J. Stuart Hunter

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...

The Exponentially Weighted Moving Average

The Shewhart and CUSUM control chart techniques have found wide application in the manufacturing industries. However, workpiece quality has also been greatly enhanced by rapid and precise individual item measurements and by improvements in automatic dynamic machine control. One consequence is a growing similarity in the control problems faced by the workpiece quality control engineer and his compatriot in the continuous process industries. The purpose of this paper is to exposit a control chart technique that may be of value to both manufacturing and continuous process quality control engineers: the exponentially weighted moving average (EWMA) control chart. The EWMA has its origins in the early work of econometricians, and although its use in quality control has been recognized, it remains a largely neglected tool. The EWMA chart is easy to plot, easy to interpret, and its control limits are easy to obtain. Further, the EWMA leads naturally to an empirical dynamic control equation.

Statistical Design Applied to Product Design

Great interest has been stimulated by Genichi Taguchi and his co-workers in the application of statistically designed experiments to industrial product design. Language difficulties (Japanese to English to Statistics) have served to obscure many of the ..

A ONE-POINT PLOT EQUIVALENT TO THE SHEWHART CHART WITH WESTERN ELECTRIC RULES

The plot of an Exponentially Weighted Moving Average (EWMA) with weighting factor λ=0.4 provides a single-point signal detection capability equivalent to the Shewhart chart for averages combined with the Western Electric rules...

Statistics as a Profession

Abstract In August of 1988 when Bob Hogg was President of the ASA he invited me as a vice-president elect to attended my first meeting of the ASA Board of Directors. I have thus been part of the ASA Boards activities for five full years. It has been a period of many changes for the Association: the new constitution, the newly structured Board, many new Sections, several new publications, a membership campaign, the assorted activities of the ASA Center for Statistical Education, and most recently the modification in the ASA dues structure with its “cafeteria plan” allowing members to select their publications. These many changes are indications that the entire statistics profession, represented at this meeting by the ASA, the IMS, and the Biometric Society, is being challenged not only to meet the needs of its membership but also those of society at large. These are exciting times, much like sailing when the wind comes up. And I still have a year and a half ahead on the ASA Board of Directors. I must reme...

Enhancing Friedman's "fundamental theorem of biomedical informatics".

In a recent issue of JAMIA 1 Charles P Friedman proposed a “Fundamental Theorem of Biomedical Informatics” to aid others in understanding the mission of the profession. The theorem states:“A person working in partnership with an information source is ‘better’ than the same person unassisted.” The theorem was accompanied by three corollaries, briefly: The discussion of the theorem was accompanied by a figure showing that a persons brain plus a computer are together greater than the persons brain alone (figure 1). Figure 1 In this authors view, the figures focus on the computer provides too narrow a view of bioinformatics and informatics. Missed is the opportunity to emphasize the crucial role of the scientific method in enhancing the learning process. The computer …

