Template:Laplace trend test rsa: Difference between revisions

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(Created page with '==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 ty…')
 
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==Laplace Trend Test==
#REDIRECT [[RGA_Appendix_B#Laplace_Trend_Test]]
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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:
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:• <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
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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> .
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'''Example'''
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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.
 
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Latest revision as of 23:03, 23 August 2012

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