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| Effect of bivariate distribution construction methods on series system reliability |
| Received:May 20, 2012 Revised:September 26, 2012 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx201306005 |
| KeyWord:joint probability density function Pearson correlation coefficient Spearman correlation coefficient series system probability of failure |
| Author | Institution |
| 李典庆 |
武汉大学 水资源与水电工程科学国家重点实验室, 武汉 ;武汉大学 水工岩石力学教育部重点实验室, 武汉 |
| 蒋水华 |
武汉大学 水资源与水电工程科学国家重点实验室, 武汉 ;武汉大学 水工岩石力学教育部重点实验室, 武汉 |
| 周创兵 |
武汉大学 水资源与水电工程科学国家重点实验室, 武汉 ;武汉大学 水工岩石力学教育部重点实验室, 武汉 |
| 方国光 |
新加坡国立大学 土木与环境工程系, 新加坡 |
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| Abstract: |
| The two approximate methods for constructing bivariate distributions,namely method P and method S,are briefly introduced first.Thereafter,the closed-form expressions for calculating the series system probability of failure using direct integration are derived.For two negatively correlated performance functions underlying a series system,a formula for calculating the upper bound of probability of failure for a series system is derived.Then,an illustrative example is presented to demonstrate the capability and validity of two approximate methods.The results indicate that the methods P and S are effectively the same from a numerical viewpoint.Both two approximate methods can produce sufficiently accurate probabilities of failure for series systems.The two approximate methods provide a tool for series system reliability analysis under incomplete probability information.The errors in series system probability of failure increase with decreasing system probability of failure when the two performance functions underlying two components are positively correlated.They will decrease with decreasing system probability of failure when the two performance functions underlying two components are negatively correlated.The maximum error in the series system probability of failure may not be associated with a large correlation.It can happen at an intermediate correlation. |
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