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| '''Normal Distribution Likelihood Ratio Bound Example (Reliability)'''
| | #REDIRECT [[The Normal Distribution]] |
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| 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%.
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| '''Solution'''
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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> .
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| [[Image:tablerbasedonsigma.gif|thumb|center|400px| ]]
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| This data set is represented graphically in the following contour plot:
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| [[Image:WB.9 reliability v sigma.png|center|400px| ]]
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| 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>
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