Template:Example: Normal Distribution Likelihood Ratio Bound (Reliability): Difference between revisions
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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> . | 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.png|center| | [[Image:tablerbasedonsigma.png|center|250px| ]] | ||
This data set is represented graphically in the following contour plot: | This data set is represented graphically in the following contour plot: | ||
Revision as of 21:13, 25 April 2012
Normal Distribution Likelihood Ratio Bound Example (Reliability)
For the data given in Example 5, determine the two-sided 80% confidence bounds on the reliability estimate for [math]\displaystyle{ t=30 }[/math] . The ML estimate for the reliability at [math]\displaystyle{ 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]\displaystyle{ t=30 }[/math] and [math]\displaystyle{ \alpha =0.8 }[/math] into the likelihood ratio equation for normal distribution, and varying [math]\displaystyle{ \sigma }[/math] until the maximum and minimum values of [math]\displaystyle{ R }[/math] are found. The following table gives the values of [math]\displaystyle{ R }[/math] based on given values of [math]\displaystyle{ \sigma }[/math] .
This data set is represented graphically in the following contour plot:
As can be determined from the table, the lowest calculated value for [math]\displaystyle{ R }[/math] is 24.776%, while the highest is 68.000%. These represent the 80% two-sided confidence limits on the reliability at [math]\displaystyle{ t=30 }[/math]