Towards Generic Simulation for Demanding Stochastic Processes

We outline and test a new methodology for genuine simulation of stochastic processes with any dependence structure and any marginal distribution. We reproduce time dependence with a generalized, time symmetric or asymmetric, moving-average scheme. This implements linear filtering of non-Gaussian white noise, with the weights of the filter determined by analytical equations, in terms of the autocovariance of the process. We approximate the marginal distribution of the process, irrespective of its type, using a number of its cumulants, which in turn determine the cumulants of white noise, in a manner that can readily support the generation of random numbers from that approximation, so that it be applicable for stochastic simulation. The simulation method is genuine as it uses the process of interest directly, without any transformation (e.g., normalization). We illustrate the method in a number of synthetic and real-world applications, with either persistence or antipersistence, and with non-Gaussian marginal distributions that are bounded, thus making the problem more demanding. These include distributions bounded from both sides, such as uniform, and bounded from below, such as exponential and Pareto, possibly having a discontinuity at the origin (intermittence). All examples studied show the satisfactory performance of the method.

Towards Generic Simulation for Demanding Stochastic Processes

We outline and test a new methodology for genuine simulation of stochastic processes with any dependence and any marginal distribution. We reproduce time dependence with a generalized, time symmetric or asymmetric, moving-average scheme. This implements linear filtering of non-Gaussian white noise, with the weights of the filter determined by analytical equations in terms of the autocovariance of the process. We approximate the marginal distribution of the process, irrespective of its type, using a number of its cumulants, which in turn determine the cumulants of white noise in a manner that can readily support the generation of random numbers from that approximation, so that it be applicable for stochastic simulation. The simulation method is genuine as it uses the process of interest directly without any transformation (e.g. normalization). We illustrate the method in a number of synthetic and real-world applications with either persistence or antipersistence, and with non-Gaussian marginal distributions that are bounded, thus making the problem more demanding. These include distributions bounded from both sides, such as uniform, and bounded form below, such as exponential and Pareto, possibly having a discontinuity at the origin (intermittence). All examples studied show the satisfactory performance of the method.

Coupled simulation of flow-induced viscous and elastic anisotropy of short-fiber reinforced composites

The present work discusses the impact of the back coupling of the fiber orientation distribution on the base flow and on the fiber orientation itself during mold filling simulations. Flows through a channel and over a backward-facing step are investigated. Different closure approximations are considered for modeling the flow-induced evolution of anisotropy. The results corresponding to the decoupled approach, in which the effect of fibers on local fluid properties is neglected, build the basis of comparison. The modeling is limited to a laminar, incompressible, and isothermal flow of a fiber suspension consisting of rigid short fibers suspended in an isotropic Newtonian matrix fluid. A linear, anisotropic constitutive law is used in combination with a uniform fiber volume fraction of 10% and an aspect ratio of 10. To evaluate the impact of back coupling and of different closure methods in view of the manufactured solid composite the resulting anisotropic elastic properties are investigated based on the Mori–Tanaka method combined with an orientation average scheme. Relative to the range [0, 1] the pointwise difference in fiber orientation between the decoupled and the coupled approach is found to be $$\pm 5{\%}$$ ± 5 % in the channel and $$\pm 30{\%}$$ ± 30 % in the backward-facing step, respectively. The viscosity and the elasticity tensor show both significant flow-induced anisotropies as well as a strong dependence on closure and coupling.

A homogenously weighted moving average scheme for observations under the effect of serial dependence and measurement inaccuracy

The combined effect of serial dependency and measurement errors is known to negatively affect the statistical efficiency of any monitoring scheme. However, for the recently proposed homogenously weighted moving average (HWMA) scheme, the research that exists concerns independent and identically distributed observations and measurement errors only. Thus, in this paper, the HWMA scheme for monitoring the process mean under the effect of within-sample serial dependence with measurement errors is proposed for both constant and linearly increasing measurement system variance. Monte Carlo simulation is used to evaluate the run-length distribution of the proposed HWMA scheme. A mixed-s&m sampling strategy is incorporated to the HWMA scheme to reduce the negative effect of serial dependence and measurement errors and its performance is compared to the existing Shewhart scheme. An example is given to illustrate how to implement the proposed HWMA scheme for use in real-life applications.

Progressive mean exponentially weighted moving average control chart for monitoring the process location

PurposeThis study aims to focus on proposing a new memory-type chart called progressive mean exponentially weighted moving average (PMEWMA) control chart. This memory-type chart is an improvement on the existing progressive mean control chart, to detect small and moderate shifts in a process.Design/methodology/approachThe PMEWMA control chart is developed by using a cumulative average of the exponentially weighted moving average scheme known as the progressive approach. This scheme is designed based on the assumption that data follow a normal distribution. In addition, the authors investigate the robustness of the proposed chart to the normality assumption.FindingsThe variance and the mean of the scheme are computed, and the mean is found to be an unbiased estimator of the population mean. The proposed chart's performance is compared with the existing charts in the literature by using the average run-length as the performance measure. Application examples from the petroleum and bottling industry are also presented for practical considerations. The comparison shows that the PMEWMA chart is quicker in detecting small shifts in the process than the other memory-type charts covered in this study. The authors also notice that the PMEWMA chart is affected by higher kurtosis and skewness.Originality/valueA new memory-type scheme is developed in this research, which is efficient in detecting small and medium shifts of a process mean.