Table of percentiles for Distribution ID Plot (Arbitrary Censoring)

The percentiles provide the age by which a percentage of the population is expected to fail.

Sometimes it may be difficult to determine the best distribution based on the probability plot and goodness-of-fit measures. Use the table of percentiles to compare the percentiles for several selected distributions to see how your conclusions change depending on the distribution chosen.

If several distributions provide a reasonable fit to the data and similar conclusions, then the choice of the distribution is less important.

However, if your conclusions differ depending on the distribution, you may want to report the most conservative conclusion, collect more data, or use additional information, such as process knowledge and expert advice.

Example output

Table of Percentiles Standard 95% Normal CI Distribution Percent Percentile Error Lower Upper Weibull 1 37265.1 938.485 35470.3 39150.6 Lognormal 1 43817.7 688.033 42489.7 45187.2 Exponential 1 941.789 32.5296 880.143 1007.75 Normal 1 39810.3 1047.34 37757.6 41863.1 Weibull 5 49434.9 841.147 47813.5 51111.3 Lognormal 5 51458.9 624.451 50249.5 52697.5 Exponential 5 4806.55 166.019 4491.93 5143.21 Normal 5 50694.9 810.524 49106.3 52283.5 Weibull 10 56006.1 759.186 54537.7 57514.0 Lognormal 10 56063.1 585.905 54926.4 57223.3 Exponential 10 9873.05 341.017 9226.79 10564.6 Normal 10 56497.5 699.183 55127.1 57867.8 Weibull 50 77639.9 501.312 76663.5 78628.7 Lognormal 50 75850.3 576.625 74728.5 76988.9 Exponential 50 64952.9 2243.49 60701.3 69502.3 Normal 50 76966.0 514.756 75957.1 77974.9

Interpretation

Based on a Weibull distribution fitted to the muffler data, 1% of the new type of mufflers are expected to fail by 37265.1 miles.

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