Template:Example: Exponential Distribution Demonstration Test Example: Difference between revisions

Latest revision as of 06:39, 15 August 2012

Redirect to:

@@ Line 1: / Line 1: @@
-'''Exponential Distribution Demonstration Test Example'''
+#REDIRECT [[Exponential_Chi-Squared_Example]]
-In this example, we desire to design a test to demonstrate a reliability of 85% at  <math>{{t}_{DEMO}}=500</math>  hours with a 90% confidence, or  <math>CL=0.9,</math>  and two allowable failures,  <math>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:
-<center><math>\chi _{1-CL;2r+2}^{2}=\chi _{0.1;6}^{2}=10.6446</math></center>
-Substituting this into the chi-squared equation, we obtain:
-<center><math>{{T}_{a}}=\frac{\tfrac{500}{-ln(0.85)}\cdot 10.6446}{2}=16,374\text{ hours}</math></center>
-This means that 16,374 hours of total test time needs to be accumulated with no more than two failures in order to demonstrate the specified reliability.
-This example solved in Weibull++ is shown next.
-[[Image: Test Design Chi-Squared.png|thumb|center|650px]]
-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.