Statistical Process Control Approach Research Articles

The funnel experiment: The Markov‐based SPC approach

AbstractThe classical funnel experiment was used by Deming to promote the idea of statistical process control (SPC). The popular example illustrates that the implementation of simple feedback rules to stationary processes violates the independence assumption and prevents the implementation of conventional SPC. However, Deming did not indicate how to implement SPC in the presence of such feedback rules. This pedagogical gap is addressed here by introducing a simple feedback rule to the funnel example that results in a nonlinear process to which the traditional SPC methods cannot be applied. The proposed method of Markov‐based SPC, which is a simplified version of the context‐based SPC method, is shown to monitor the modified process well. Copyright © 2007 John Wiley & Sons, Ltd.

Monitoring Variability and Analyzing Multivariate Autocorrelated Processes

Traditional multivariate quality control charts are based on independent observations. In this paper, we explain how to extend univariate residual charts to multivariate cases and how to combine the traditional statistical process control (SPC) approaches to monitor changes in process variability in a dynamic environment. We propose using Alt's (1984) W chart on vector autoregressive (VAR) residuals to monitor the variability for multivariate processes in the presence of autocorrelation. We study examples jointly using the Hotelling T2 chart on VAR residuals, the W chart, and the Portmanteau test to diagnose the types of shift in process parameters.

A statistical process control approach to business activity monitoring

Statistical Process Control (SPC) techniques have been successfully used in manufacturing industries to trigger and identify the root cause of variations so as to promote quality improvement. This paper develops a SPC framework to identify important changes deserved in business activity monitoring. To model and track thousands of diversified customer behaviors, the proposed SPC system consists of efficient and robust profiling methods to accommodate different behavior patterns including business changes, structural breakdowns, and unnecessary errors. Several customer profiling techniques are discussed and the activity monitoring performance based on the profiling algorithms is compared in a simulation example and a customer churn detection example in a telecommunications setting. The enhanced system will allow business managers and engineers to establish successful customer loyalty programs for churn prevention and fraud detection.

Statistical Process Control for Variance Shift Detections of Multivariate Autocorrelated Processes

A statistical process control (SPC) approach is proposed to detect variance changes in a multivariate autocorrelated process. The initial step involves a multivariate dynamic linear model (DLM) to remove the autocorrelated data structure. Then diagonal elements of the variance-covariance matrix are then calculated from sample residual vectors obtained from DLM filtering. A multivariate exponential weighted moving average (EWMA) control chart is applied to the vectors of diagonal elements. The proposed control charts called MEWMV for monitoring multivariate variance responses are compared to a multivariate sample generalized variance | S | charts, individual S charts and individual EWMS control charts in term of average run length (ARL). Simulation results based on bivariate AR(1) data show that the proposed MEWMV chart applying to observations without log transformation performs the best for various magnitudes of variance shifts regardless of sample sizes and autocorrelation structures.

MULTISCALE PROCESS MONITORING WITH SINGULAR SPECTRUM ANALYSIS

Multivariate statistical process control (MSPC) approaches are now widely used for performance monitoring, fault detection and diagnosis in chemical processes. Conventional MSPC approaches are based on latent variable projection methods such as principal component analysis and partial least squares. These methods are suitable for handling linearly correlated data sets, with minimal autocorrelation in the variables. Industrial plant data invariably violate these conditions, and several extensions to conventional MSPC methodologies have been proposed to account for these limitations. In this paper a multiscale methodology based on the use of singular spectrum analysis is proposed and its advantages are demonstrated via illustrative case studies.

A statistical process control approach to selecting a warm-up period for a discrete-event simulation

The selection of a warm-up period for a discrete-event simulation continues to be problematic. A variety of selection methods have been devised, and are briefly reviewed. It is apparent that no one method can be recommended above any other. A new approach, based upon the principles of statistical process control, is described (SPC method). Because simulation output data are often highly autocorrelated and potentially non-normal, the batch means method is employed in constructing the control chart. The SPC method is tested on seven data sets and encouraging results are obtained concerning its accuracy. The approach is also discussed with respect to its ease of implementation, simplicity, generality of use and requirements for parameter estimation.

