Template:Bayesian test design - Revision history

Kate Racaza: Redirected page to Reliability Test Design

2012-06-29T08:04:09Z

Redirected page to Reliability Test Design

← Older revision		Revision as of 08:04, 29 June 2012
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	~~== Bayesian Non-Parametric~~ Test Design ==		#REDIRECT [[Reliability Test Design]]

	The regular non-parametric analyses performed based on either the binomial or the chi-squared equation were performed with only the direct system test data. However, if prior information regarding system performance is available, it can be incorporated into a Bayesian non-parametric analysis. This subsection will demonstrate how to incorporate prior information about system reliability and also how to incorporate prior information from subsystem tests into system test design.

	~~=== Assumption on System Reliability ===~~

	If we assume the system reliability follows a beta distribution, the values of system reliability, ''R'', confidence level, ''CL'', number of units tested, ''n'', and number of failures, ''r, ''are related by the following equation:

	~~<center><math>1-CL=\text{Beta}\left(R,\alpha,\beta\right)=\text{Beta}\left(R,n-r+\alpha_{0},r+\beta_{0}\right)</math></center>~~

	where <math>Beta</math> is the incomplete beta function. If <span class="texhtml" sab="459">α<sub sab="460">0</sub></span> and <span class="texhtml" sab="461">β<sub sab="462">0</sub></span> are known, then any quantity of interest can be calculated using the remaining three. The next two examples demonstrate how to calculate <span class="texhtml" sab="463">α<sub sab="464">0</sub></span> and <span class="texhtml" sab="465">β<sub sab="466">0</sub></span> depending on the type of prior information available.

	~~{{btd w info on reliability}}~~

	~~{{btd w info from subsystem tests}}~~

Lisa Hacker: /* Assumption on System Reliability */

2012-03-29T23:48:13Z

Assumption on System Reliability

← Older revision		Revision as of 23:48, 29 March 2012
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	=== Assumption on System Reliability ===		=== Assumption on System Reliability ===

	If we assume the system reliability follows a ~~Beta~~ distribution, the values of system reliability, ''R'', confidence level, ''CL'', number of units tested, ''n'', and number of failures, ''r, ''are related by the following equation:		If we assume the system reliability follows a beta distribution, the values of system reliability, ''R'', confidence level, ''CL'', number of units tested, ''n'', and number of failures, ''r, ''are related by the following equation:

	<center><math>1-CL=\text{Beta}\left(R,\alpha,\beta\right)=\text{Beta}\left(R,n-r+\alpha_{0},r+\beta_{0}\right)</math></center>		<center><math>1-CL=\text{Beta}\left(R,\alpha,\beta\right)=\text{Beta}\left(R,n-r+\alpha_{0},r+\beta_{0}\right)</math></center>

	where Beta is the incomplete ~~Beta~~ function. If <span class="texhtml" sab="459">α<sub sab="460">0</sub></span> and <span class="texhtml" sab="461">β<sub sab="462">0</sub></span> are known, then any quantity of interest can be calculated using the remaining three. The next two examples demonstrate how to calculate <span class="texhtml" sab="463">α<sub sab="464">0</sub></span> and <span class="texhtml" sab="465">β<sub sab="466">0</sub></span> depending on the type of prior information available.		where <math>Beta</math> is the incomplete beta function. If <span class="texhtml" sab="459">α<sub sab="460">0</sub></span> and <span class="texhtml" sab="461">β<sub sab="462">0</sub></span> are known, then any quantity of interest can be calculated using the remaining three. The next two examples demonstrate how to calculate <span class="texhtml" sab="463">α<sub sab="464">0</sub></span> and <span class="texhtml" sab="465">β<sub sab="466">0</sub></span> depending on the type of prior information available.

	{{btd w info on reliability}}		{{btd w info on reliability}}

	{{btd w info from subsystem tests}}		{{btd w info from subsystem tests}}

Lisa Hacker: /* Bayesian Non-Parametric Test Design */

2012-03-29T23:47:43Z

Bayesian Non-Parametric Test Design

← Older revision		Revision as of 23:47, 29 March 2012
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	== Bayesian Non-Parametric Test Design ==		== Bayesian Non-Parametric Test Design ==

	The regular ~~nonparametric analysis~~ performed based on either the binomial or the chi-squared equation ~~was~~ performed with only the direct system test data. However, if prior information regarding system performance is available, it can be incorporated into a Bayesian ~~nonparametric~~ analysis. This subsection will demonstrate how to incorporate prior information about system reliability and also how to incorporate prior information from subsystem tests into system test design.		The regular non-parametric analyses performed based on either the binomial or the chi-squared equation were performed with only the direct system test data. However, if prior information regarding system performance is available, it can be incorporated into a Bayesian non-parametric analysis. This subsection will demonstrate how to incorporate prior information about system reliability and also how to incorporate prior information from subsystem tests into system test design.

