Template:Determining units for available test time: Difference between revisions
No edit summary |
Chris Kahn (talk | contribs) No edit summary |
||
| Line 1: | Line 1: | ||
'''Determining Units for Available Test Time''' | '''Determining Units for Available Test Time''' | ||
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. | 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: | This should be a simple procedure since: | ||
<br> | |||
::<math>{{R}_{TEST}}=g({{t}_{TEST}};\theta ,\phi )</math> | ::<math>{{R}_{TEST}}=g({{t}_{TEST}};\theta ,\phi )</math> | ||
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. | <br> | ||
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: | 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: | ||
<br> | |||
::<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> | ::<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> | ||
<br> | |||
where: | where: | ||
<br> | |||
::<math>\begin{align} | ::<math>\begin{align} | ||
| Line 22: | Line 32: | ||
\end{align}</math> | \end{align}</math> | ||
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. | <br> | ||
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. | |||
Revision as of 00:30, 9 March 2012
Determining Units for Available Test Time
If one knows that the test is to last a certain amount of time, [math]\displaystyle{ {{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]\displaystyle{ {{R}_{TEST}} }[/math] value.
This should be a simple procedure since:
- [math]\displaystyle{ {{R}_{TEST}}=g({{t}_{TEST}};\theta ,\phi ) }[/math]
and [math]\displaystyle{ {{t}_{DEMO}} }[/math], [math]\displaystyle{ \theta }[/math] and [math]\displaystyle{ \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:
- [math]\displaystyle{ 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]
where:
- [math]\displaystyle{ \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]
Since [math]\displaystyle{ CL }[/math] and [math]\displaystyle{ f }[/math] are required inputs to the process and [math]\displaystyle{ {{R}_{TEST}} }[/math] has already been calculated, it merely remains to solve the cumulative binomial equation for [math]\displaystyle{ n }[/math], the number of units that need to be tested.