Template:Example: Exponential Distribution Demonstration Test Example

Exponential Distribution Demonstration Test Example

In this example, we desire to design a test to demonstrate a reliability of 85% at $${{t}_{DEMO}}=500$$  hours with a 90% confidence, or  $$CL=0.9,$$  and two allowable failures,  $$f=2$$. The chi-squared value can be determined from tables or the Quick Statistical Reference in Weibull++. In this example, the value is calculated as:


 * $$\chi _{1-CL;2r+2}^{2}=\chi _{0.1;6}^{2}=10.6446$$

Substituting this into the Chi-Squared equation, we obtain:


 * $${{T}_{a}}=\frac{\tfrac{500}{-ln(0.85)}\cdot 10.6446}{2}=16,374\text{ hours}$$

This means that 16,374 hours of total test time need to be accumulated with two failures in order to demonstrate the specified reliability.

This example solved in Weibull++ is shown next.



Given the test time, one can now solve for the number of units using the Chi-Squared equation. Similarly, if the number of units is given, one can determine the test time from the Chi-Squared equation for exponential test design.