《船舶与海洋工程结构风险评估》课程教学课件（讲稿）Lecture 2-Tutorials on Statistics &Probability

ASRAnetStructural Reliability and Risk Assessment4 - 8 July 2016, Wuhan, ChinaLECTURE 3Tutorials on Statistics & Probability

Structural Reliability and Risk Assessment 4 - 8 July 2016, Wuhan, China LECTURE 3 Tutorials on Statistics & Probability

Problem1The air pollution in a city is caused mainly by industrial and automobile exhausts. In the next 5 years,the chances of successfully controlling these two sources of pollution are, respectively, 75% and 60%.Assumethat ifonlyoneofthetwosources issuccessfullycontrolled,theprobabilityofbringingthepollutionbelowanacceptablelevelwouldbe80%.(a) What is the probability of successfully controlling air pollution in the next 5 years?(b) if, in the next 5 years, the pollution level is not sufficiently controlled, what is the probabilitythat itis entirely caused bythefailureto controlautomobileexhaust?Problem2.Twopowergeneratingunitsaandb operate inparalleltosupplythepower requirementsof a smallcity.The demand of power is subject to considerablefluctuation, and it is known that each unit has acapacity so that it can supply the city's full power requirement 75% of the time in the case the otherunit fails.Theprobability of failure of eachunit is O.1o,whereas theprobabilitythat both theunitswill fail is 0.02.If there is afailure inthepowergeneration,what is theprobabilitythatthe citywill have its supplyoffull power?Problem3:

Problem 1 The air pollution in a city is caused mainly by industrial and automobile exhausts. In the next 5 years, the chances of successfully controlling these two sources of pollution are, respectively, 75% and 60%. Assume that if only one of the two sources is successfully controlled, the probability of bringing the pollution below an acceptable level would be 80%. (a) What is the probability of successfully controlling air pollution in the next 5 years? (b) If, in the next 5 years, the pollution level is not sufficiently controlled, what is the probability that it is entirely caused by the failure to control automobile exhaust? Problem 2. Two power generating units a and b operate in parallel to supply the power requirements of a small city. The demand of power is subject to considerable fluctuation, and it is known that each unit has a capacity so that it can supply the city’s full power requirement 75% of the time in the case the other unit fails. The probability of failure of each unit is 0.10, whereas the probability that both the units will fail is 0.02. If there is a failure in the power generation, what is the probability that the city will have its supply of full power? Problem 3: