tailieunhanh - SIMULATION AND THE MONTE CARLO METHOD Episode 5

Tham khảo tài liệu 'simulation and the monte carlo method episode 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 100 STATISTICAL ANALYSIS OF DISCRETE-EVENT SYSTEMS interested in the expected maximal project duration say . Letting X be the vector of activity lengths and H X be the length of the critical path we have E H X E where is the j-th complete path from start to finish and p is the number of such paths. Confidence Interval In order to specify how accurate a particular estimate is that is how close it is to the actual unknown parameter Ể one needs to provide not only a point estimate but a confidence interval as well. To do so recall from Section that by the central limit theorem has approximately a Nự ơ2 TV distribution where cr2 is the variance of X . Usually Ơ2 is unknown but it can be estimated with the sample variance t l which by the law of large numbers tends to T2 as TV 00. Consequently for large TV we see that is approximately N f S2 N distributed. Thus if z-f denotes the 7-quantile of the N o 1 distribution this is the number such that z7 7 where denotes the standard normal cdf for example since i then p ự - Zỵ_aị 2 1 a . In other words an approximate 1 a 100 confidence interval for is 21-a 2 ợ I where the notation a b is shorthand for the interval a b a b . It is common practice in simulation to use and report the absolute and relative widths of this confidence interval defined as wo 2zi_q 2 and wr Wg respectively provided that 0. The absolute and relative widths may be used as stopping rules criteria to control the length of a simulation run. The relative width is particularly useful when is very small. For example think of as the unreliability 1 minus the reliability of a system in which all the components are very reliable. In such a case could be as small as Ể 10 10 sothatreportingaresultsuchaswa is almost meaningless DYNAMIC SIMULATION MODELS 101 while in contrast reporting wr is quite meaningful. Another important quantity is the relative error RE of the estimator Ể defined see also as