Multivariate control charts based on Bayesian state space models

This paper develops a new multivariate control charting method for vector autocorrelated and serially correlated processes. The main idea is to propose a Bayesian multivariate local level model, which is a generalization of the Shewhart-Deming model for autocorrelated processes, in order to provide the predictive error distribution of the process and then to apply a univariate modified EWMA control chart to the logarithm of the Bayes' factors of the predictive error density versus the target error density. The resulting chart is proposed as capable to deal with both the non-normality and the autocorrelation structure of the log Bayes' factors. The new control charting scheme is general in application and it has the advantage to control simultaneously not only the process mean vector and the dispersion covariance matrix, but also the entire target distribution of the process. Two examples of London metal exchange data and of production time series data illustrate the capabilities of the new control chart.Comment: 19 pages, 6 figure

Improved performance of MCUSUM control chart with autocorrelation

In recent years, the importance of quality has become increasingly apparent, and quality control in manufacturing has moved from detecting nonconforming products through inspection to detecting quality abnormalities in the process using statistical process control [1]. where it is used effectively, SPC plays an important role in reducing variation in manufactured items and in increasing the competitiveness of the manufacturer by improving product quality while at the same time decreasing production costs. Charts like the Shewhart X and R charts have found wide use in industry because of their ease of use for technicians and others with minimal training in statistics, since the calculations and plotting can be done by hand. An MCUSUM control chart was constructed with autocorrelated data at different levels of autocorrelation and found to be ineffective in detecting shifts as it occurs. In this article, we have proposed new techniques that can improve the performance of the MCUSUM with autocorrelation using run rule schemes. The techniques was evaluated using ARL measures of performance with 10000 iterations to simulate. The results showed that the performance of MCUSUM with autocorrelation has improved significantly with the new technique which was compared to the existing conventional MCUSUM control chart

Integrated Projection and Regression Models for Monitoring Multivariate Autocorrelated Cascade Processes

This dissertation presents a comprehensive methodology of dual monitoring for the multivariate autocorrelated cascade processes using principal component analysis and regression. Principle Components Analysis is used to alleviate the multicollinearity among input process variables and reduce the dimension of the variables. An integrated principal components selection rule is proposed to reduce the number of input variables. An autoregressive time series model is used and imposed on the time correlated output variable which depends on many multicorrelated process input variables. A generalized least squares principal component regression is used to describe the relationship between product and process variables under the autoregressive regression error model. The combined residual based EWMA control chart, applied to the product characteristics, and the MEWMA control charts applied to the multivariate autocorrelated cascade process characteristics, are proposed. The dual EWMA and MEWMA control chart has advantage and capability over the conventional residual type control chart applied to the residuals of the principal component regression by monitoring both product and the process characteristics simultaneously. The EWMA control chart is used to increase the detection performance, especially in the case of small mean shifts. The MEWMA is applied to the selected set of variables from the first principal component with the aim of increasing the sensitivity in detecting process failures. The dual implementation control chart for product and process characteristics enhances both the detection and the prediction performance of the monitoring system of the multivariate autocorrelated cascade processes. The proposed methodology is demonstrated through an example of the sugar-beet pulp drying process. A general guideline for controlling multivariate autocorrelated processes is also developed

A review on the influence of drinking water quality towards human health

An adequate supply of safe drinking water is one of the major prerequisites for a healthy life. Inadequate of safe drinking water produce waterborne disease and a major cause of death in many parts of the world, particularly in children. Therefore, it must be treated properly before it can be used and consumed. This chapter provides the guidelines of important parameters for drinking water standard in order to ensure the safeness of drinking water. All the selected parameters were elaborated on the effect of high concentration if human consume the drinking water directly

