William H. Woodall

Exponentially weighted moving average control schemes: properties and enhancements

Roberts (1959) first introduced the exponentially weighted moving average (EWMA) control scheme. Using simulation to evaluate its properties, he showed that the EWMA is useful for detecting small shifts in the mean of a process. The recognition that an EWMA control scheme can be represented as a Markov chain allows its properties to be evaluated more easily and completely than has previously been done. In this article, we evaluate the properties of an EWMA control scheme used to monitor the mean of a normally distributed process that may experience shifts away from the target value. A design procedure for EWMA control schemes is given. Parameter values not commonly used in the literature are shown to be useful for detecting small shifts in a process. In addition, several enhancements to EWMA control schemes are considered. These include a fast initial response feature that makes the EWMA control scheme more sensitive to start-up problems, a combined Shewhart EWMA that provides protection against both larg...

A multivariate exponentially weighted moving average control chart

A multivariate extension of the exponentially weighted moving average (EWMA) control chart is presented, and guidelines given for designing this easy-to-implement multivariate procedure. A comparison shows that the average run length (ARL) performance of this chart is similar to that of multivariate cumulative sum (CUSUM) control charts in detecting a shift in the mean vector of a multivariate normal distribution. As with the Hotellings χ2 and multivariate CUSUM charts, the ARL performance of the multivariate EWMA chart depends on the underlying mean vector and covariance matrix only through the value of the noncentrality parameter. Worst-case scenarios show that Hotellings χ2 charts should always be used in conjunction with multivariate CUSUM and EWMA charts to avoid potential inertia problems. Examples are given to illustrate the use of the proposed procedure.

RESEARCH ISSUES AND IDEAS IN STATISTICAL PROCESS CONTROL

An overview is given of current research on control charting methods for process monitoring and improvement. A historical perspective and ideas for future research also are given. Research topics include: variable sample size and sampling interval met..

The Use of Control Charts in Health-Care and Public-Health Surveillance

There are many applications of control charts in health-care monitoring and in public-health surveillance. We introduce these applications to industrial practitioners and discuss some of the ideas that arise that may be applicable in industrial monitoring. The advantages and disadvantages of the charting methods proposed in the health-care and public-health areas are considered. Some additional contributions in the industrial statistical process control literature relevant to this area are given. There are many application and research opportunities available in the use of control charts for health-related monitoring.

Using Control Charts to Monitor Process and Product Quality Profiles

In most statistical process control (SPC) applications, it is assumed that the quality of a process or product can be adequately represented by the distribution of a univariate quality characteristic or by the general multivariate distribution of a vector consisting of several correlated quality characteristics. In many practical situations, however, the quality of a process or product is better characterized and summarized by a relationship between a response variable and one or more explanatory variables. Thus, at each sampling stage, one observes a collection of data points that can be represented by a curve (or profile). In some calibration applications, the profile can be represented adequately by a simple straight-line model, while in other applications, more complicated models are needed. In this expository paper, we discuss some of the general issues involved in using control charts to monitor such process- and product-quality profiles and review the SPC literature on the topic. We relate this application to functional data analysis and review applications involving linear profiles, nonlinear profiles, and the use of splines and wavelets. We strongly encourage research in profile monitoring and provide some research ideas.

Effects of parameter estimation on control chart properties : A literature review

Control charts are powerful tools used to monitor the quality of processes. In practice, control chart limits are often calculated using parameter estimates from an in-control Phase I reference sample. In Phase II of the monitoring scheme, statistics based on new samples are compared with the estimated control limits to monitor for departures from the in-control state. Many studies that evaluate control chart performance in Phase II rely on the assumption that the in-control parameters are known. Although the additional variability introduced into the monitoring scheme through parameter estimation is known to affect the chart performance, many studies do not consider the effect of estimation on the performance of the chart. This paper contains a review of the literature that explicitly considers the effect of parameter estimation on control chart properties. Some recommendations are made and future research ideas in this area are provided.

Controversies and Contradictions in Statistical Process Control

Statistical process control (SPC) methods are widely used to monitor and improve manufacturing processes and service operations. Disputes over the theory and application of these methods are frequent and often very intense. Some of the controversies and issues discussed are the relationship between hypothesis testing and control charting, the role of theory and the modeling of control chart performance, the relative merits of competing methods, the relevance of research on SPC and even the relevance of SPC itself. One purpose of the paper is to offer a resolution of some of these disagreements in order to improve the communication between practitioners and researchers.

ON THE MONITORING OF LINEAR PROFILES

We propose control chart methods for process monitoring when the quality of a process or product is characterized by a linear function. In the historical analysis of Phase I data, we recommend methods including the use of a bivariate T2 chart to check for stability of the regression coefficients in conjunction with a univariate Shewhart chart to check for stability of the variation about the regression line. We recommend the use of three univariate control charts in Phase II. These three charts are used to monitor the 𝘠-intercept, the slope, and the variance of the deviations about the regression line, respectively. A simulation study shows that this type of Phase II method can detect sustained shifts in the parameters better than competing methods in terms of average run length performance. We also relate the monitoring of linear profiles to the control charting of regression-adjusted variables and other methods.

Exact results for shewhart control charts with supplementary runs rules

This article gives a simple and efficient method, using Markov chains, to obtain the exact run-length properties of Shewhart control charts with supplementary runs rules. Average run-length comparisons are made among the Shewhart chart with supplementary runs rules, the basic Shewhart chart, and the cumulative sum (CUSUM) chart.

Multivariate CUSUM Quality- Control Procedures

It is a common practice to use, simultaneously, several one-sided or two-sided CUSUM procedures of the type proposed by Page (1954). In this article, this method of control is considered to be a single multivariate CUSUM (MCUSUM) procedure. Methods are given for approximating parameters of the distribution of the minimum of the run lengths of the univariate CUSUM charts. Using a new method of comparing multivariate control charts, it is shown that an MCUSUM procedure is often preferable to Hotellings TZ procedure for the case in which the quality characteristics are bivariate normal random variables.