Template:Demonstration test design

Demonstration Test Design
Frequently, a manufacturer will have to demonstrate that a certain product has met a goal of a certain reliability at a given time with a specific confidence. Often, it will be desired to demonstrate that this goal has been met with a zero-failure test. In order to design and conduct such a test, something about the behavior of the product will need to be known, i.e. the shape parameter of the product's life distribution. Beyond this, nothing more about the test is known, and usually the engineer designing the test will have to study the financial trade-offs between the number of units and amount of test time needed to demonstrate the desired goal. In cases like this, it is useful to have a ``carpet plot'' that shows the possibilities of how a certain specification can be met.

This methodology requires the use of the cumulative binomial distribution in addition to the assumed distribution of the products' lifetimes. Not only does the life distribution of the products need to be assumed beforehand, but a reasonable assumption of the distribution's shape parameter must be provided as well. Additional information that must be supplied includes the reliability to be demonstrated, the confidence level at which the demonstration takes place, the acceptable number of failures and either the number of available units or the amount of available test time. The output of this analysis can be the amount of time required to test the available units or the required number of units that need to be tested during the available test time.

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:


 * $$\begin{align}

& & {{t}_{DEMO}}\text{ is the time at which the demonstrated reliability is specified} \\ & & \theta \text{ is the shape parameter} \\ & & \phi \text{ is the scale parameter} \end{align}$$

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 in 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 find how long to test an available number of test units.