Economic Control of Quality of Manufactured Product.

Dependence modeling with copulas

How do the multiple large-scale climate oscillations trigger extreme precipitation?

Some robust approaches based on copula for monitoring bivariate processes and component-wise assessment

The purpose of this research was to prepare silver nanoparticles in a tubular reactor using tannic acid as both a reducing agent and a stabiliser. The stability of the process was determined using statistical analysis with control charts. The qualitative analysis of the resulting colloidal silver nanoparticles was investigated using UV–Vis spectroscopy, dynamic light scattering method and the transmission electron microscopy. Particles with average sizes ranging from 14 to 60 nm were obtained. Stability of the process was achieved mainly through the use of 0.5 Tannic acid/AgNO3 molar ratios and temperature ranging from 20 to 45 °C. The proposed technique is consistent with the principles of green chemistry and can be an alternative for traditional nanosilver synthesis.

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Continuous Production of Silver Nanoparticles and Process Control

In this paper, we propose five types of copulas on the Hotelling's T2 control chart when observations are from exponential distribution and use the Monte Carlo simulation to compare the performance of the control chart, which is based on the Average Run Length (ARL) for each copula. Five types of copulas function for specifying dependence between random variables are used and measured by Kendall's tau. The results show that the copula approach can be fitted the observation and we can use copula as an option for application on Hotelling's T2 control chart.

Bivariate copulas on the Hotelling's T2 control chart

This paper proposes four types of copulas on the Exponentially Weighted Moving Average (EWMA) control chart when observations are from an exponential distribution using a Monte Carlo simulation approach. The performance of the control chart is based on the Average Run Length (ARL) which is compared for each copula. Copula functions for specifying dependence between random variables are used and measured by Kendall’s tau. The results show that the Normal copula can be used for almost all shifts.

Bivariate copulas on the exponentially weighted moving average control chart

The copula approach is a popular method for multivariate modeling applied in several fields; it defines non-parametric measures of dependence between random variables. In this paper, three families are proposed from elliptical and Archimedean copulas on the multivariate cumulative sum (MCUSUM) control chart when observations are draw from an exponential distribution. The performance of the control chart is based on the average run length (ARL)—via Monte Carlo simulations. A copula function for specifying the dependence between random variables is measured by Kendall’s tau. The numerical results indicate that the observations can be fitted and that the copula can be used on the MCUSUM for cases of small and large dependencies.

Multivariate copulas on the MCUSUM control chart

Control charts are quality control procedures to detect a change of manufacturing product. They are used both univariate and multivariate quality characteristics which are random, independent and identically distributed (i.i.d.). Copulas approach can be applied to dependencies and non-normal variables with marginal distributions when the joint distribution could not be found in multivariate cases except normal distribution process. Therefore, the objective of this work is to compare three control charts from three copulas, when observations are exponential distribution via Average Run Length ( ARL ). For specifying dependence between random variables are proposed and measured by Kendall’s tau through Monte Carlo simulation . The numerical results show that the Normal copula of Multivariate Exponentially Weighted Moving Average (MEWMA ) control chart is inferior to other control charts for all magnitudes of shifts.

Sasigarn Kuvattana

Papers

Bivariate copulas on the Hotelling's T2 control chart

Bivariate copulas on the exponentially weighted moving average control chart

Multivariate copulas on the MCUSUM control chart

Comparative the Performance of Control Charts Based on Copulas