Template:Simple actuarial method

Simple Actuarial Method
The simple actuarial method is an easy-to-use form of nonparametric data analysis that can be used for multiply censored data that are arranged in intervals. This method is based on calculating the number of failures in a time interval, $${{r}_{j}},$$  versus the number of operating units in that time period,  $${{n}_{j}}$$. The equation for the reliability estimator for the standard actuarial method is given by:


 * $$\widehat{R}({{t}_{i}})=\underset{j=1}{\overset{i}{\mathop \prod }}\,\left( 1-\frac \right),\text{ }i=1,...,m$$


 * where:


 * $$\begin{align}

& m= & \text{the total number of intervals} \\ & n= & \text{the total number of units} \end{align}$$

The variable $${{n}_{i}}$$  is defined by:


 * $${{n}_{i}}=n-\underset{j=0}{\overset{i-1}{\mathop \sum }}\,{{s}_{j}}-\underset{j=0}{\overset{i-1}{\mathop \sum }}\,{{r}_{j,}}\text{ }i=1,...,m$$


 * where:


 * $$\begin{align}

& {{r}_{j}}= & \text{the number of failures in interval }j \\ & {{s}_{j}}= & \text{the number of suspensions in interval }j \end{align}$$

Example 2: