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| '''Determining Units for Available Test Time'''
| | #REDIRECT [[Reliability Test Design]] |
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| If one knows that the test is to last a certain amount of time, <math>{{t}_{TEST}}</math>, the number of units that must be tested to demonstrate the specification must be determined. The first step in accomplishing this involves calculating the <math>{{R}_{TEST}}</math> value.
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| This should be a simple procedure since:
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| <br>
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| ::<math>{{R}_{TEST}}=g({{t}_{TEST}};\theta ,\phi )</math>
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| <br>
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| and <math>{{t}_{DEMO}}</math>, <math>\theta </math> and <math>\phi </math> are already known, and it is just a matter of plugging these values into the appropriate reliability equation.
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| We now incorporate a form of the cumulative binomial distribution in order to solve for the required number of units. This form of the cumulative binomial appears as:
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| <br>
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| ::<math>1-CL=\underset{i=0}{\overset{f}{\mathop \sum }}\,\frac{n!}{i!\cdot (n-i)!}\cdot {{(1-{{R}_{TEST}})}^{i}}\cdot R_{TEST}^{(n-i)}</math>
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| <br>
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| where:
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| <br>
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| ::<math>\begin{align}
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| & CL= \text{the required confidence level} \\
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| & f= \text{the allowable number of failures} \\
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| & n= \text{the total number of units on test} \\
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| & {{R}_{TEST}}= \text{the reliability on test}
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| \end{align}</math>
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| <br>
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| Since <math>CL</math> and <math>f</math> are required inputs to the process and <math>{{R}_{TEST}}</math> has already been calculated, it merely remains to solve the cumulative binomial equation for <math>n</math>, the number of units that need to be tested.
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