Stability Index of Stochastic Processes: The Statistical Process Control Approach

The article addresses the stability index of stochastic processes (time series) based on the statistical process control approach. The proposed stability index reveals the relation between assignable and common variabilities: the higher the proportion of the assignable variability, the lower the stability. It is calculated as a ratio of the average moving range to the maximum range between the time series mean and the means of the samples with the fixed end. To address sensitivity of the stability index to process changes such as mean and variance shifts, trends, seasonality, autocorrelation, and sudden changes (outliers), hundred of thousands of simulated time series are analyzed. Considering the impact of sample size, amplitude of process change, moment of process change, and type of distribution, the full factorial design of experiment has been applied. The proposed calculation of the stability index and suggested target levels serve as a guide for interpreting stability of the stochastic processes by index. A combination of stability and capability indexes emphasizes dynamic aspects of the process ability regarding specifications and are presented as a dynamic capability index.

Multi-Scale Statistical Process Monitoring in Machining

Most practical industrial process data contain contributions at multiple scales in time and frequency. Unfortunately, conventional statistical process control approaches often detect events at only one scale. This paper addresses a new method, called multiscale statistical process monitoring, for tool condition monitoring in a machining process, which integrates discrete wavelet transform (WT) and statistical process control. Firstly, discrete WT is applied to decompose the collected data from the manufacturing system into uncorrelated components. Next, the detection limits are formed for each decomposed component by using Shewhart control charts. A case study, i.e., tool condition monitoring in turning using an acoustic emission signal, demonstrates that the new method is able to detect abnormal events (serious tool wear or breakage) in the machining process.

A Multivariate Subgroup Rationality Test

In one of our recent articles (Holmes, D. S., Mergen, A. E. (2003). Testing rationality of subgroups in multivariate control charts. In: The 2003 Northeast Decision Sciences Institute Meeting Proceedings. Providence, Rhode Island, March 27–29, Fariborz Partovi, 286–288.) we proposed an aggregate measure for checking rationality of the subgroups in multivariate control charts, such as T 2 charts. The purpose of this article is to build on that measure and propose a similar multivariate test to check the rationality of each subgroup used in the chart. The proposed test uses the statistical process control (SPC) approach; i.e., maintains the time sequence of the data. The method is based on a test for equality of two covariance matrices (Kramer, C. Y., Jensen, D. R. (1969). Fundamentals of multivariate analysis—part II: inference about two treatments. Journal of Quality Technology 1(3):189–204.). The first covariance matrix is the one normally described in statistical literature (for example Johnson and Wichern (Johnson, R. A., Wichern, D. W. (1992). Applied Multivariate Statistical Analysis. New Jersey: Prentice Hall 92–122.) The second matrix used in the test is the multivariate mean square successive difference (MSSD) covariance matrix (Holmes, D. S., Mergen, A. E. (1993). Improving the performance of T-square control chart. Quality Engineering 5(4):619–625.). If the test indicates a significant difference of these two matrices, this is an indication of the lack of rationality of the corresponding subgroup(s) being used on the multivariate control chart. The test result for each subgroup can then be plotted on a control chart to explore which subgroup(s) may be the cause of the nonrationality. Two examples of the use of the proposed method are given.

Multiscale SPC using wavelets: Theoretical analysis and properties

AbstractMost practical process data contain contributions at multiple scales in time and frequency, but most existing SPC methods are best for detecting events at only one scale. For example, Shewhart charts are best for detecting large, localized changes, while EWMA and CUSUM charts are best for detecting small changes at coarse scales. A multiscale approach for SPC, adaptable to the scale of relevant signal features and developed based on wavelet analysis, detects abnormal events at multiple scales as relatively large wavelet coefficients. Univariate and multivariate multiscale SPC (MSSPC) for detecting abnormal operation are theoretically analyzed, and their properties are compared with existing SPC methods based on their average run lengths. SPC methods are best for detecting features over a narrow range of scales. Their performance can deteriorate rapidly if abnormal features lie outside this limited range. Since in most industrial processes, the nature of abnormal features is not known a priori, MSSPC performs better on average due to its adaptability to the scale of the features and for monitoring autocorrelated measurements since dyadic wavelets decorrelate most stochastic processes. MSSPC with dyadic discretization is appropriate for SPC of highly autocorrelated or nonstationary stochastic processes. If normal measurements are uncorrelated or contain only mild autocorrelation, it is better to use MSSPC with integer or uniformly discretized wavelets. Many existing methods such as MA, EWMA, CUSUM, Shewhart, batch means charts, and their multivariate extensions are special cases of MSSPC.

