Template:Kaplan-Meier

Kaplan-Meier
The Kaplan-Meier estimator (also known as the product limit estimator) is used as an alternative to the median ranks method for calculating the estimates of the unreliability for probability plotting purposes. The equation of the estimator is given by:
 * $$\widehat{F}({{t}_{i}})=1-\underset{j=1}{\overset{i}{\mathop \prod }}\,\frac{{{n}_{j}}-{{r}_{j}}},\text{ }i=1,...,m$$

where:
 * $$\begin{align}

m = & {\text{total number of data points}} \\ n = & {\text{the total number of units}} \\ {n_i} = & n - \sum_{j = 0}^{i - 1}{s_j} - \sum_{j = 0}^{i - 1}{r_j}, \text{i = 1,...,m }\\ {r_j} = & {\text{ number of failures in the }}{j^{th}}{\text{ data group, and}} \\ {s_j} = & {\text{number of surviving units in the }}{j^{th}}{\text{ data group}} \\ \end{align} $$