Template:Example: Exponential Distribution Demonstration Test Example - Revision history

Lisa Hacker: Redirected page to Exponential Chi-Squared Example

2012-08-15T06:39:57Z

Redirected page to Exponential Chi-Squared Example

← Older revision		Revision as of 06:39, 15 August 2012
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	[[~~Category: For Deletion~~]]		#REDIRECT [[Exponential_Chi-Squared_Example]]

Kate Racaza: Merged content with page: Reliability_Test_Design

2012-08-01T05:32:04Z

Merged content with page: Reliability_Test_Design

← Older revision		Revision as of 05:32, 1 August 2012
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	~~'''Exponential Distribution Demonstration Test Example'''~~		[[Category: For Deletion]]

	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.

Chris Kahn at 10:27, 18 July 2012

2012-07-18T10:27:14Z

← Older revision		Revision as of 10:27, 18 July 2012
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	This example solved in Weibull++ is shown next.		This example solved in Weibull++ is shown next.

	[[Image: Test Design Chi-Squared.png\|thumb\|center\|~~400px~~]]		[[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.		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.

Lisa Hacker at 23:45, 29 March 2012

2012-03-29T23:45:07Z

← Older revision		Revision as of 23:45, 29 March 2012
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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:		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:

	::<math>\chi _{1-CL;2r+2}^{2}=\chi _{0.1;6}^{2}=10.6446</math>		<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:		Substituting this into the chi-squared equation, we obtain:

	::<math>{{T}_{a}}=\frac{\tfrac{500}{-ln(0.85)}\cdot 10.6446}{2}=16,374\text{ hours}</math>		<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 ~~need~~ to be accumulated with two failures in order to demonstrate the specified reliability.		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.		This example solved in Weibull++ is shown next.
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	[[Image: Test Design Chi-Squared.png\|thumb\|center\|400px]]		[[Image: Test Design Chi-Squared.png\|thumb\|center\|400px]]

	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.		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.

Harry Guo at 19:10, 23 February 2012

2012-02-23T19:10:32Z

← Older revision		Revision as of 19:10, 23 February 2012
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	This example solved in Weibull++ is shown next.		This example solved in Weibull++ is shown next.

	[[Image: Test Design Chi-Squared.png\|thumb\|center]]		[[Image: Test Design Chi-Squared.png\|thumb\|center\|400px]]

	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.		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.

Harry Guo at 19:10, 23 February 2012

2012-02-23T19:10:15Z

← Older revision		Revision as of 19:10, 23 February 2012
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	This example solved in Weibull++ is shown next.		This example solved in Weibull++ is shown next.

	[[Image: Test Design Chi-Squared.png\|thumb\|center~~\|400px~~]]		[[Image: Test Design Chi-Squared.png\|thumb\|center]]

	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.		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.

Harry Guo at 19:09, 23 February 2012

2012-02-23T19:09:58Z

← Older revision		Revision as of 19:09, 23 February 2012
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	This example solved in Weibull++ is shown next.		This example solved in Weibull++ is shown next.

			[[Image: Test Design Chi-Squared.png\|thumb\|center\|400px]]

	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.		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.

Harry Guo at 19:04, 23 February 2012

2012-02-23T19:04:43Z

← Older revision		Revision as of 19:04, 23 February 2012
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	Substituting this into ~~Eqn. (expchi1)~~, we obtain:		Substituting this into the Chi-Squared equation, we obtain:

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

Harry Guo at 19:03, 23 February 2012

2012-02-23T19:03:25Z

← Older revision		Revision as of 19:03, 23 February 2012
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	This example solved in Weibull++ is shown next.		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)~~.		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.

Harry Guo: moved Template:Example: Exponential Distribution Example to Template:Example: Exponential Distribution Demonstration Test Example

2012-02-23T00:04:23Z

moved Template:Example: Exponential Distribution Example to Template:Example: Exponential Distribution Demonstration Test Example

← Older revision	Revision as of 00:04, 23 February 2012
(No difference)