An integrated SPC approach for manufacturing processes

Control charts have been widely used in the manufacturing industry as the most important statistical process control (SPC) technique. One assumption for successfully applying control charts is that the process is stable to begin with and adjustments are made only at a later point when the process is deemed to be out of control. A situation that often arises is when the process is subject to a slow trend caused by factors such as equipment deterioration, power decline during its consumption, or other reasons. For this type of situation, an integrated monitoring and adjustment approach can be considered and the relevant issues involved are discussed in this paper. This problem of implementing SPC is studied from the point of view of process management, together with the concept of engineering process control. A general approach is then formulated for monitoring processes with trend and subject to regular adjustments and a specific model for a general case with linear trend is studied in more detail.

SHIFTS RECOGNITION IN CORRELATED MANUFACTURING PROCESS PARAMETERS USING NEURAL NETWORK

ABSTRACT Because of the existence of the autocorrelation in the data series, traditional statistical process control (SPC) techniques of control charting are not applicable in many process industries. Therefore how to reduce the process variability obtained through the use of SPC techniques has been discussed for years in process industries. Techniques are needed to serve the same functions as SPC control charts that are to identify shifts, in correlated parameters. Neural networks are a massively parallel system and are a potential tool that can be used to identify shifts in correlated process parameters. In this research, backpropagation neural networks are developed to identify shifts in process parameter values from papermaking and viscosity data set available in literature. For finding the appropriate number of input nodes to use in a neural network model, the all-possible-regression selection procedure is applied. For comparison, the time series residual control charts are also developed for the data sets. As the results reveal, networks were successful at identifying data that were shifted one, one and half, and two standard deviations from non-shifted data for both utilized cases. The SPC control charts were not able to classify the same process shifts. In the other words, the neural networks outperform than the traditional SPC approaches in identifying shifts in process parameters. Therefore, it is allowing improved control in manufacturing processes that generate correlated process data.

Statistical and causal model‐based approaches to fault detection and isolation

AbstractBoth fundamental and practical differences between two common approaches to fault detection and isolation are examined. One approach is based on causal state‐variable or parity‐relation models developed from theory or identified from plant test data. The faults are then detected and isolated using structured or directional residuals from these models. The multivariate statistical process control approaches are based on noncausal models built from historical process data using multivariate latent variable methods such as PCA and PLS. The faults are then detected by referencing future data against these covariance models, and isolation is attempted through examining contributions to the breakdown of the covariance structure. There are major differences between these approaches arising mainly from the different types of models and data utilized to build them. Each of them has clear, but complementary, strengths and weaknesses. These are discussed using simulated data from a CSTR process.

Relationships Between Statistical and Causal Model Based Approaches to Fault Detection and Isolation

Abstract This paper examines both the fundamental and the practical differences between two common approaches to fault detection and isolation. One approach is based on causal state variable or parity relation models developed from theory or identified from plant test data. The faults are then detected and isolated using structured or directional residuals from these models. The multivariate statistical process control approaches are based on non-causal models built from historical process data using multivariate latent variable methods such as PCA and PLS. The faults are then detected by referencing future data against these covariance models, and isolation is attempted through examining contributions to the breakdown of the covariance structure. There are major differences between these approaches arising mainly from the different types of models and data utilized to build them. Each of them has clear, but complementary strengths and weaknesses. These are discussed in some detail and illustrated using simulated data from a CSTR process.

