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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:
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| ::<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>
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| where:
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| ::<math>\begin{align}
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| & m= \text{the total number of intervals} \\
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| & n= \text{the total number of units}
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| \end{align}</math>
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| The variable <math>{{n}_{i}}</math> is defined by:
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| ::<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>
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| where:
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| ::<math>\begin{align}
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| & {{r}_{j}}= \text{the number of failures in interval }j \\
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| & {{s}_{j}}= \text{the number of suspensions in interval }j
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| \end{align}</math>
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| '''Example 2:'''
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| {{Example: Simple-Actuarial Example}}
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