Integrating SPC and EPC for Multivariate Autocorrelated Process

Statistical process control (SPC) is a widely employed quality control method in industry. SPC is mainly designed for monitoring single quality characteristic. However, as the design of a product/process becomes complex, a process usually has multiple quality characteristics related to it. These characteristics must be monitored by multivariate SPC. When the autocorrelation is present in the process data, the traditional SPC may mislead the results. Hence, the autocorrelated data must be treated to eliminate the autocorrelation effect before employing SPC to detect the assignable causes. Besides, chance causes also have impact on the processes. When the process is out of control but no assignable cause is found, it can be adjusted by employing engineering process control (EPC). However, only using EPC to adjust the process may make inappropriate adjustments due to external disturbances or assignable causes. This study presents an integrated SPC and EPC procedure for multivariate autocorrelated process. The SPC procedure constructs a predicting model using group method of data handling (GMDH), which can transfer the autocorrelated data into uncorrelated data. Then, the Hotelling’s T2 and multivariate cumulative sum control charts are constructed to monitor the process. The EPC procedure constructs a controller utilizing data mining technique to adjust the multiple quality characteristics to their target values. Industry can employ this procedure to monitor and adjust the multivariate autocorrelated process

Fault detection in the Tennessee Eastman benchmark process using dynamic principal components analysis based on decorrelated residuals (DPCA-DR)

Current multivariate control charts for monitoring large scale industrial processes are typically based on latent variable models, such as principal component analysis (PCA) or its dynamic counterpart when variables present auto-correlation (DPCA). In fact, it is usually considered that, under such conditions, DPCA is capable to effectively deal with both the cross- and auto-correlated nature of data. However, it can easily be verified that the resulting monitoring statistics (T2 and Q, also referred by SPE) still present significant auto-correlation. To handle this issue, a set of multivariate statistics based on DPCA and on the generation of decorrelated residuals were developed, that present low auto-correlation levels, and therefore are better positioned to implement SPC in a more consistent and stable way (DPCA-DR). The monitoring performance of these statistics was compared with that from other alternative methodologies for the well-known Tennessee Eastman process benchmark. From this study, we conclude that the proposed statistics had the highest detection rates on 19 out of the 21 faults, and are statistically superior to their PCA and DPCA counterparts. DPCA-DR statistics also presented lower auto-correlation, which simplifies their implementation and improves their reliability

Data Visualization: Graphical Representation in the Evaluation of Experimental Group Therapy Education Outcomes

Introduction: An important methodological consideration in the social sciences is the evaluation of the effectiveness of groups and specific group interventions. There is an increasing demand for service accountability in practice settings both in social services and public health services. Group services are rising as a practice modality. Emerging technology shows promise of providing the means for practitioners untrained in advanced research methods to gain useful information and improved decision- making capacities related to groups and group services. Computer based graphical representation of data patterns at multiple levels of analysis can provide the bases for data exploration and lead to further advances in the evaluation of complex group dimensions associated with group effectiveness. Objectives: The purpose of this study was to evaluate group therapy experiential education outcomes using conventional data analytic methods for time series data. These include traditional methods of visual evaluation of single subject information, as well as, less common graphical representation methods that permit the simultaneous display of group process and outcomes and provide visual evaluation information across units of analysis. Methods: Group level time series data for 16 experiential group therapy education groups were evaluated using a variety of graphical and statistical methods. This study demonstrates a range of graphical representations, which provide differing levels of evaluative information and time series statistical information. The limitations of inferences available when evaluating non-probability samples were addressed. Results: Using widely ava ilable technology a number of graphical methods were demonstrated that present multilevel time series information to include group process and outcome simultaneously for both individuals and groups, as well as, for multiple variables of change. Data visualization evaluative methods were presented that illustrate levels of group participant concordance and variability over time. Graphical representations were generated that demonstrate the proportional contribution of multiple variables to group outcome over time. Graphical representations methods were also presented that represent multiple levels of analysis over time and for multiple groups with varying durations of group length for simultaneous comparison over time. The difficulties associated with identifying autocorrelation in time series data and with non-probability samples using graphical and statistical methods were addressed