The 100th anniversary of the control chart

This spring marks the 100th anniversary of the control chart. In May 1924, Walter A. Shewhart wrote a short technical memorandum for his supervisor at Bell Telephone Laboratories, George Edwards. This document contained a diagram of a control chart. He explained how this control chart could identify assignable causes of variability. By identifying and eliminating these assignable causes, manufacturers could reduce the variability that arose from ongoing arbitrary adjustments to the process that were reactions to non-conforming units being produced. This could reduce the overall variability in the output and significantly improve product quality.

This memo came at an important time. Western Electric, the manufacturing arm of the Bell System, was producing telecommunications equipment that would form the backbone of the telephone system in the US. This equipment needed to be as defect-free and reliable as possible, or this enormous business venture could fail. Western Electric successfully adopted Shewhart control charts and the accompanying theory of chance and assignable causes. Shewhart continued to work at Bell Labs until he retired in 1956. He continued to publish technical papers in the Bell System Technical Journal. He authored two books that described his theories in detail: The Economic Control of Quality of Manufactured Product (Van Nostrand 1931) and Statistical Methods from the Viewpoint of Quality Control (US Department of Agriculture Graduate School 1939). Both books are considered classics.

With the start of World War II, the US Department of War (as the US Department of Defense was known then) recognized that the huge manufacturing potential of US industry would be instrumental in winning the war. However, it was going to be necessary to convert many of these organizations from producing consumer goods to military products for wartime use. This was further complicated by the depression, which, while winding down at the start of the war, had left many manufacturing organizations operating at less than full capacity and with significant problems with productivity and the quality of the items they produced. The War Department recognized that rapidly and efficiently converting industry to wartime production of high-quality and reliable products was essential. Because they were familiar with the successful implementation of Shewhart’s methods at Western Electric, the War Department recommended and later mandated the use of these methods in wartime production. They also conducted training courses in statistical quality control techniques for wartime industry. This resulted in spreading the control chart and Shewhart’s theories to a wider audience of industries.

The American Society for Quality Control was formed in 1946. They began publishing the journal Industrial Quality Control shortly afterward. Many of the early volumes of this journal featured articles describing the successful wartime implementation of statistical quality control techniques. This journal ceased publication when the Journal of Quality Technology, and the monthly magazine Quality Progress, were founded in 1968.

One of the most successful and well-known stories of a consumer products company shifting to wartime manufacturing is Ford Motor Company and the production of the B-24 Liberator bomber at their Willow Run factory. Working two 9-h shifts daily, Ford manufactured almost 7,000 B-24 bombers and produced nearly 1,900 kits for other aircraft companies to assemble. This is about half of the total B-24 production during the war. One of the classic aircraft of the era, the B-24 was in service with US Army Air Force Units in every theater. They were used as Pathfinders for the 8^th Air Force operating out of England, and specially equipped versions flew in antisubmarine warfare missions over the Atlantic Ocean during the Battle of the Atlantic. The B-29 Superfortress ultimately replaced this classic airplane.

The classic Western Electric Quality Control Handbook was published in 1956. This book summarized all the knowledge and experience gained at Western Electric about the practical implementation of Shewhart’s methods. The four Western Electric Zone Rules for interpreting control charts were explained and illustrated. There also was an extensive and very helpful presentation on the interpretation of patterns such as cycles and stratification on control charts. Later, Nelson (1984) added several more rules to the original four, which are now often collectively referred to as the “Nelson Rules.” Champ and Woodall (1987) studied the performance of the Shewhart control chart in conjunction with the original Zone Rules. They found that the use of the rules did improve the capability of the control chart to detect small shifts in the process mean but at the expense of a huge increase in the false alarm rate.

Nominally, a Shewhart control chart with the standard 3-sigma limits has an in-control average run length of about 370 samples. So, a false alarm is relatively rare. Champ and Woodall reported that the addition of the 4 original Zone Rules reduced the in-control average run length to about 90 samples. Shewhart had chosen the 3-sigma limits based on his practical experiences at Western Electric. Limits that are narrower than 3-sigma result in more false alarms. Operating personnel were discouraged by too many false alarms, which often resulted in process shutdown and wasted effort searching for assignable causes. Consequently, if there were too many false alarms, operators would begin to ignore the control chart, assuming that an out-of-control system was just another false alarm.

The years following World War II saw many new developments in control chart methodology and the field of statistical process control that were catalyzed by Shewhart’s methods. Hotelling (1947) introduced the multivariate analog of the Shewhart $\overline{X}$ control chart, the T² control chart. The two papers by Jackson (1956, 1959) were also very influential in the adoption of these techniques. Cumulative sum (CUSUM) control charts were introduced by Page (1961), and the exponentially weighted moving average (EWMA) control chart was introduced by Roberts (2000). Both charts have superior capability to detect small shifts compared to the standard Shewhart chart, and they maintain the desirable property of a low false alarm rate, so adding the sensitizing rules mentioned above is not necessary. Multivariate versions of the CUSUM were proposed by Crosier (1988) and Pignatiello and Runger (1990). The book on CUSUMs by Hawkins and Olwell (1998) is highly recommended. Lowry et al. (1992) introduced the multivariate EWMA control chart. Other useful developments include control charts for profile monitoring (see Woodall 2007; Woodall et al. 2004) and modifications of control charts to deal effectively with autocorrelated process data which occurs frequently in the chemical and process industries (Montgomery and Mastrangelo 1991).

Duncan (1956) introduced economic considerations into the design of control charts (choosing the sample size, sampling frequency, and out-of-control criteria to minimize an overall cost function). This spurred a lot of research in the area, the founding of the journal Economic Quality Control, and a review paper on the topic published in this journal (Montgomery 1980). There is very little evidence that these methods were ever formally incorporated into the design of control charts used in practice, but thinking about the costs of sampling, testing, the costs of producing defective items, the costs of false alarms, and Type II errors had some impact on how control chart design decision were made. Saniga (1989) showed how statistical considerations and process economics could be combined to design control charts.

There have been many applications of statistical process monitoring techniques including control charts beyond traditional manufacturing processes. Some examples include risk-adjusted control charts for monitoring surgical and other errors in hospitals. Grigg and Farewell (2004) is a good review paper on this topic. Levey and Jennings (1950) describe how control charts can be used in clinical laboratory settings. Woodall (2006) and Fricker (2013) write about how control charts and other related methods can be used in healthcare monitoring and biosurveillance. Control charts can be used for monitoring errors in software discovered during routine performance testing (Gardiner and Montgomery 1987) and monitoring social networks (Woodall et al. 2017) The paper by Woodall (2000) on some of the apparent contradictions and controversies in statistical process control is good contemporary reading. Montgomery, Jennings, and Kulahci (2015) describe and illustrate how forecast errors from time series models can be analyzed and evaluated with control charts. Jones-Farmer, Ezell, and Hazen (2014) show how the quality of data used in data science applications can be enhanced through the use of control charts. The paper by Woodall and Montgomery (2014) describes some trends and possible future directions of this field, which while celebrating its 100^th birthday, shows no lack of opportunity for application in many diverse fields.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Douglas C. Montgomery

Douglas C. Montgomery is Regents’ Professor and ASU Foundation Professor of Engineering. He is an Honorary Member of ASQ.