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Using Multivariate Statistics to Build Confidence Interval for Means of Steady State Stochastic Processes: New Approach

Rajabi, Reza | 2012

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 43081 (01)
  4. University: Sharif University of Technology
  5. Department: Industrial Engineering
  6. Advisor(s): Akhavan Niaki, Taghi
  7. Abstract:
  8. Nowadays,The use of employ of Simulation techniques to estimate different determine characteristics and analyze of any kinds of various systems performance measures has increaseds drastically. The output analysis in simulation plays a key role to obtain the estimates. Consequently, in a given simulation project, whether it is terminating or steady state, the use of statistical approaches to analyze output data derived by running the simulation model is inevitable.During a given Simulation project, most of time is devoted to build, and run a model; however, to analyze the outputs of model plays a key role to obtain desire goals of project. Consequently, in a predefine simulation project, whether in finite or infinite manner, using statistical approaches to analyzing data which is gained from running a model is inevitable.ThisThe data which that is derived from steady state processes is typically dependent and hence, employing classical deploying of classical statisticals toolsechniques is is inappropriate.It is due to the fact that in such cases, determining means and variance of those processes requires complex calculations. To face such problem, it is likely to use an estimation of confidence interval for desire variable, rather than calculate exact value. Data which is used to do so usually does not have normal distribution or independency. Numerous ways have been suggested to tackle these problems which all have their advantages or disadvantages. In this thesis, the factor analysis is used to first determine the main factors causing autocorrelation among data. Then, data is clustered by their dependencies using the K-means procedure so that data within e given cluster are highly correlated, but data between different clusters are almost uncorrelated. Finally, confidence interval on the means of the output data is obtained based on the cluster’s means. The results of employing both the proposed method of the usual batch means on the data obtained by M/M/1. M/M/2, and AR(1) processes show the superiority of the proposal procedure over the batch means method. following thesis, the ordinary methods to face those problems is described comprehensively and then, new method will be proved to overcome some existent problems of building confidence intervals of steady state stochastic processes
  9. Keywords:
  10. Steady State Simulation ; Autocorrelation ; Independent Data ; Confidence Interval ; Output Analysing Simulation

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