Univariate and multivariate process yield indices based on location-scale family of distributions

Several measures of process yield, defined on univariate and multivariate normal process characteristics, have been introduced and studied by several authors. These measures supplement several well-known Process Capacity Indices (PCI) used widely in assessing the quality of products before being released into the marketplace. In this paper, we generalise these yield indices to the location-scale family of distributions which includes the normal distribution as one of its member. One of the key contributions of this paper is to demonstrate that under appropriate conditions, these indices converge in distribution to a normal distribution. Several numerical examples will be used to illustrate our procedures and show how they can be applied to perform statistical inferences on process capability.

Rapid discrimination and determination of polyunsaturated fatty acid composition in marine oils by FTIR Spectroscopy and Multivariate Data Analysis

A rapid analytical approach for discrimination and quantitative determination of polyunsaturated fatty acid (PUFA) contents, particularly eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA), in a range of oils extracted from marine resources has been developed by using attenuated total reflection Fourier transform infrared spectroscopy and multivariate data analysis. The spectral data were collected without any sample preparation; thus, no chemical preparation was involved, but data were rather processed directly using the developed spectral analysis platform, making it fast, very cost effective, and suitable for routine use in various biotechnological and food research and related industries. Unsupervised pattern recognition techniques, including principal component analysis and unsupervised hierarchical cluster analysis, discriminated the marine oils into groups by correlating similarities and differences in their fatty acid (FA) compositions that corresponded well to the FA profiles obtained from traditional lipid analysis based on gas chromatography (GC). Furthermore, quantitative determination of unsaturated fatty acids, PUFAs, EPA and DHA, by partial least square regression analysis through which calibration models were optimized specifically for each targeted FA, was performed in both known marine oils and totally independent unknown n - 3 oil samples obtained from an actual commercial product in order to provide prospective testing of the developed models towards actual applications. The resultant predicted FAs were achieved at a good accuracy compared to their reference GC values as evidenced through (1) low root mean square error of prediction, (2) good coefficient of determination close to 1 (i.e., R 2≥ 0.96), and (3) the residual predictive deviation values that indicated the predictive power at good and higher levels for all the target FAs. © 2014 Springer Science+Business Media New York.

Estimating capability index in multivariate processes using bootstrap sequential sampling procedures

Capability indices in both univariate and multivariate processes are extensively employed in quality control to assess the quality status of production batches before their release for operational use. It is traditionally a measure of the ratio of the allowable process spread and the actual spread. In this paper, we will adopt a bootstrap and sequential sampling procedures to determine the optimal sample size for estimating a multivariate capability index introduced by Pearns et. al. [12]. Bootstrap techniques have the distinct advantage of placing very minimum requirement on the distributions of the underlying quality characteristics, thereby rendering them more relevant under a wide variety of situations. Finally, we provide several numerical examples where the sequential sampling procedures are evaluated and compared.

Energy consumption and income in six Asian developing countries: a multivariate cointegration analysis

 This article examines the short- and long-run causal relationship between energy consumption and GDP of six emerging economies of Asia. Based on cointegration and vector error correction modeling the empirical results show that there exists unidirectional short- and long-run causality running from energy consumption to GDP for China, uni-directional short-run causality from output to energy consumption for India, whilst bi-directional short-run causality for Thailand. Neutrality between energy consumption and income is found for Indonesia, Malaysia and Philippines. Both the generalized variance decompositions and impulse response functions confirm the direction of causality. These findings have important policy implications for the countries concerned. The results suggest that while India may directly initiate energy conservation measures, China and Thailand may opt for a balanced combination of alternative polices.

Application of extended multivariate modeling for information flow analysis of event related responses

Event related potential (ERP) analysis is one of the most widely used methods in cognitive neuroscience research to study the physiological correlates of sensory, perceptual and cognitive activity associated with processing information. To this end information flow or dynamic effective connectivity analysis is a vital technique to understand the higher cognitive processing under different events. In this paper we present a Granger causality (GC)-based connectivity estimation applied to ERP data analysis. In contrast to the generally used strictly causal multivariate autoregressive model, we use an extended multivariate autoregressive model (eMVAR) which also accounts for any instantaneous interaction among variables under consideration. The experimental data used in the paper is based on a single subject data set for erroneous button press response from a two-back with feedback continuous performance task (CPT). In order to demonstrate the feasibility of application of eMVAR models in source space connectivity studies, we use cortical source time series data estimated using blind source separation or independent component analysis (ICA) for this data set.

