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

Latest revision as of 02:23, 13 August 2012

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-'''Normal Distribution Likelihood Ratio Bound Example (Time)'''
+#REDIRECT [[The Normal Distribution]]
-For the data given in Example 5, determine the two-sided 80% confidence bounds on the time estimate for a reliability of 40%.  The ML estimate for the time at  <math>R(t)=40%</math>  is 31.637.
-'''Solution'''
-In this example, we are trying to determine the two-sided 80% confidence bounds on the time estimate of 31.637. This is accomplished by substituting  <math>R=0.40</math>  and  <math>\alpha =0.8</math>  into the likelihood ratio equation for the normal distribution, and varying  <math>\sigma </math>  until the maximum and minimum values of  <math>t</math>  are found. The following table gives the values of  <math>t</math>  based on given values of  <math>\sigma </math> .
-[[Image:tabletbasedonsigma.png|center|400px| ]]
-<math></math>
-This data set is represented graphically in the following contour plot:
-[[Image:WB.9 time v sigma contour.png|center|400px| ]]
-As can be determined from the table, the lowest calculated value for  <math>t</math>  is 25.046, while the highest is 39.250. These represent the 80% confidence limits on the time at which reliability is equal to 40%.