	=== Assumption on System Reliability ===		=== Assumption on System Reliability ===
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	If we assume the system reliability follows a Beta distribution, the values of system reliability, ''R'', confidence level, ''CL'', number of units tested, ''n'', and number of failures, ''r, ''are related by the following equation:		If we assume the system reliability follows a Beta distribution, the values of system reliability, ''R'', confidence level, ''CL'', number of units tested, ''n'', and number of failures, ''r, ''are related by the following equation:

	::<math>1-CL=\text{Beta}\left(R,\alpha,\beta\right)=\text{Beta}\left(R,n-r+\alpha_{0},r+\beta_{0}\right)</math>		<center><math>1-CL=\text{Beta}\left(R,\alpha,\beta\right)=\text{Beta}\left(R,n-r+\alpha_{0},r+\beta_{0}\right)</math></center>

	where Beta is the incomplete Beta function. If <span class="texhtml" sab="459">α<sub sab="460">0</sub></span> and <span class="texhtml" sab="461">β<sub sab="462">0</sub></span> are known, then any quantity of interest can be calculated using the remaining three. The next two examples demonstrate how to calculate <span class="texhtml" sab="463">α<sub sab="464">0</sub></span> and <span class="texhtml" sab="465">β<sub sab="466">0</sub></span> depending on the type of prior information available.		where Beta is the incomplete Beta function. If <span class="texhtml" sab="459">α<sub sab="460">0</sub></span> and <span class="texhtml" sab="461">β<sub sab="462">0</sub></span> are known, then any quantity of interest can be calculated using the remaining three. The next two examples demonstrate how to calculate <span class="texhtml" sab="463">α<sub sab="464">0</sub></span> and <span class="texhtml" sab="465">β<sub sab="466">0</sub></span> depending on the type of prior information available.

Chris Kahn: /* Bayesian Non-Parameteric Test Design */

2012-03-08T18:55:15Z

Bayesian Non-Parameteric Test Design

← Older revision		Revision as of 18:55, 8 March 2012
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	== Bayesian Non-~~Parameteric~~ Test Design ==		== Bayesian Non-Parametric Test Design ==

	The regular nonparametric analysis performed based on either the binomial or the chi-squared equation was performed with only the direct system test data. However, if prior information regarding system performance is available, it can be incorporated into a Bayesian nonparametric analysis. This subsection will demonstrate how to incorporate prior information about system reliability and also how to incorporate prior information from subsystem tests into system test design.		The regular nonparametric analysis performed based on either the binomial or the chi-squared equation was performed with only the direct system test data. However, if prior information regarding system performance is available, it can be incorporated into a Bayesian nonparametric analysis. This subsection will demonstrate how to incorporate prior information about system reliability and also how to incorporate prior information from subsystem tests into system test design.

Chris Kahn: /* Assumption on System Reliability */

2012-03-08T18:53:55Z

Assumption on System Reliability

← Older revision		Revision as of 18:53, 8 March 2012
Line 5:		Line 5:
	=== Assumption on System Reliability ===		=== Assumption on System Reliability ===

	If we assume the system ~~reliablity~~ follows a Beta distribution, the values of system reliability, ''R'', confidence level, ''CL'', number of units tested, ''n'', and number of failures, ''r, ''are related by the following equation:		If we assume the system reliability follows a Beta distribution, the values of system reliability, ''R'', confidence level, ''CL'', number of units tested, ''n'', and number of failures, ''r, ''are related by the following equation:

	::<math>1-CL=\text{Beta}\left(R,\alpha,\beta\right)=\text{Beta}\left(R,n-r+\alpha_{0},r+\beta_{0}\right)</math>		::<math>1-CL=\text{Beta}\left(R,\alpha,\beta\right)=\text{Beta}\left(R,n-r+\alpha_{0},r+\beta_{0}\right)</math>

