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| '''Exponential Distribution Demonstration Test Example'''
| | #REDIRECT [[Exponential_Chi-Squared_Example]] |
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| 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:
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| ::<math>\chi _{1-CL;2r+2}^{2}=\chi _{0.1;6}^{2}=10.6446</math>
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| Substituting this into the Chi-Squared equation, we obtain:
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| ::<math>{{T}_{a}}=\frac{\tfrac{500}{-ln(0.85)}\cdot 10.6446}{2}=16,374\text{ hours}</math>
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| This means that 16,374 hours of total test time need to be accumulated with two failures in order to demonstrate the specified reliability.
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| This example solved in Weibull++ is shown next.
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| [[Image: Test Design Chi-Squared.png|thumb|center|400px]] | |
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| 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.
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