Visualizing the Exact Median Rank

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The median rank function is used to estimate the cumulative probability of failure of the of identically stressed samples. There are several simple formulas proposed by Weibull and others [1] that give approximate values for the median rank.


The exact median rank function is related to the incomplete beta function , which is hard to calculate. Jacquelin [2] recommends an algorithm based on the Newton-Raphson method.

This Demonstration presents the exact median rank using Jacquelin's method and plots it in different ways.


Contributed by: Frederick Wu (March 2011)
Based on work by: Jean Jacquelin
Open content licensed under CC BY-NC-SA




[1] W. Weibull, Fatigue Testing and Analysis of Results, New York: Pergamon Press, 1961 pp. 193–199.

[2] J. Jacquelin, "A Reliable Algorithm for the Exact Median Rank Function," IEEE Transactions on Electrical Insulation, 28(2), 1993 pp. 168–171.

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