Chris Kahn: /* Bayesian Nonparameteric Test Design */

2012-03-08T18:53:35Z

Bayesian Nonparameteric Test Design

← Older revision		Revision as of 18:53, 8 March 2012
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	== Bayesian ~~Nonparameteric~~ Test Design ==		== Bayesian Non-Parameteric Test Design ==

	The regular nonparametric analysis performed based on either the binomial or the chi-squared equation was performed with only the direct system test data. However, if prior information regarding system performance is available, it can be incorporated into a Bayesian nonparametric analysis. This subsection will demonstrate how to incorporate prior information about system reliability and also how to incorporate prior information from subsystem tests into system test design.		The regular nonparametric analysis performed based on either the binomial or the chi-squared equation was performed with only the direct system test data. However, if prior information regarding system performance is available, it can be incorporated into a Bayesian nonparametric analysis. This subsection will demonstrate how to incorporate prior information about system reliability and also how to incorporate prior information from subsystem tests into system test design.

Lisa Hacker at 16:18, 6 March 2012

2012-03-06T16:18:12Z

← Older revision		Revision as of 16:18, 6 March 2012
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	==~~Bayeisan~~ Nonparameteric Test Design==		== Bayesian Nonparameteric Test Design ==

	The regular nonparametric analysis performed based on either the ~~Binomial~~ or the ~~Chi~~-~~Square~~ equation was performed with only the direct system test data. However, if prior information regarding system performance is available, it can be incorporated into a Bayesian nonparametric analysis. This subsection will demonstrate how to incorporate prior information about system reliability and also how to incorporate prior information from subsystem tests into system test design.		The regular nonparametric analysis performed based on either the binomial or the chi-squared equation was performed with only the direct system test data. However, if prior information regarding system performance is available, it can be incorporated into a Bayesian nonparametric analysis. This subsection will demonstrate how to incorporate prior information about system reliability and also how to incorporate prior information from subsystem tests into system test design.

	===Assumption on System Reliability===		=== Assumption on System Reliability ===
	If we assume the system reliablity follows a Beta ~~distribuiton~~, the values of system reliability ''R'', confidence level ''CL'', number of units tested ''n'', and number of failures ''r'' are related by the equation.
			If we assume the system reliablity follows a Beta distribution, the values of system reliability, ''R'', confidence level, ''CL'', number of units tested, ''n'', and number of failures, ''r, ''are related by the following equation:

	::<math>1-CL=\text{Beta}\left(R,\alpha,\beta\right)=\text{Beta}\left(R,n-r+\alpha_{0},r+\beta_{0}\right)</math>		::<math>1-CL=\text{Beta}\left(R,\alpha,\beta\right)=\text{Beta}\left(R,n-r+\alpha_{0},r+\beta_{0}\right)</math>

	where Beta is the incomplete Beta function. If <~~math~~>~~\alpha_{~~0}</~~math~~> and <~~math~~>~~\beta_{~~0}</~~math~~> are known, then any quantity of interest can be calculated using the remaining three. The next two examples demonstrate how to calculate <~~math~~>~~\alpha_{~~0}</~~math~~> and <~~math~~>~~\beta_{~~0}</~~math~~> depending on the type of prior information available.		where Beta is the incomplete Beta function. If <span class="texhtml" sab="459">α<sub sab="460">0</sub></span> and <span class="texhtml" sab="461">β<sub sab="462">0</sub></span> are known, then any quantity of interest can be calculated using the remaining three. The next two examples demonstrate how to calculate <span class="texhtml" sab="463">α<sub sab="464">0</sub></span> and <span class="texhtml" sab="465">β<sub sab="466">0</sub></span> depending on the type of prior information available.

	{{btd w info on reliability}}		{{btd w info on reliability}}

	{{btd w info from subsystem tests}}		{{btd w info from subsystem tests}}

Harry Guo: /* Assumption on System Reliability */

2012-02-23T16:58:07Z

Assumption on System Reliability

← Older revision		Revision as of 16:58, 23 February 2012
Line 8:		Line 8:
	::<math>1-CL=\text{Beta}\left(R,\alpha,\beta\right)=\text{Beta}\left(R,n-r+\alpha_{0},r+\beta_{0}\right)</math>		::<math>1-CL=\text{Beta}\left(R,\alpha,\beta\right)=\text{Beta}\left(R,n-r+\alpha_{0},r+\beta_{0}\right)</math>

	where Beta is the incomplete Beta function. If <math>\alpha_{0}</math> and <math>\~~beta\,\!_~~{0}</math> are known, then any quantity of interest can be calculated using the remaining three. The next two examples demonstrate how to calculate <math>\~~alpha\,\!_~~{0}</math> and <math>\~~beta\,\!_~~{0}</math> depending on the type of prior information available.		where Beta is the incomplete Beta function. If <math>\alpha_{0}</math> and <math>\beta_{0}</math> are known, then any quantity of interest can be calculated using the remaining three. The next two examples demonstrate how to calculate <math>\alpha_{0}</math> and <math>\beta_{0}</math> depending on the type of prior information available.

