Wolfram Demonstrations Project

The median rank function

is used to estimate the cumulative probability of failure of the

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.

Reference:

[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.

Contributed by: Frederick Wu

Based on work by: Jean Jacquelin

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Visualizing the Exact Median Rank