The article “Reliability-Based Service-Life Assessment of Aging Concrete Structures” (J. Structural Engr., 1993: 1600–1621) suggests that a Poisson process can be used to represent the occurrence of structural loads over time. Suppose the mean time between occurrences of loads is .5 year. a.? ow many loads can be expected to occur during a 2- year period? b.? ?What is the probability that more than five loads occur during a 2-year period? c. ?How long must a time period be so that the probability of no loads occurring during that period is at most .1?

Answer: Step 1 of 1 Suppose the mean time between occurrences of loads is 0.5 year. Here, T exp() and E(T ) = 1/ = 0.5. Therefore = 2. a. Let Y be the number of occurrences during a 2-year period, then t = 4 and Y = X2 Poisson(4). So E(Y ) = 4 Hence, expected number of loads to occur during a 2- year period is 4. b. The probability that more than five loads occur during a 2-year period is given below, Apply a poisson model with = 4 P(X > 5) = 1 P(X 5) = 1 F(5; 4)[Using excel function “=poisson(5,4,TRUE)”] = 1 - 0.7851 = 0.2149. Therefore, the probability that more than five loads occur during a 2-year period is 0.2149. 2t 0 e (2t) c. We know that P(X = 0t = 0! 2t e 0.1 = 2t ln(0.1) t 1.1513years. Hence, the probability of no loads occurring during that period is at most 0.1 is 1.1513 years.