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‎The study of many scientific and natural phenomena in laboratory condition is sometimes impossible‎, ‎therefore theire expresed by mathemathical models and simulated by complex computer models (codes)‎. ‎Running a computer model with different inputs is called a computer expriment‎.

‎Statistical issues allocated a wide range of applications for computer expriment to itself‎. ‎In this paper‎, ‎the‎ ‎structure of computer models is described‎, ‎and one of statistical applications‎, ‎that is variance-based sensitivity analysis is expressed‎. ‎Sensitivity analysis‎, ‎involves a set of methods that determine the effect on model inputs on the output by using sensitivity indices‎. ‎The indices are defined based on the concept‎ ‎of condition variance and the since explicit mathematical form of the model is unclear‎, ‎hence the essues monte carlo based them are proposed‎.

‎Due to the inherent complexity of the model‎, ‎execuation time is problem.Therefore a specifict design of expriment‎, ‎base on Quasi-random number‎, ‎is proposed‎ ‎to reduce the runnig costs‎. ‎As an application‎, ‎the INCA-N model that simulates amount of Nitrogen in river‎ ‎and underground sources was used‎. ‎Using the sensitivity indices‎, ‎we could found the effective‎ ‎variable on this danger pollution that threaten human life and inviromental‎.

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Life testing often is consuming a very long time for testing. Therefore, the engineers and statisticians are looking for some approaches to reduce the running time. There is a recommended method for reducing the time of failure, such that the stress level of the test units will increase, and then they will fail earlier than normal operating conditions. These approaches are called accelerated life tests. One of the most common tests is called the step stress accelerated life test. In this procedure, the stress applied to the units under the test is increased step by step at a predetermined time. The most important aspect to deal with the step stress model is the optimization of test design. In order to optimize the test plan, the best time to increase the level of stress should be chosen. In this paper, at first the step stress testing described. Then, this test is used for exponential lifetime distribution. Since life data are often not complete, this model is applied to type I censored data. By minimizing the asymptotic variance of the maximum likelihood estimator of reliability at time $xi$, the optimal test plan will be obtained. Finally, the simulation studies and one real data are discussed to illustrate the results. A sensitivity analysis shows that the proposed optimum plan is robust.

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The occurrence of lifetime data is a problem which is commonly encountered in various researches, including surveys, clinical trials and epidemioligical studies. Recently there has been extensive methodological resarech on analyzing lifetime data. Howerver, because usually little information from data is available to corretly estimate, the inferences might be sensitive to untestable assumptions which this calls for a sensitivity analysis to be performed.
In this paper, we describe how to evaluate the  effect  that  perturbations to the  Log-Beta Weibull Regression  Responses. Also, we review and extend the application and  interpretation of influence analysis methods using censored data analysis. A full likelihood-based approach that allows yielding maximum likelihood estimates of the model parameters is used. Some simulation studies are conducted to evalute the performance of the proposed indices in ddetecting sensitivity of key model parameters. We illustrate the methods expressed by analyzing the  cancer data.

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In today’s world, using the statistical modeling process, natural phenomena can be used to analyze and predict the events under study. ‎ Many hydrological modeling methods do not make the best use of available information because hydrological models show a wide range of environmental processes that complex the model‎‏. ‎‎‎‎In particular, when predicting, parameters affect the performance of statistical models. In many risk assessment issues, the presence of uncertainty in the parameters leads to uncertainty in predicting the model. Global sensitivity analysis is a tool used to show uncertainty and
is used in decision making, risk assessment, model simplifcation and so on. Minkowski distance sensitivity analysis and regional sensitivity analysis are two broad methods that can work with a given sample set of model input-output pair. One signifcant difference between them is that minkowski distance sensitivity analysis analyzes output distributions conditional on input values (forward), while regional sensitivity analysis analyzes input distributions conditional on output values (reverse). In this dissertation, we study the relationship between these two approaches and show that regional sensitivity analysis (reverse), when focusing on probability density functions of input, converges towards minkowski distance sensitivity analysis (forward) as the number of classes for conditioning model outputs in the reverse method increases. Similar to the existing general form of forward sensitivity indices, we derive a general form of the reverse sensitivity indices and provide the corresponding reverse given-data method. Finally, the sensitivity analysis of a water storage design with high dimensions of the model outputs is performed.