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

		Standard Error	95.0% Fiducial CI
Percent	Percentile	Standard 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.