Template:Stress-Strength Expected Probability: Difference between revisions
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[math]\displaystyle{ F=P[Stress\ge Strength]=\int_{0}^{\infty }{{{f}_{Strength}}(x)\cdot {{R}_{Stress}}(x)}dx }[/math]
[math]\displaystyle{ R=P[Stress\le Strength]=\int_{0}^{\infty }{{{f}_{Stress}}(x)\cdot {{R}_{Strength}}(x)}dx }[/math]
[math]\displaystyle{ 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]
(Created page with '===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 s…') |
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===The Expected Probability=== | ===The Expected Probability=== | ||
Stress- | 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 | 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> | ||
Revision as of 01:20, 30 March 2012
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:
The expected probability of success or the expected Reliability is calculated as:
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:
where:
- [math]\displaystyle{ L\le {{X}_{1}}\le U }[/math],
- [math]\displaystyle{ \begin{align} & {{X}_{1}}:\text{ Stress; } \\ & {{X}_{2}}:\text{ Strength; } \\ \end{align} }[/math]
When U = infinite and L = 0, the above two equations are the same.