Template:Determining units for available test time: Difference between revisions

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'''Determining Units for Available Test Time'''
#REDIRECT [[Reliability Test Design]]
 
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. 
 
This should be a simple procedure since:
 
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::<math>{{R}_{TEST}}=g({{t}_{TEST}};\theta ,\phi )</math>
 
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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.
 
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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::<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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where:
 
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::<math>\begin{align}
  & CL=  \text{the required confidence level} \\
& f= \text{the allowable number of failures} \\
& n=  \text{the total number of units on test} \\
& {{R}_{TEST}}=  \text{the reliability on test} 
\end{align}</math>
 
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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.

Latest revision as of 08:03, 29 June 2012

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