Template: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]\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.