the following equation:		The Laplace trend test evaluates the hypothesis that a trend does not exist within the data. The Laplace trend test is applicable to the following data types:

			*Times-to-failure
			**Multiple Systems - Concurrent Operating Times
			**Multiple Systems with Dates
			**Multiple Systems with Event Codes
			*Repairable Systems
			*Fleet

			The Laplace trend test can determine whether the system is deteriorating, improving, or if there is no trend at all. Calculate the test statistic, <math>U\,\!</math>, using the following equation:

	:<math>U=\frac{\tfrac{\underset{i=1}{\overset{N}{\mathop{\sum }}}\,{{X}_{i}}}{N}-\tfrac{T}{2}}{T\sqrt{\tfrac{1}{12N}}}\,\!</math>		:<math>U=\frac{\tfrac{\underset{i=1}{\overset{N}{\mathop{\sum }}}\,{{X}_{i}}}{N}-\tfrac{T}{2}}{T\sqrt{\tfrac{1}{12N}}}\,\!</math>

Chris Kahn: /* Common Beta Hypothesis Example */

2014-06-12T17:51:35Z

Common Beta Hypothesis Example

← Older revision		Revision as of 17:51, 12 June 2014
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	{\|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"		{\|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
	\|-		\|-
	\|colspan="4" style="text-align:center"\|'''Repairable ~~system data~~'''		\|colspan="4" style="text-align:center"\|'''Repairable System Data'''
	\|-		\|-
	\| \|\|System 1\|\|System 2\|\|System 3		\| \|\|System 1\|\|System 2\|\|System 3

David J. Groebel at 21:35, 2 June 2014

2014-06-02T21:35:19Z

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