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  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  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.