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 Error	95% Normal CI
Distribution	Percent	Percentile	Standard 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.