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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:
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| ::<math>U=\frac{\tfrac{\underset{i=1}{\overset{N}{\mathop{\sum }}}\,{{X}_{i}}}{N}-\tfrac{T}{2}}{T\sqrt{\tfrac{1}{12N}}}</math>
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| where:
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| :• <math>T</math> = total operating time (termination time)
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| :• <math>{{X}_{i}}</math> = age of the system at the <math>{{i}^{th}}</math> successive failure
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| :• <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).
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| ::<math>U=-2.6121</math>
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| 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>
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| If <math>U>1.645</math> then a deteriorating trend would exist.
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