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 [math]\displaystyle{ {{t}_{DEMO}}=500 }[/math] hours with a 90% confidence, or [math]\displaystyle{ CL=0.9, }[/math] and two allowable failures, [math]\displaystyle{ f=2 }[/math] . The chi-squared value can be determined from tables or the Quick Statistical Reference in Weibull++. In this example, the value is calculated as:

[math]\displaystyle{ \chi _{1-CL;2r+2}^{2}=\chi _{0.1;6}^{2}=10.6446 }[/math]

Substituting this into Eqn. (expchi1), we obtain:

[math]\displaystyle{ {{T}_{a}}=\frac{\tfrac{500}{-ln(0.85)}\cdot 10.6446}{2}=16,374\text{ hours} }[/math]

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 Eqn. (expchipv1). Similarly, if the number of units is given, one can determine the test time from Eqn. (expchipv1).