Table of percentiles – 95.0% Fiducial confidence intervals for Probit Analysis

Use the Fiducial confidence intervals to determine a range of stress values that meet predetermined reliability standards. The Fiducial confidence intervals provide 95% confidence that a given percentage of units will fail at a stress level that is within the range set by the lower and upper confidence bounds.

Often, you may want to examine only the upper or lower bound rather than the entire confidence interval. Remember the following when you have a 95% confidence interval:
  • 95% of the time, the stress variable will be contained within the interval (between the upper and lower bounds).
  • 2.5% of the time, the stress variable will be contained in the area below the lower bound.
  • 2.5% of the time, the stress variable will be contained in the area above the upper bound.

Therefore, you can be 97.5% confident (95% from confidence interval + 2.5% from area below lower bound) that the stress variable is located below the upper bound. For more information on fiducial confidence intervals, go to What is a fiducial confidence interval?.

Example output

Table of Percentiles 95.0% Fiducial Standard CI Percent Percentile Error Lower Upper 1 432.767 45.8542 300.019 501.649 2 463.192 41.0355 345.266 525.291 3 482.496 38.0450 373.838 540.427 4 497.018 35.8391 395.242 551.902 5 508.830 34.0781 412.585 561.304 6 518.884 32.6067 427.289 569.364 7 527.699 31.3403 440.133 576.480 8 535.592 30.2277 451.589 582.896 9 542.771 29.2352 461.967 588.771 10 549.379 28.3398 471.482 594.217 20 598.480 22.4304 540.595 636.280 30 633.886 19.4337 587.639 669.400 40 664.139 18.1881 624.815 700.723 50 692.416 18.3649 656.409 733.152 60 720.692 19.8068 685.039 768.545 70 750.945 22.4716 713.104 808.979 80 786.351 26.5977 743.723 858.524 90 835.453 33.3805 783.926 929.497 91 842.060 34.3538 789.210 939.174 92 849.239 35.4233 794.925 949.712 93 857.132 36.6126 801.183 961.326 94 865.948 37.9558 808.140 974.328 95 876.002 39.5048 816.041 989.192 96 887.814 41.3455 825.280 1006.70 97 902.335 43.6350 836.585 1028.27 98 921.639 46.7171 851.535 1057.03 99 952.065 51.6465 874.954 1102.50

Interpretation

For the windshield data, you can be 95% confident that 1% of the windshields will fail at a velocity between 300.019 mph and 501.649 mph. That is, in repeated testing, 1% of the windshields will break at a velocity between 300.019 mph and 501.649 mph 95% of the time.

In terms of confidence bounds, you can predict that 1% of the windshields will break at a velocity below 300.019 2.5% of the time and 1% of the windshields will break at a velocity above 501.649 2.5% of the time.

Thus, if the velocity is less than the lower bound limit of 300.019 mph, then you can be 97.5% confident (95% + the upper bound area of 2.5%) that no more than 1% of the windshields will break. Or, at the 97.5% confidence level, if the velocity is less than 300.019 mph, then at least 99% of the windshields will withstand the impact.

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