	{{btd w info on reliability}}		{{btd w info on reliability}}

	{{btd w info from subsystem tests}}		{{btd w info from subsystem tests}}

Harry Guo: /* Bayeisan Nonparameteric Test Design */

2012-02-23T16:57:34Z

Bayeisan Nonparameteric Test Design

← Older revision		Revision as of 16:57, 23 February 2012
Line 1:		Line 1:
	==Bayeisan Nonparameteric Test Design==		==Bayeisan Nonparameteric Test Design==

	The nonparametric analysis performed in the ~~last section made no assumptions about the underlying distribution of~~ the ~~data and~~ was performed with only the ~~immediate~~ data ~~at hand~~. However, if prior information regarding system performance is available, it can be incorporated into a Bayesian nonparametric analysis. This subsection will demonstrate how to incorporate prior information about system reliability and also how to incorporate prior information from subsystem tests.		The regular nonparametric analysis performed based on either the Binomial or the Chi-Square equation was performed with only the direct system test data. However, if prior information regarding system performance is available, it can be incorporated into a Bayesian nonparametric analysis. This subsection will demonstrate how to incorporate prior information about system reliability and also how to incorporate prior information from subsystem tests into system test design.

	===Assumption on System Reliability===		===Assumption on System Reliability===
Line 8:		Line 8:
	::<math>1-CL=\text{Beta}\left(R,\alpha,\beta\right)=\text{Beta}\left(R,n-r+\alpha_{0},r+\beta_{0}\right)</math>		::<math>1-CL=\text{Beta}\left(R,\alpha,\beta\right)=\text{Beta}\left(R,n-r+\alpha_{0},r+\beta_{0}\right)</math>

	where Beta is the incomplete Beta function. If <math>\~~alpha\,\!_~~{0}</math> and <math>\beta\,\!_{0}</math> are known, then any quantity of interest can be calculated using the remaining three. The next two examples demonstrate how to calculate <math>\alpha\,\!_{0}</math> and <math>\beta\,\!_{0}</math> depending on the type of prior information available.		where Beta is the incomplete Beta function. If <math>\alpha_{0}</math> and <math>\beta\,\!_{0}</math> are known, then any quantity of interest can be calculated using the remaining three. The next two examples demonstrate how to calculate <math>\alpha\,\!_{0}</math> and <math>\beta\,\!_{0}</math> depending on the type of prior information available.

	{{btd w info on reliability}}		{{btd w info on reliability}}

	{{btd w info from subsystem tests}}		{{btd w info from subsystem tests}}

Harry Guo: /* Assumption on System Reliablity */

2012-02-23T00:19:21Z

Assumption on System Reliablity

← Older revision		Revision as of 00:19, 23 February 2012
Line 3:		Line 3:
	The nonparametric analysis performed in the last section made no assumptions about the underlying distribution of the data and was performed with only the immediate data at hand. However, if prior information regarding system performance is available, it can be incorporated into a Bayesian nonparametric analysis. This subsection will demonstrate how to incorporate prior information about system reliability and also how to incorporate prior information from subsystem tests.		The nonparametric analysis performed in the last section made no assumptions about the underlying distribution of the data and was performed with only the immediate data at hand. However, if prior information regarding system performance is available, it can be incorporated into a Bayesian nonparametric analysis. This subsection will demonstrate how to incorporate prior information about system reliability and also how to incorporate prior information from subsystem tests.

	===Assumption on System ~~Reliablity~~===		===Assumption on System Reliability===
	If we assume the system reliablity follows a Beta distribuiton, the values of system reliability ''R'', confidence level ''CL'', number of units tested ''n'', and number of failures ''r'' are related by the equation.		If we assume the system reliablity follows a Beta distribuiton, the values of system reliability ''R'', confidence level ''CL'', number of units tested ''n'', and number of failures ''r'' are related by the equation.