Template:Stress-Strength Expected Probability - Revision history

Richard House: Redirected page to Stress-Strength Analysis

2012-08-13T06:22:57Z

Redirected page to Stress-Strength Analysis

← Older revision		Revision as of 06:22, 13 August 2012
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	~~===The Expected Probability===~~		#REDIRECT [[Stress-Strength_Analysis]]
	Stress-strength analysis has been used in mechanical component design. The probability of failure is based on the probability of stress exceeding strength. The following equation is used to calculate the expected probability of failure, ''F'':

	~~<center><math>F=P~~[~~Stress\ge Strength]=\int_{0}^{\infty }{{{f}_{Strength}}(x)\cdot {{R}_{Stress}}(x)}dx</math></center>~~

	~~The expected probability of success or the expected reliability, ''R'' , is calculated as:~~

	~~<center><math>R=P~~[Stress~~\le Strength~~]~~=\int_{0}^{\infty }{{{f}_{Stress}}(x)\cdot {{R}_{Strength}}(x)}dx</math></center>~~

	~~The above calculation assumes both stress and strength are in the positive domain. For general cases, the expected reliability can be calculated using the following equation:~~

	~~<center><math>R=P[{{X}_{1}}\le {{X}_{2}}~~]~~=\frac{1}{{{F}_{1}}(U)-{{F}_{1}}(L)}\int_{L}^{U}{{{f}_{1}}(x)\cdot {{R}_{2}}(x)}dx</math></center>~~

	~~where:~~
	~~:: <math>L\le {{X}_{1}}\le U</math>~~
	~~::<math>\begin{align}~~
	~~& {{X}_{1}}:\text{ Stress } \\~~
	~~& {{X}_{2}}:\text{ Strength } \\~~
	~~\end{align}</math>~~
	~~<br>~~
	~~When U = infinite and L = 0, the above two equations are the same.~~

Lisa Hacker: /* The Expected Probability */

2012-03-30T18:54:06Z

The Expected Probability

← Older revision		Revision as of 18:54, 30 March 2012
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	\end{align}</math>		\end{align}</math>
	<br>		<br>
	When ~~<math>~~U = infinite~~</math>~~ and ~~<math>~~L = 0~~</math>~~, the above two equations are the same.		When U = infinite and L = 0, the above two equations are the same.

Lisa Hacker: /* The Expected Probability */

2012-03-30T18:53:10Z

The Expected Probability

← Older revision		Revision as of 18:53, 30 March 2012
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	===The Expected Probability===		===The Expected Probability===
	Stress-strength analysis has been used in mechanical component design. The probability of failure is based on the probability of stress exceeding strength. The following equation is used to calculate the expected probability of failure:		Stress-strength analysis has been used in mechanical component design. The probability of failure is based on the probability of stress exceeding strength. The following equation is used to calculate the expected probability of failure, ''F'':

	<center><math>F=P[Stress\ge Strength]=\int_{0}^{\infty }{{{f}_{Strength}}(x)\cdot {{R}_{Stress}}(x)}dx</math></center>		<center><math>F=P[Stress\ge Strength]=\int_{0}^{\infty }{{{f}_{Strength}}(x)\cdot {{R}_{Stress}}(x)}dx</math></center>

Lisa Hacker: /* The Expected Probability */

2012-03-30T18:52:44Z

The Expected Probability

← Older revision		Revision as of 18:52, 30 March 2012
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	<center><math>F=P[Stress\ge Strength]=\int_{0}^{\infty }{{{f}_{Strength}}(x)\cdot {{R}_{Stress}}(x)}dx</math></center>		<center><math>F=P[Stress\ge Strength]=\int_{0}^{\infty }{{{f}_{Strength}}(x)\cdot {{R}_{Stress}}(x)}dx</math></center>

	The expected probability of success or the expected reliability ''R'' is calculated as:		The expected probability of success or the expected reliability, ''R'' , is calculated as:

	<center><math>R=P[Stress\le Strength]=\int_{0}^{\infty }{{{f}_{Stress}}(x)\cdot {{R}_{Strength}}(x)}dx</math></center>		<center><math>R=P[Stress\le Strength]=\int_{0}^{\infty }{{{f}_{Stress}}(x)\cdot {{R}_{Strength}}(x)}dx</math></center>

Lisa Hacker: /* The Expected Probability */

2012-03-30T01:22:03Z

The Expected Probability

← Older revision		Revision as of 01:22, 30 March 2012
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	\end{align}</math>		\end{align}</math>
	<br>		<br>
	When <math>U = infinite</math> and L = 0, the above two equations are the same.		When <math>U = infinite</math> and <math>L = 0</math>, the above two equations are the same.

