Richard House: Redirected page to RGA Appendix B#Laplace Trend Test

2012-08-23T23:03:36Z

Redirected page to RGA Appendix B#Laplace Trend Test

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	~~==Laplace Trend Test==~~		#REDIRECT [[RGA_Appendix_B#Laplace_Trend_Test]]
	~~<br>~~
	The Laplace Trend Test tests 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:


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


	~~where:~~
	~~<br>~~
	~~:• <math>T</math> = total operating time (termination time)~~
	~~:• <math>{{X}_{i}}</math> = age of the system at the <math>{{i}^{th}}</math> successive failure~~
	~~:• <math>N</math> = total number of failures~~
	~~<br>~~
	The test statistic <math>U</math> is approximately a standard normal random variable. The critical value is read from the Standard Normal tables with a given significance level, <math>\alpha </math> .
	~~<br>~~
	~~<br>~~
	~~'''Example'''~~
	~~<br>~~
	~~Consider once again the data in Table B.1. Check for a trend within System 1 assuming a significance level of 0.10. Calculate the test statistic <math>U</math> for System 1 using Eqn. (Utatistic).~~


	~~::<math>U=-2.6121</math>~~


	From the Standard Normal tables with a significance level of 0.10, the critical value is equal to 1.645. If <math>-1.645<U<1.645</math> then we would fail to reject the hypothesis of no trend. However, since <math>U<-1.645</math> then an improving trend exists within System 1. <br>
	~~If <math>U>1.645</math> then a deteriorating trend would exist.~~

	~~<br>~~

Nicolette Young: Created page with '==Laplace Trend Test==
The Laplace Trend Test tests the hypothesis that a trend does not exist within the data. The Laplace Trend test is applicable to the following data ty…'

2012-01-10T23:10:31Z

Created page with '==Laplace Trend Test== The Laplace Trend Test tests the hypothesis that a trend does not exist within the data. The Laplace Trend test is applicable to the following data ty…'

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==Laplace Trend Test==
 
The Laplace Trend Test tests 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:

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

where:
 
:• <math>T</math> = total operating time (termination time)
:• <math>{{X}_{i}}</math> = age of the system at the <math>{{i}^{th}}</math> successive failure
:• <math>N</math> = total number of failures
 
The test statistic <math>U</math> is approximately a standard normal random variable. The critical value is read from the Standard Normal tables with a given significance level, <math>\alpha </math> .
 
 
'''Example'''
 
Consider once again the data in Table B.1. Check for a trend within System 1 assuming a significance level of 0.10. Calculate the test statistic <math>U</math> for System 1 using Eqn. (Utatistic).

::<math>U=-2.6121</math>

From the Standard Normal tables with a significance level of 0.10, the critical value is equal to 1.645. If <math>-1.645<U<1.645</math> then we would fail to reject the hypothesis of no trend. However, since <math>U<-1.645</math> then an improving trend exists within System 1. 
If <math>U>1.645</math> then a deteriorating trend would exist.

Template:Laplace trend test rsa - Revision history

Richard House: Redirected page to RGA Appendix B#Laplace Trend Test

Nicolette Young: Created page with '==Laplace Trend Test== The Laplace Trend Test tests the hypothesis that a trend does not exist within the data. The Laplace Trend test is applicable to the following data ty…'

Nicolette Young: Created page with '==Laplace Trend Test==
The Laplace Trend Test tests the hypothesis that a trend does not exist within the data. The Laplace Trend test is applicable to the following data ty…'