Multivariate Statistical Process Control Charts: An Overview

In this paper we discuss the basic procedures for the implementation of multivariate statistical process control via control charting. Furthermore, we review multivariate extensions for all kinds of univariate control charts, such as multivariate Shewhart-type control charts, multivariate CUSUM control charts and multivariate EWMA control charts. In addition, we review unique procedures for the construction of multivariate control charts, based on multivariate statistical techniques such as principal components analysis (PCA) and partial lest squares (PLS). Finally, we describe the most significant methods for the interpretation of an out-of-control signal.quality control, process control, multivariate statistical process control, Hotelling's T-square, CUSUM, EWMA, PCA, PLS

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

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

Multivariate process variability monitoring for high dimensional data

In today’s competitive market, the quality of a product or service is no longer measured by a single variable but by a number of variables that define the quality of the final product or service. It is known that these quality variables of products or services are correlated with each other, and it is therefore important to monitor these correlated quality characteristics simultaneously. Multivariate quality control charts are capable of such monitoring. Multivariate monitoring of industrial or clinical procedures often involves more than three correlated quality characteristics, and the status of the process is judged using a sample of one size. The majority of existing control charts for monitoring multivariate process variability for individual observations are capable of monitoring up to three quality characteristics. One of the hurdles in designing optimal variability control charts for large dimension data is the enormous computing resources and time that is required by the simulation algorithm to estimate the charts parameters. In this research, a novel algorithm based on the parallelised Monte Carlo simulation has been developed to improve the ability of the Multivariate Exponentially Weighted Mean Squared Deviation (MEWMS) and Multivariate Exponentially Weighted Moving Variance (MEWMV) charts to monitor multivariate process variability with a greater number of quality characteristics. Different techniques have been deployed to reduce computing space and the time complexity taken by the algorithm. The novelty of this algorithm is its ability to estimate the optimal control limit L (optimal L) for any given number of correlated quality characteristics, size of the shifts to be detected based on the smoothing constant, and the given in-control average run length in a computationally efficient way. The optimal L for the MEWMS and MEWMV charts to detect small, medium and large shifts in the covariance matrix of up to fifteen correlated quality characteristics has been provided. Furthermore, utilising the large number of optimal L values generated by the algorithm has enabled us to develop two mathematical functions that are capable of predicting L values for MEWMS and MEWMV charts. This would eliminate the need for further execution of the parallelised Monte Carlo simulation for high dimension data. One of the main challenges in deploying multivariate control charts is to identify which characteristics are responsible for the out-of-control signal detected by the charts, and what is the extent of their contribution to the signal. In this research, a smart diagnostic technique has been developed by using a hybrid of the wrapper filter approach to effectively identify the variables that are responsible for the process faults and to classify the percentage of their contribution to the faults. The robustness of the proposed techniques has been demonstrated through their application to a range of clinical and industrial multivariate processes where the percentage of correct classifications is presented for different scenarios. The majority of the existing multivariate control charts have been developed to monitor processes that follow multivariate normal distribution. In this thesis, the author has proposed a control chart for a non-normal high dimensional multivariate process based on the percentile point of Burr XII distribution. Geometric distance variables are fitted to the subset of correlated quality characteristics to reduce the dimension of the data, which is then followed by fitting the Burr XII distribution to each geometric distance variable. Since individual distance variables are independent, each can be monitored by individual control charts based on the percentile points of the fitted Burr XII distributions. A simulated annealing approach is used to estimate parameters of the Burr XII distribution. The proposed hybrid is utilised to identify and rank the variables responsible for the out-of-control signals of geometric distance variables

Thread Quality Control in High-Speed Tapping Cycles

Thread quality control is becoming a widespread necessity in manufacturing to guarantee the geometry of the resulting screws on the workpiece due to the high industrial costs. Besides, the industrial inspection is manual provoking high rates of manufacturing delays. Therefore, the aim of this paper consists of developing a statistical quality control approach acquiring the data (torque signal) coming from the spindle drive for assessing thread quality using different coatings. The system shows a red light when the tap wear is critical before machining in unacceptable screw threads. Therefore, the application could reduce these high industrial costs because it can work self-governance.This research was funded by the vice‐counseling of technology, innovation and competitiveness of the Basque Government grant agreements IT‐2005/00201, ZL‐2019/00720 (HARDCRAFT project) and KK‐2019/00004 (PROCODA project)

Dynamic latent variable modelling and fault detection of Tennessee Eastman challenge process

Dynamic principal component analysis (DPCA) is commonly used for monitoring multivariate processes that evolve in time. However, it is has been argued in the literature that, in a linear dynamic system, DPCA does not extract cross correlation explicitly. It does not also give the minimum dimension of dynamic factors with non zero singular values. These limitations reduces its process monitoring effectiveness. A new approach based on the concept of dynamic latent variables is therefore proposed in this paper for extracting latent variables that exhibit dynamic correlations. In this approach, canonical variate analysis (CVA) is used to capture process dynamics instead of the DPCA. Tests on the Tennessee Eastman challenge process confirms the workability of the proposed approach

Neonatal Diagnostics: Toward Dynamic Growth Charts of Neuromotor Control

© 2016 Torres, Smith, Mistry, Brincker and Whyatt. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY).The current rise of neurodevelopmental disorders poses a critical need to detect risk early in order to rapidly intervene. One of the tools pediatricians use to track development is the standard growth chart. The growth charts are somewhat limited in predicting possible neurodevelopmental issues. They rely on linear models and assumptions of normality for physical growth data – obscuring key statistical information about possible neurodevelopmental risk in growth data that actually has accelerated, non-linear rates-of-change and variability encompassing skewed distributions. Here, we use new analytics to profile growth data from 36 newborn babies that were tracked longitudinally for 5 months. By switching to incremental (velocity-based) growth charts and combining these dynamic changes with underlying fluctuations in motor performance – as the transition from spontaneous random noise to a systematic signal – we demonstrate a method to detect very early stunting in the development of voluntary neuromotor control and to flag risk of neurodevelopmental derail.Peer reviewedFinal Published versio