A Measurement Approach for Process Improvement

Many organisations today have embarked on a process improvement or re-engineering project. They do so through planned rearchitecting of their processes to engender higher magnitudes of improvements. However, in almost all the organisations undertaking process re-engineering, they do so blindly without any means for checking the efficacy of the newly introduced processes. This paper introduces a blue print measurement approach for gauging the effects of newly introduced processes called REFINE. Whereas most existing measurement approaches are used in the measurement of software processes, REFINE is used for the measurement of business processes. The paper looks at the history of measurement and the definition of measures, and then presents some of the early measurement approaches like the Statistical Process Control approach, the Software Engineering Institute's Capability Maturity Model, the Goal Question Metrics (GQM) Paradigm and the AMI approach to process evaluation and improvement. LBS Management Review Vol.4(1) 1999: 29-48

Statistical Quality Control Methods in Infection Control and Hospital Epidemiology, Part II: Chart Use, Statistical Properties, and Research Issues

ABSTRACTThis is the second in a two-part series discussing and illustrating the application of statistical process control (SPC) in hospital epidemiology. The basic philosophical and theoretical foundations of statistical quality control and their relation to epidemiology are emphasized in order to expand the mutual understanding and cross-fertilization between these two disciplines. Part I provided an overview of the philosophy and general approach of SPC, illustrated common types of control charts, and provided references for further information or statistical formulae. Part II now discusses alternate possible SPC approaches, statistical properties of control charts, chart-design issues and optimal control limit widths, some common misunderstandings, and more advanced issues. The focus of both articles is mostly nonmathematical, emphasizing important concepts and practical examples rather than academic theory and exhaustive calculations.

Statistical Quality Control Methods in Infection Control and Hospital Epidemiology, Part II: Chart Use, Statistical Properties, and Research Issues

This is the second in a two-part series discussing and illustrating the application of statistical process control (SPC) in hospital epidemiology. The basic philosophical and theoretical foundations of statistical quality control and their relation to epidemiology are emphasized in order to expand the mutual understanding and cross-fertilization between these two disciplines. Part I provided an overview of the philosophy and general approach of SPC, illustrated common types of control charts, and provided references for further information or statistical formulae. Part II now discusses alternate possible SPC approaches, statistical properties of control charts, chart-design issues and optimal control limit widths, some common misunderstandings, and more advanced issues. The focus of both articles is mostly nonmathematical, emphasizing important concepts and practical examples rather than academic theory and exhaustive calculations.

Statistical quality control methods in infection control and hospital epidemiology, part I: Introduction and basic theory.

This article is the first in a two-part series discussing and illustrating the application of statistical process control (SPC) to processes often examined by hospital epidemiologists. The basic philosophical and theoretical foundations of statistical quality control and their relation to epidemiology are emphasized in order to expand mutual understanding and cross-fertilization between these two disciplines. Part I provides an overview of quality engineering and SPC, illustrates common types of control charts, and provides references for further information or statistical formulae. Part II discusses statistical properties of control charts, issues of chart design and optimal control limit widths, alternate possible SPC approaches to infection control, some common misunderstandings, and more advanced issues. The focus of both articles is mostly non-mathematical, emphasizing important concepts and practical examples rather than academic theory and exhaustive calculations.

A statistical process control approach to process diagnosis in discrete manufacturing environments

Suggests that there is justification for the use of a new methodology for process diagnosis which is simple to understand and realistic to implement. The control of quality of a process typically requires that multiple process variables be monitored simultaneously. Due to the multi‐dimensionality of the data collected, process diagnosis is complex and the data often are not efficiently integrated to capitalize on the wealth of available information. A two‐phased diagnostic approach for process diagnosis and identification of suspect causes for this multi‐dimensional problem is introduced in Krishnamurthi et al. (1993). Provides an in‐depth analysis of phase two of the statistical process control (SPC) diagnostic approach. Specifically, simulation is used to generate different cause and effect scenarios to determine the effectiveness of the SPC approach in correctly diagnosing a process disorder. The analysis utilizes analysis of variance to estimate the effect of various process variables, process steps, and associated out‐of‐control conditions on the performance of the SPC approach and its ability to diagnose correctly an out‐of‐control condition. As a result of these findings, the critical means are plotted and the findings are presented. Additionally, a comparison between the SPC approach and parsimonious covering theory (PCT) is made. Concludes that for the process scenarios considered, which are of practical size, the more simple approach of the SPC diagnostic approach is recommended.

A Statistical Process Control Approach to Homework Assignments (or, Practicing What We Preach)

Abstract This article describes a process in which problems are randomly selected from an assigned homework set and given to students as in-class quizzes. Students take the quizzes seriously because the scores contribute a substantial portion of their grades and, because the problems are specified in advance, they feel that studying is effective. Faculty like the random quizzes because grading is simplified and incentives for students to engage in low-effort homework completion methods are removed.