Exponential Chi-Squared Example - Revision history

Lisa Hacker at 18:55, 18 September 2023

2023-09-18T18:55:33Z

← Older revision		Revision as of 18:55, 18 September 2023
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	<noinclude>{{Banner Weibull Examples}}		<noinclude>{{Banner Weibull Examples}}
	''This example appears in the [~~[Reliability_Test_Design\|~~Life ~~Data Analysis Reference book]~~]''.		''This example appears in the [https://help.reliasoft.com/reference/life_data_analysis Life data analysis reference]''.

	</noinclude>		</noinclude>

Kate Racaza at 17:14, 9 December 2015

2015-12-09T17:14:17Z

← Older revision		Revision as of 17:14, 9 December 2015
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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\|center\|~~650px~~]]		[[Image: Test Design Chi-Squared.png\|center\|800px]]

	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.

Richard House at 19:52, 26 September 2012

2012-09-26T19:52:01Z

← Older revision		Revision as of 19:52, 26 September 2012
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	</noinclude>		</noinclude>
	In this example, we will use the exponential chi-squared method to design a test that will demonstrate a reliability of 85% at <math>{{t}_{DEMO}}=500\,\!</math> hours with a 90% confidence (or <math>CL=0.9\,\!</math>) if no more than 2 failures occur during the test (<math>f=2\,\!</math>). The chi-squared value can be determined from tables or the Quick Statistical Reference (QSR) tool in Weibull++. In this example, the value is calculated as:		In this example, we will use the exponential chi-squared method to design a test that will demonstrate a reliability of 85% at <math>{{t}_{DEMO}}=500\,\!</math> hours with a 90% confidence (or <math>CL=0.9\,\!</math>) if no more than 2 failures occur during the test (<math>f=2\,\!</math>). The chi-squared value can be determined from tables or the Quick Statistical Reference (QSR) tool 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>		::<math>\chi _{1-CL;2r+2}^{2}=\chi _{0.1;6}^{2}=10.6446\,\!</math>

	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>		::<math>{{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 needs to be accumulated with no more than 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.

Richard House at 22:59, 26 August 2012

2012-08-26T22:59:57Z

← Older revision		Revision as of 22:59, 26 August 2012
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	</noinclude>		</noinclude>
	In this example, we will use the exponential chi-squared method to design a test that will demonstrate a reliability of 85% at <math>{{t}_{DEMO}}=500</math> hours with a 90% confidence (or <math>CL=0.9</math>) if no more than 2 failures occur during the test (<math>f=2</math>). The chi-squared value can be determined from tables or the Quick Statistical Reference (QSR) tool in Weibull++. In this example, the value is calculated as:		In this example, we will use the exponential chi-squared method to design a test that will demonstrate a reliability of 85% at <math>{{t}_{DEMO}}=500\,\!</math> hours with a 90% confidence (or <math>CL=0.9\,\!</math>) if no more than 2 failures occur during the test (<math>f=2\,\!</math>). The chi-squared value can be determined from tables or the Quick Statistical Reference (QSR) tool 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>		::<math>\chi _{1-CL;2r+2}^{2}=\chi _{0.1;6}^{2}=10.6446</math>

Chris Kahn at 05:11, 22 August 2012

2012-08-22T05:11:21Z

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	</noinclude>		</noinclude>
	~~'''Example: Using Exponential Chi-Squared Method'''~~		In this example, we will use the exponential chi-squared method to design a test that will demonstrate a reliability of 85% at <math>{{t}_{DEMO}}=500</math> hours with a 90% confidence (or <math>CL=0.9</math>) if no more than 2 failures occur during the test (<math>f=2</math>). The chi-squared value can be determined from tables or the Quick Statistical Reference (QSR) tool 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 (QSR) tool 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>		::<math>\chi _{1-CL;2r+2}^{2}=\chi _{0.1;6}^{2}=10.6446</math>

Chris Kahn at 06:12, 17 August 2012

2012-08-17T06:12:21Z

← Older revision		Revision as of 06:12, 17 August 2012
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	'''Example: Using Exponential Chi-Squared Method'''		'''Example: Using Exponential Chi-Squared Method'''

	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 (QSR) tool 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>		::<math>\chi _{1-CL;2r+2}^{2}=\chi _{0.1;6}^{2}=10.6446</math>

Lisa Hacker at 03:03, 15 August 2012

2012-08-15T03:03:09Z

← Older revision		Revision as of 03:03, 15 August 2012
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	</noinclude>		</noinclude>
	'''Example: Using Exponential Chi-Squared Method'''		'''Example: Using Exponential Chi-Squared Method'''

	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:

Lisa Hacker: Created page with '{{Banner Weibull Examples}} ''This example appears in the Life Data Analysis Reference book''. '''Example: Using Exponential …'

2012-08-15T03:02:56Z

Created page with '<noinclude>{{Banner Weibull Examples}} ''This example appears in the Life Data Analysis Reference book''. </noinclude> '''Example: Using Exponential …'

New page

<noinclude>{{Banner Weibull Examples}}
''This example appears in the [[Reliability_Test_Design|Life Data Analysis Reference book]]''.

</noinclude>
'''Example: Using Exponential Chi-Squared Method'''
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>

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>

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|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.