Template:Simple actuarial method

Actuarial-Simple Method
The actuarial-simple method is an easy-to-use form of non-parametric data analysis that can be used for multiple censored data that are arranged in intervals. This method is based on calculating the number of failures in a time interval, rj, versus the number of operating units in that time period, nj. 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 ni 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: