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In the past few years, several capability indices have been developed for evaluating the performance of multivariate manufacturing processes under the normality assumption. However, this assumption may not be true in most practical situations. Thus, the purpose of this paper is to develop new capability indices for evaluating the performance of multivariate processes subject to non-normal distributions.

In this paper, the authors propose three non-normal multivariate process capability indices (MPCIs) RNMC _p , RNMC _pm and RNMC _pu by relieving the normality assumption. Using the two normal MPCIs proposed by Pan and Lee, a weighted standard deviation method (WSD) is used to modify the NMC _p and NMC _pm indices for the-nominal-the-best case. Then the WSD method is applied to modify the multivariate ND index established by Niverthi and Dey for the-smaller-the-better case.

A simulation study compares the performance of the various multivariate indices. Simulation results show that the actual non-conforming rates can be correctly reflected by the proposed capability indices. The numerical example further demonstrates that the actual quality performance of a non-normal multivariate process can properly reflected by the proposed capability indices.

Process capability index is an important SPC tool for measuring the process performance. If the non-normal process data are mistreated as a normal one, it will result in an improper decision and thereby lead to an unnecessary quality loss. The new indices can provide practicing managers and engineers with a better decision-making tool for correctly measuring the performance for any multivariate process or environmental system.

Once the existing multivariate quality/environmental problems and their Key Performance Indicators are identified, one may apply the new capability indices to evaluate the performance of various multivariate processes subject to non-normal distributions.

The purpose of this paper is to show that multivariate t-distribution assumption provides a better description of stock return data than multivariate normality assumption.

The EM algorithm is applied to solve the statistical estimation problem almost analytically, and the asymptotic theory is provided for inference.

The authors find that the multivariate normality assumption is almost always rejected by real stock return data, while the multivariate t-distribution assumption can often be adequate. Conclusions under normality vs under t can be drastically different for estimating expected returns and Jensen’s αs, and for testing asset pricing models.

The results provide improved estimates of cost of capital and asset moment parameters that are useful for corporate project evaluation and portfolio management.

The authors proposed new procedures that makes it easy to use a multivariate t-distribution, which models well the data, as a simple and viable alternative in practice to examine the robustness of many existing results.

The purpose of this study is to extend the classical noncentral F-distribution under normal settings to noncentral closed skew F-distribution for dealing with independent samples from multivariate skew normal (SN) distributions.

Based on generalized Hotelling's T² statistics, confidence regions are constructed for the difference between location parameters in two independent multivariate SN distributions. Simulation studies show that the confidence regions based on the closed SN model outperform the classical multivariate normal model if the vectors of skewness parameters are not zero. A real data analysis is given for illustrating the effectiveness of our proposed methods.

This study’s approach is the first one in literature for the inferences in difference of location parameters under multivariate SN settings. Real data analysis shows the preference of this new approach than the classical method.

For the real data applications, the authors need to remove outliers first before applying this approach.

This study’s approach may apply many multivariate skewed data using SN fittings instead of classical normal fittings.

This paper is the research paper and the authors’ new approach has many applications for analyzing the multivariate skewed data.

The purpose of this paper is to provide an analysis of the dependence structure between returns from real estate investment trusts (REITS) and a stock market index. Further, the aim is to illustrate how copula approaches can be applied to model the complex dependence structure between the assets and for risk measurement of a portfolio containing investments in REIT and equity indices.

The usually suggested multivariate normal or variance‐ covariance approach is applied, as well as various copula models in order to investigate the dependence structure between returns of Australian REITS and the Australian stock market. Different models including the Gaussian, Student t, Clayton and Gumbel copula are estimated and goodness‐of‐fit tests are conducted. For the return series, both the Gaussian and a non‐parametric estimate of the distribution is applied. A risk analysis is provided based on Monte Carlo simulations for the different models. The value‐at‐risk measure is also applied for quantification of the risks for a portfolio combining investments in real estate and stock markets.

The findings suggest that the multivariate normal model is not appropriate to measure the complex dependence structure between the returns of the two asset classes. Instead, a model using non‐parametric estimates for the return series in combination with a Student t copula is clearly more suitable. It further illustrates that the usually applied variance‐covariance approach leads to a significant underestimation of the actual risk for a portfolio consisting of investments in REITS and equity indices. The nature of risk is better captured by the suggested copula models.

To the authors', knowledge, this is one of the first studies to apply and test different copula models in real estate markets. Results help international investors and portfolio managers to deepen their understanding of the dependence structure between returns from real estate and equity markets. Additionally, the results should be helpful for implementation of a more adequate risk management for portfolios containing investments in both REITS and equity indices.

Portfolio theory suggests that geographical diversification of production units could potentially help manage the risks associated with farming, yet little research has been done to evaluate the effectiveness of a geographical diversification strategy in agriculture. The paper aims to discuss this issue.

The paper utilizes several tools from modern finance theory, including Conditional Value-at-Risk (CVaR) and copulas, to construct a model for the evaluation of a diversification strategy. The proposed model – the copula-based mean-CVaR model – is then applied to the producer’s acreage allocation problem to examine the potential benefits of risk reduction from a geographical diversification strategy in US wheat farming. Along with the copula-based model, the multivariate-normal mean-CVaR model is also estimated as a benchmark.

The mean-CVaR optimization results suggest that geographical diversification is a viable risk management strategy from a farm’s profit margin perspective. In addition, the copula-based model appears more appropriate than the traditional multivariate-normal model for conservative agricultural producers who are concerned with the extreme losses of farm profitability in that the later model tends to underestimate the minimum level of risk faced by the producers for a given level of profitability.

The effectiveness of geographical diversification in US wheat farming is evaluated. As a methodological contribution, the copula approach is used to model the joint distribution of profit margins and CVaR is employed as a measure of downside risk.

The purpose of this study is to propose an effective unsupervised one-class-classifier (OCC) support vector machine (SVM)-based single multivariate control chart (OCC-SVM) to simultaneously monitor “location” and “scale” shifts of a manufacturing process.

The step-by-step approach to developing, implementing and fine-tuning the intrinsic parameters of the OCC-SVM chart is demonstrated based on simulation and two real-life case examples.

A comparative study, considering varied known and unknown response distributions, indicates that the OCC-SVM is highly effective in detecting process shifts of samples with individual observations. OCC-SVM chart also shows promising results for samples with a rational subgroup of observations. In addition, the results also indicate that the performance of OCC-SVM is unaffected by the small reference sample size.

The sample responses are considered identically distributed with no significant multivariate autocorrelation between sample observations.

The proposed easy-to-implement chart shows satisfactory performance to detect an out-of-control signal with known or unknown response distributions.

Various multivariate (e.g. parametric or nonparametric) control chart(s) are recommended to monitor the mean (e.g. location) and variance (e.g. scale) of multiple correlated responses in a manufacturing process. However, real-life implementation of a parametric control chart may be complex due to its restrictive response distribution assumptions. There is no evidence of work in the open literature that demonstrates the suitability of an unsupervised OCC-SVM chart to simultaneously monitor “location” and “scale” shifts of multivariate responses. Thus, a new efficient OCC-SVM single chart approach is proposed to address this gap to monitor a multivariate manufacturing process with unknown response distributions.

This study aims to monitor the overall equipment effectiveness (OEE) indicator that is one of the best indicators used to monitor the performance of the company by the multivariate control chart.

To improve continually the performance of a company, many research studies tend to apply Lean six sigma approach. It is one of the best ways used to reduce the variability in the process by using the univariate control chart to know the trend of the variable and make the action before process deviation. Nevertheless, and when the need is to monitor two or more correlated characteristics simultaneously, the univariate control chart will be unable to do it, and the multivariate control chart will be the best way to successfully monitor the correlated characteristics.

For this study, the authors have applied the multivariate control chart to control the OEE performance rate which is composed by the quality rate, performance rate and availability rate, and the relative work from which the authors have adopted the same methodology (Hadian and Rahimifard, 2019) was done for project monitoring, which is done by following different indicators such as cost, and time; the results of this work shows that by applying this tool, all project staff can meet the project timing with the cost already defined at the beginning of the project. The idea of monitoring the OEE rate comes because the OEE contains the three correlated indicators, we can’t do the monitoring of the OEE just by following one of the three because data change and if today we have the performance and quality rate are stable, and the availability is not, tomorrow we can another indicator impacted and, in this case, the univariate control chart can’t response to our demand. That’s why we have choose the multivariate control chart to prevent the trend of OEE performance rate. Otherwise, and according to production planning work, they try to prevent the downtime by switching to other references, but after applying the OEE monitoring using the multivariate control chart, the company can do the monitoring of his ability to deliver the good product at time to meet customer demand.

The application was done per day, it will be good to apply it per shift in order to have the ability to take the fast reaction in case of process deviation. The other perspective point we can have is to supervise the process according to the control limits found and see if the process still under control after the implementation of the Multivariate control chart at the OEE Rate and if we still be able to meet customer demand in terms of Quantity and Quality of the product by preventing the process deviation using multivariate control chart.

The implication of this work is to provide to the managers the trend of the performance of the workshop by measuring the OEE rate and by following if the process still under control limits, if not the reaction plan shall be established before the process become out of control.

The OEE indicator is one of the effective indicators used to monitor the ability of the company to produce good final product, and the monitoring of this indicator will give the company a visibility of the trend of performance. For this reason, the authors have applied the multivariate control chart to supervise the company performance. This indicator is composed by three different rates: quality, performance and availability rate, and because this tree rates are correlated, the authors have tried to search the best tool which will give them the possibility to monitor the OEE rate. After literature review, the authors found that many works have used the multivariate control chart, especially in the field of project: to monitor the time and cost simultaneously. After that, the authors have applied the same approach to monitor the OEE rate which has the same objective : to monitor the quality, performance and availability rate in the same time.

Empirical research on European stock markets has shown that they behave differently according to the performance of the leading financial market identified as the US market. A positive sign is viewed as good news in the international financial markets, a negative sign means, conversely, bad news. As a result, we assume that European stock market returns are affected by endogenous and exogenous shocks. The former raise in the market itself, the latter come from the US market, because of its most influential role in the world. Under standard assumptions, the distribution of the European market index returns conditionally on the sign of the one-day lagged US return is skew-normal. The resulting model is denoted Skew-GARCH. We study the properties of this new model and illustrate its application to time-series data from three European financial markets.

This chapter develops a framework for quantile regression in binary longitudinal data settings. A novel Markov chain Monte Carlo (MCMC) method is designed to fit the model and its computational efficiency is demonstrated in a simulation study. The proposed approach is flexible in that it can account for common and individual-specific parameters, as well as multivariate heterogeneity associated with several covariates. The methodology is applied to study female labor force participation and home ownership in the United States. The results offer new insights at the various quantiles, which are of interest to policymakers and researchers alike.