In Memoriam: George E. P. Box

George Edward Pelham Box died peacefully in his home in Wisconsin on Thursday March 28, 2013. Closely attended by his wife Claire he had been ill for many months, gradually losing his physical wellbeing. Nevertheless, he continued throughout to be mentally alert, professionally productive, and with his many friends wonderfully full of stories, songs, and repartee. George Box was George Box to the very end. For confirmation do read his memoir An Accidental Statistician: The Life and Memories of G. E. P. Box (John Wiley), completed shortly before his death and now available in both print and online. George Box’s contributions to statistics, both applied and theoretical, are profound. His early work on response surface and fractional factorial designs significantly influenced the growth of statistical practice throughout industry. His theoretical study of the “robustness” of statistics led later to elucidating the value of Bayesian approaches to the modeling and analyses of data. His work in time series reorganized the field with its emphasis of nonstationarity and its AutoRegressive Integrated Moving Average (ARIMA) models’ classification. His continuing interest in the problems of industrial quality control led him to new insights into the dynamic forecasting and control of industrial processes. His repeated emphasis on the iterative nature of the learning process (conjecture to design to data analysis leading to new conjecture) is now recognized as relevant to all the sciences. Read his paper “Science and Statistics,” JASA 71, pp. 791–799 (1976) or his ASA Presidential Address in JASA 74, pp. 1–4 (1979). His personal history begins with his birth on October 18, 1919, in Gravesend, England. He grew up in humble circumstances but his talents were early recognized by his boyhood teachers and he was thus enabled to attend the more elite public schools. He found early work as a chemist and wrote his first scientific paper, at age 19, concerning an activated sludge treatment process. WWII found him in the army and late in the war working on determining the efficacy of new poison gases being manufactured in Germany. His analyses of laboratory data led him to self-study statistics and to meet with R. A. Fisher. For his war work, he received the British Empire Medal in 1946. In 1947, he obtained a B.Sc. in Mathematical Statistics with first class honors at London University and went to work for Imperial Chemical Industries, ICI, as an in-house statistical consultant. Box’s article with K. B. Wilson, “On the Experimental Attainment of Optimum Conditions,” JRSS B, 13, pp. 1–45 (1951) provided the catalyst for bringing him to the United States at the invitation of Miss Gertrude Cox of the Institute of Statistics in Raleigh, NC. In his reply to Miss Cox’s invitation, he mentioned that in addition to work on experimental design he would like to investigate the robustness of the t and F statistics, the earliest mention of the word “robust” in a statistical context. He arrived in the United States on a 1 year leave from ICI in January 1953. Beginning with his 1953 visit, and during the interim before his return to the USA in 1956, many industrial short courses expositing Box’s work on experimental design were sponsored by the American Society for Quality Control (ASQC) and the American Institute of Chemical Engineers (AIChE). His article “Evolutionary Operation: A Method for Increasing Industrial Productivity,” Applied Statistics VI, pp. 3–23 (1957) proved almost explosive in generating an interest in statistics. At Society meetings and Gordon Conferences, the needs for expanded technical communication on the statistical arts applied to problems of engineering and industrial productivity were thus much discussed. The journal Technometrics you are now reading is one consequence. The financial resources required for launching Technometrics in February 1959 were provided by revenues derived exclusively from the many industrial short courses elucidating the works of George Box. Box returned to the USA in 1956 to assume leadership of the Statistical Techniques Research Group (STRG) at Princeton, a continuation of Princeton’s earlier WWII Statistical Research Group chaired by S. S. Wilks. The STRG quickly grew into an exciting interactive mixture of academic, professional, and student statisticians. Early permanent members were John Tukey, Merve Muller, and J. S. Hunter. Others who stayed a year or more include Henry Scheffe, H. L. Lucas, Colin Mallows, Gwilym Jenkins, G. S. Watson, Martin Beale, N. R. Draper, and D. W. Behnken with briefer visits by R. A. Fisher, George Barnard, Cuthbert Daniel, and other notables. The statistics profession continues indebted to this day for the many papers and books that found their inspiration at the STRG. In 1959, George left Princeton for the University of Wisconsin, Madison to establish a Department of Statistics, first investing a year in preparation as a member of the Mathematics Research Center on campus. Now “Professor” Box, he taught his first classes in September 1960. By 1968 the Wisconsin Statistics Department was one of the largest in the nation with 17 faculty members. In 1970, he became visiting professor at the University of Essex in Colchester England. He returned to Wisconsin in 1971 and was appointed to the newly created Ronald A. Fisher Chair of Statistics. In 1980, he took leave of direct departmental responsibilities to become Vilas Research Professor of Mathematics and Statistics. In 1985, in collaboration with W. G. Hunter, he established the Center for Quality and Productivity Improvement (CQPI) at the University for the purpose of conducting research on quality problems. In 1991, Box officially retired from University activities. He is remembered by his many students as a superb teacher and mentor

Ellis Ott: Prince of Quality

An article in recognition of the life and work of quality educator and quality technology leader, Ellis Ott (1906–1981).

George Box: Some Reminiscences

In a short essay honoring George Box, the author tells of his personal experiences which began when he was one of Box’s graduate students in 1953. Box returned to England to work at Imperial Chemical Industries before returning to Princeton to head up t..