Lisa Hacker: /* The Expected Probability */

2012-03-30T01:21:42Z

The Expected Probability

← Older revision		Revision as of 01:21, 30 March 2012
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	\end{align}</math>		\end{align}</math>
	<br>		<br>
	When U = infinite and L = 0, the above two equations are the same.		When <math>U = infinite</math> and L = 0, the above two equations are the same.

Lisa Hacker: /* The Expected Probability */

2012-03-30T01:21:17Z

The Expected Probability

← Older revision		Revision as of 01:21, 30 March 2012
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	& {{X}_{2}}:\text{ Strength } \\		& {{X}_{2}}:\text{ Strength } \\
	\end{align}</math>		\end{align}</math>
			<br>
	When U = infinite and L = 0, the above two equations are the same.		When U = infinite and L = 0, the above two equations are the same.

Lisa Hacker: /* The Expected Probability */

2012-03-30T01:21:08Z

The Expected Probability

← Older revision		Revision as of 01:21, 30 March 2012
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	where:		where:
	:: <math>L\le {{X}_{1}}\le U</math>,		:: <math>L\le {{X}_{1}}\le U</math>
	::<math>\begin{align}		::<math>\begin{align}
	& {{X}_{1}}:\text{ Stress; } \\		& {{X}_{1}}:\text{ Stress } \\
	& {{X}_{2}}:\text{ Strength; } \\		& {{X}_{2}}:\text{ Strength } \\
	\end{align}</math>		\end{align}</math>

	When U = infinite and L = 0, the above two equations are the same.		When U = infinite and L = 0, the above two equations are the same.

Lisa Hacker: /* The Expected Probability */

2012-03-30T01:20:40Z

The Expected Probability

← Older revision		Revision as of 01:20, 30 March 2012
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	<center><math>F=P[Stress\ge Strength]=\int_{0}^{\infty }{{{f}_{Strength}}(x)\cdot {{R}_{Stress}}(x)}dx</math></center>		<center><math>F=P[Stress\ge Strength]=\int_{0}^{\infty }{{{f}_{Strength}}(x)\cdot {{R}_{Stress}}(x)}dx</math></center>

	The expected probability of success or the expected ''~~Reliability~~'' is calculated as:		The expected probability of success or the expected reliability ''R'' is calculated as:

	<center><math>R=P[Stress\le Strength]=\int_{0}^{\infty }{{{f}_{Stress}}(x)\cdot {{R}_{Strength}}(x)}dx</math></center>		<center><math>R=P[Stress\le Strength]=\int_{0}^{\infty }{{{f}_{Stress}}(x)\cdot {{R}_{Strength}}(x)}dx</math></center>

Lisa Hacker: /* The Expected Probability */

2012-03-30T01:20:14Z

The Expected Probability

← Older revision		Revision as of 01:20, 30 March 2012
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	===The Expected Probability===		===The Expected Probability===
	Stress-~~Strength~~ analysis has been used in mechanical component design. The probability of failure is based on the probability of stress exceeding strength. The following equation is used to calculate the expected probability of failure:		Stress-strength analysis has been used in mechanical component design. The probability of failure is based on the probability of stress exceeding strength. The following equation is used to calculate the expected probability of failure:

	<center><math>F=P[Stress\ge Strength]=\int_{0}^{\infty }{{{f}_{Strength}}(x)\cdot {{R}_{Stress}}(x)}dx</math></center>		<center><math>F=P[Stress\ge Strength]=\int_{0}^{\infty }{{{f}_{Strength}}(x)\cdot {{R}_{Stress}}(x)}dx</math></center>
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	<center><math>R=P[Stress\le Strength]=\int_{0}^{\infty }{{{f}_{Stress}}(x)\cdot {{R}_{Strength}}(x)}dx</math></center>		<center><math>R=P[Stress\le Strength]=\int_{0}^{\infty }{{{f}_{Stress}}(x)\cdot {{R}_{Strength}}(x)}dx</math></center>

	The above calculation assumes both stress and ~~strenght have~~ positive domain. For general cases, the expected reliability can be ~~calcualted~~ using the following equation:		The above calculation assumes both stress and strength are in the positive domain. For general cases, the expected reliability can be calculated using the following equation:

	<center><math>R=P[{{X}_{1}}\le {{X}_{2}}]=\frac{1}{{{F}_{1}}(U)-{{F}_{1}}(L)}\int_{L}^{U}{{{f}_{1}}(x)\cdot {{R}_{2}}(x)}dx</math></center>		<center><math>R=P[{{X}_{1}}\le {{X}_{2}}]=\frac{1}{{{F}_{1}}(U)-{{F}_{1}}(L)}\int_{L}^{U}{{{f}_{1}}(x)\cdot {{R}_{2}}(x)}dx</math></center>