Template:Reliability demonstration

Reliability Demonstration
Frequently, the entire purpose of designing a test with few or no failures is to demonstrate a certain reliability, $${{R}_{DEMO}}$$, at a certain time. With the exception of the exponential distribution (and ignoring the location parameter for the time being), this reliability is going to be a function of time, a shape parameter and a scale parameter.

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

where:


 * $${{t}_{DEMO}}$$ is the time at which the demonstrated reliability is specified.
 * $$\theta$$ is the shape parameter.
 * $$\phi$$ is the scale parameter.

Since required inputs to the process include $${{R}_{DEMO}}$$, $${{t}_{DEMO}}$$  and  $$\theta$$, the value of the scale parameter can be backed out of the reliability equation of the assumed distribution, and will be used in the calculation of another reliability value,  $${{R}_{TEST}}$$, which is the reliability that is going to be incorporated into the actual test calculation. How this calculation is performed depends on whether one is attempting to solve for the number of units to be tested in an available amount of time, or attempting to determine how long to test an available number of test units.