Template:Example: Normal Distribution Likelihood Ratio Bound (Reliability): Difference between revisions

Latest revision as of 02:25, 13 August 2012

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-'''Normal Distribution Likelihood Ratio Bound Example (Reliability)'''
+#REDIRECT [[The Normal Distribution]]
-For the data given in Example 5, determine the two-sided 80% confidence bounds on the reliability estimate for  <math>t=30</math> .  The ML estimate for the reliability at  <math>t=30</math>  is 45.739%.
-'''Solution'''
-In this example, we are trying to determine the two-sided 80% confidence bounds on the reliability estimate of 45.739%. This is accomplished by substituting  <math>t=30</math>  and  <math>\alpha =0.8</math>  into the likelihood ratio equation for normal distribution, and varying  <math>\sigma </math>  until the maximum and minimum values of  <math>R</math>  are found. The following table gives the values of  <math>R</math>  based on given values of  <math>\sigma </math> .
-[[Image:tablerbasedonsigma.gif|thumb|center|400px| ]]
-This data set is represented graphically in the following contour plot:
-[[Image:crazyoplot.gif|thumb|center|400px| ]]
-As can be determined from the table, the lowest calculated value for  <math>R</math>  is 24.776%, while the highest is 68.000%. These represent the 80% two-sided confidence limits on the reliability at  <math>t=30</math>