Dynamic Multivariate Statistical Process Control using Subspace Identification

This paper points out a serious flaw in dynamic multivariate statistical process control (MSPC). The principal component analysis of a linear time series model that is employed to capture auto- and cross-correlation in recorded data may produce a considerable number of variables to be analysed. To give a dynamic representation of the data (based on variable correlation) and circumvent the production of a large time-series structure, a linear state space model is used here instead. The paper demonstrates that incorporating a state space model, the number of variables to be analysed dynamically can be considerably reduced, compared to conventional dynamic MSPC techniques.

Improved Principal Component Monitoring of Large-Scale Processes

This is the first paper that shows and theoretically analyses that the presence of auto-correlation can produce considerable alterations in the Type I and Type II errors in univariate and multivariate statistical control charts. To remove this undesired effect, linear inverse ARMA filter are employed and the application studies in this paper show that false alarms (increased Type I errors) and an insensitive monitoring statistics (increased Type II errors) were eliminated.

Statistical Monitoring of Dynamic Multivariate Processes: Part I: Modeling Auto- and Cross-Correlation

The work in this paper is of particular significance since it considers the problem of modelling cross- and auto-correlation in statistical process monitoring. The presence of both types of correlation can lead to fault insensitivity or false alarms, although in published literature to date, only autocorrelation has been broadly considered. The proposed method, which uses a Kalman innovation model, effectively removes both correlations. The paper (and Part 2 [2]) has emerged from work supported by EPSRC grant GR/S84354/01 and is of direct relevance to problems in several application areas including chemical, electrical, and mechanical process monitoring.

Statistical Monitoring of Dynamic Multivariate Processes: Part II: Identifying Fault Magnitude and Signature

This paper builds on work presented in the first paper, Part 1 [1] and is of equal significance. The paper proposes a novel compensation method to preserve the integrity of step-fault signatures prevalent in various processes that can be masked during the removal of both auto- and cross correlation. Using industrial data, the paper demonstrates the benefit of the proposed method, which is applicable to chemical, electrical, and mechanical process monitoring. This paper, (and Part 1 [1]), has led to further work supported by EPSRC grant GR/S84354/01 involving kernel PCA methods.

Multivariate prediction of clarified butter composition using Raman spectroscopy

Raman spectroscopy has been used to predict the abundance of the FA in clarified butterfat that was obtained from dairy cows fed a range of levels of rapeseed oil in their diet. Partial least squares regression of the Raman spectra against FA compositions obtained by GC showed good prediction for the five major (abundance >5%) FA with R-2=0.74-0.92 and a root mean SE of prediction (RMSEP) that was 5-7% of the mean. In general, the prediction accuracy fell with decreasing abundance in the sample, but the RMSEP was 1.25%. The Raman method has the best prediction ability for unsaturated FA (R-2=0.85-0.92), and in particular trans unsaturated FA (best-predicted FA was 18:1 tDelta9). This enhancement was attributed to the isolation of the unsaturated modes from the saturated modes and the significantly higher spectral response of unsaturated bonds compared with saturated bonds. Raman spectra of the melted butter samples could also be used to predict bulk parameters calculated from standard analyzes, such as iodine value (R-2=0.80) and solid fat content at low temperature (R-2=0.87). For solid fat contents determined at higher temperatures, the prediction ability was significantly reduced (R-2=0.42), and this decrease in performance was attributed to the smaller range of values in solid fat content at the higher temperatures. Finally, although the prediction errors for the abundances of each of the FA in a given sample are much larger with Raman than with full GC analysis, the accuracy is acceptably high for quality control applications. This, combined with the fact that Raman spectra can be obtained with no sample preparation and with 60-s data collection times, means that high-throughput, on-line Raman analysis of butter samples should be possible.

Higher order statistics for lognormal small-scale fading in mobile radio channels

This letter reports the statistical characterization and modeling of the indoor radio channel for a mobile wireless personal area network operating at 868 MHz. Line of sight (LOS) and non-LOS conditions were considered for three environments: anechoic chamber, open office area and hallway. Overall, the Nakagami-m cdf best described fading for bodyworn operation in 60% of all measured channels in anechoic chamber and open office area environments. The Nakagami distribution was also found to provide a good description of Rician distributed channels which predominated in the hallway. Multipath played an important role in channel statistics with the mean recorded m value being reduced from 7.8 in the anechoic chamber to 1.3 in both the open office area and hallway.

Higher order statistics for the κ–μ distribution

Closed-form expressions for the level crossing rate and average fade duration of a kappa–mu distributed fading signal envelope are presented. The proposed equations are validated by reduction to known Rice, Rayleigh and Nakagami-m special cases. They are also compared with measured data obtained from field trials analysing human body to body radio channels and shown to provide good agreement.

The structure of the Statistics Anxiety Rating Scale: A confirmatory factor analysis using UK psychology students

This study aimed to examine the structure of the statistics anxiety rating scale. Responses from 650 undergraduate psychology students throughout the UK were collected through an on-line study. Based on previous research three different models were specified and estimated using confirmatory factor analysis. Fit indices were used to determine if the model fitted the data and a likelihood ratio difference test was used to determine the best fitting model. The original six factor model was the best explanation of the data. All six subscales were intercorrelated and internally consistent. It was concluded that the statistics anxiety rating scale was found to measure the six subscales it was designed to assess in a UK population.