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Statistical Design Optimization
Published in Wai-Kai Chen, Computer Aided Design and Design Automation, 2018
sampling N points ui with the p.d.f. gθ(θ). The variance of this estimator is var {Y˜}=E{[ϕ(θ)/gθ(θ)−Y]2}/N. If it is possible to choose gθ(θ) such that it mimics (or is similar to) ϕ(θ)fθ(θ)/Y, the variability of [ϕ(θ)fθ(θ)/gθ(θ)−Y] is reduced, and thus the variance of Y^. This can be accomplished if some approximation to f(u) i.e., to the acceptability region A is known. Some possibilities of using importance sampling techniques were studied, e.g., in [16]. One of such methods, called parametric sampling was used in [36], and other variants of important sampling were used in [2,40] for yield optimization. There are several other methods of variance reduction, such as the method of control variates, correlated sampling, stratified sampling, antithetic variates, and others [7,34,39]. Some of them have been used for statistical circuit design [7,39].
Principles of Design and Analysis of Simulation Experiments
Published in Naim A. Kheir, Systems Modeling and Computer Simulation, 2018
Simulation experiments may generally be regarded as statistical experiments driven by random inputs. Therefore, the results of any simulation model represent estimates (random outputs) characterized by experimental errors. To obtain improved estimates and to increase the statistical efficiency of the simulation (as measured by the variances of the output random variables), various types of variance reduction techniques are utilized. These techniques include common random numbers, antithetic variates, control variates, stratified sampling, and importance sampling.
Use of Simulation for Decision Models
Published in Gerald W. Evans, Multiple Criteria Decision Analysis for Industrial Engineering, 2016
There are many variance reduction techniques available for use in simulation studies, including common random numbers, antithetic variates, control variates, indirect estimation, and conditioning. In this section, we will focus briefly on common random numbers, which is probably the easiest and most commonly used of the various techniques. The reader is referred to any of several books on simulation such as Law (2007, Chapter 11) for additional information on common random numbers and the other techniques.
Combination of sensitivity-based and random sampling-based methodologies for efficient uncertainty quantification calculations with control variates method
Published in Journal of Nuclear Science and Technology, 2019
The control variates (CV) method [3] is one of variance reduction methods in Monte Carlo calculations. With this method, one can efficiently estimate a mean value of a target parameter by using another parameter whose mean value is well known and is highly correlated to the target parameter. Efficiency of the CV method depends on this similarity, and high efficiency is expected when one can prepare a parameter whose similarity to the target parameter is high.
Design of the cross-structural cathodes in electrochemical machining of aero-engine blades
Published in Machining Science and Technology, 2018
Zhu Dong, Yu Lingguo, Zhang Ronghui
Simulations were conducted using the control variate method. During simulations of the height, the value of H was varied, while the value of L was held constant at 0 mm. During simulations of the offset, the value of L was varied, while the value of H was held constant at 0.75 mm.