Multivariate adaptive autoregressive modeling and kalman filtering for motor imagery BCI

Adaptive autoregressive (AAR) modeling of the EEG time series and the AAR parameters has been widely used in Brain computer interface (BCI) systems as input features for the classification stage. Multivariate adaptive autoregressive modeling (MVAAR) also has been used in literature. This paper revisits the use of MVAAR models and propose the use of adaptive Kalman filter (AKF) for estimating the MVAAR parameters as features in a motor imagery BCI application. The AKF approach is compared to the alternative short time moving window (STMW) MVAAR parameter estimation approach. Though the two MVAAR methods show a nearly equal classification accuracy, the AKF possess the advantage of higher estimation update rates making it easily adoptable for on-line BCI systems.

Multivariate autoregressive-based neuronal network flow analysis for in-vitro recorded bursts

Neuroscientific studies of in vitro neuron cell cultures has attracted paramount attention to investigate the behaviour of neuronal networks in response to different environmental conditions and external stimuli such as drugs, optical and electrical stimulations. Microelec trodearray (MEA) technology has been widely adopted as a tool for this investigation. In this work, we present a new approach to estimate interconnectivity of neural spikes using multivariate autoregressive (MVAR) analysis and Partial Directed Coherence (PDC). The proposed approach has the potential to discover hidden intra-burst causal connectivity patterns and to help understand the spatiotemporal communication patterns within bursts, pre and post stimulations.

Learning entry profiles of children with autism from multivariate treatment information using restricted boltzmann machines

Entry profiles can be generated before children with Autism Spectrum Disorders (ASD) begin to traverse an intervention program. They can help evaluate the progress of each child on the dedicated syllabus in addition to enabling narrowing down the best intervention course over time. However, the traits of ASD are expressed in different ways in every individual affected. The resulting spectrum nature of the disorder makes it challenging to discover profiles of children with ASD. Using data from 491 children, traversing the syllabus of a comprehensive intervention program on iPad called TOBY Playpad, we learn the entry profiles of the children based on their age, sex and performance on their first skills of the syllabus. Mixed-variate restricted Boltzmann machines allow us to integrate the heterogeneous data into one model making it a suitable technique. The data based discovery of entry profiles may assist in developing systems that can automatically suggest best suitable paths through the syllabus by clustering the children based on the characteristics they present at the beginning of the program. This may open the pathway for personalised intervention.

Tail conditional expectation for multivariate distributions : a game theory approach

This paper proposes using the Shapley values in allocating the total tail conditional expectation (TCE) to each business line (X j, j = 1, ... , n) when there are n correlated business lines. The joint distributions of X j and S (S = X1 + X2 + ⋯ + X n) are needed in the existing methods, but they are not required in the proposed method.

A transformation-based multivariate chart to monitor process dispersion

Multivariate monitoring techniques such as multivariate control charts are used to control the processes that contain more than one correlated characteristic. Although the majority of previous researches are focused on controlling only the mean vector of multivariate processes, little work has been performed to monitor the covariance matrix. In this research, a new method is presented to detect possible shifts in the covariance matrix of multivariate processes. The basis of the proposed method is to eliminate the correlation structure between the quality characteristics by transformation technique and then use an S chart for each variable. The performance of the proposed method is then compared to the ones from other existing methods and a real case is presented.

A note on multivariate non-normal process capability analysis using "mvtnorm" library in R

In this note we examine using Genzbretz and Miwa algorithms to improve estimation of proposition of non-conformance in multivariate normal distributions. This estimation is required in the procedure outlined in Abbasi and Niaki (Int J Adv Manuf Technol 50(5-8):823-830, 2010) to determine process capability index of multivariate non-normal processes.