Template:Simple actuarial method: Difference between revisions

Latest revision as of 07:35, 29 June 2012

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-==Simple Actuarial Method==
+#REDIRECT [[Non-Parametric Life Data Analysis]]
-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,  <math>{{r}_{j}},</math>  versus the number of operating units in that time period,  <math>{{n}_{j}}</math> . The equation for the reliability estimator for the standard actuarial method is given by:
-::<math>\widehat{R}({{t}_{i}})=\underset{j=1}{\overset{i}{\mathop \prod }}\,\left( 1-\frac{{{r}_{j}}}{{{n}_{j}}} \right),\text{ }i=1,...,m</math>
-where:
-::<math>\begin{align}
-  & m= \text{the total number of intervals} \\
- & n= \text{the total number of units}
-\end{align}</math>
-The variable  <math>{{n}_{i}}</math>  is defined by:
-::<math>{{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</math>
-where:
-::<math>\begin{align}
-  & {{r}_{j}}= \text{the number of failures in interval }j \\
- & {{s}_{j}}= \text{the number of suspensions in interval }j
-\end{align}</math>
-'''Example 2:'''
-{{Example: Simple-Actuarial Example}}