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, $${{t}_{TEST}}$$, the number of units that must be tested to demonstrate the specification must be determined. The first step in accomplishing this involves calculating the $${{R}_{TEST}}$$  value.

This should be a simple procedure since:


 * $${{R}_{TEST}}=g({{t}_{TEST}};\theta ,\phi )$$

and $${{t}_{DEMO}}$$,  $$\theta $$  and  $$\phi $$  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:


 * $$1-CL=\underset{i=0}{\overset{f}{\mathop \sum }}\,\frac{n!}{i!\cdot (n-i)!}\cdot {{(1-{{R}_{TEST}})}^{i}}\cdot R_{TEST}^{(n-i)}$$


 * where:


 * $$\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}$$

Since $$CL$$  and  $$f$$  are required inputs to the process and  $${{R}_{TEST}}$$  has already been calculated, it merely remains to solve the cumulative binomial equation for  $$n$$, the number of units that need to be tested.