Statistical process monitoring in the 21st century

Introduction: The term "statistical process control" (SPC) refers to a loosely defined collection of techniques for monitoring a process so as to prevent deterioration and facilitate improvement. These techniques are used for monitoring a process (Box and Kramer, 1992), so the phrase "process monitoring" seems more appropriate than "process control" and I have used the former in the title. However, this is just a matter of terminology: SPC techniques always were about monitoring rather than control, and as the use of the word control causes problems - as we will see below - it is sensible to replace it with a more accurate term. I will use the term SPC/M in this paper. The most prominent of these techniques, and the traditional focus of SPC/M, is the Shewhart control chart, named after its originator, Walter Shewhart. There are different types of Shewhart chart: the most widely used are charts for the mean (X-bar) and range (R), proportion defective (p), and number of defects (c). In each case, a graph of the appropriate statistic (mean, range, etc) of successive samples is plotted, and "control lines" superimposed to indicate points which are "out of control". These indicate "special" or "assignable" causes of variation which should be investigated and, if appropriate, action taken to adjust the process. There are also a number of more sophisticated control charting methods (although, according to Gunter, 1998, these are "rarely used"). These include multivariate methods for monitoring several related variables simultaneously (Montgomery, 1996), methods for monitoring a single measurement (as opposed to one based on a sample) such as moving average charts and exponentially weighted moving average (EWMA) charts (see, for example, Montgomery, 1996), and cumulative sum (cusum) methods which are more sensitive than Shewhart charts for detecting small but consistent changes in the level of the measurement (Hawkins and Olwell, 1998). In addition to control charts, the conventional SPC/M package incorporates ways of establishing the capability of a process (Rodriguez, 1992) - the most commonly used index here being cpk - and a number of more elementary methods for solving problems and improving quality. For example, Montgomery (1996, p. 130) lists the "magnificent seven": histogram or stem-and-leaf-display, check sheet, Pareto chart, cause and effect diagram, defect concentration diagram, scatter diagram, as well as the control chart. These methods, their implementation, and the concepts and philosophy underlying them, are covered in the many texts on SPC/M and related areas: eg Oakland (1999), Woodall and Adams (1998), Montgomery (1996), Bissell (1994), Mitra (1993). Woodall and Montgomery (1999) provide a helpful recent review of current issues and research in the area. The purpose of this chapter is not to provide a summary of SPC/M and how to implement it. There are many excellent texts - such as those mentioned above - to which readers can refer for the technical and organizational details of the procedures, and an analysis of their potential benefits. Instead, this chapter aims to provide a critique of SPC/M, and some suggestions about how it needs to be adapted to the twenty first century. I am assuming that the reader has some familiarity with the main SPC/M techniques - although not necessarily with the details of formulae or the more advanced methods. The value of SPC/M has been widely recognised over the last half century. According to Stoumbous et al (2000)control charts are among the most important and widely used tools in statistics. Their applications have now moved far beyond manufacturing into engineering, environmental science, biology, genetics, epidemiology, medicine, finance, and even law enforcement and athletics. However, there is little recent, empirical evidence of widespread benefits from SPC/M in business, and, indeed, a few suggestions that all is not well. For example Gunter (1998, p. 117) suggests that "it is time to move beyond these now archaic and simplistic tools [control charts]" and complains that We have become a shockingly ingrown community of mathematical specialists with little interest in the practical applications that give real science and engineering their vitality. Woodall and Montgomery (1999) suggest that the problem is that "in much of academia, the rewards are for publications, not usefulness" (p. 18). In the world of real applications, on the other hand: Many, if not most of the users of control charts have had little training in statistics. Thus, there is a reluctance to introduce more complex topics, such as the study of autocorrelation, into training materials. (p. 17) The result of this situation is, as might be expected, disappointing. Dale and Shaw (1991, p. 40), on the basis of research in the late eighties, concluded that the findings of this piece of research must bring into question the effectiveness of the current methods of educating company managements on the use of SPC/M. The time, resources, and cost committed to SPC/M by organizations has been considerable and if a cost benefit analysis were to be performed it would be unfavourable. Hoerl and Palm (1992) also comment on the "limited success" of many efforts to use Shewhart charts in industry, which, they say, is typically due to using the wrong formula, a poorly chosen sampling plan, or that the "improvement work demanded by the charts is so radical in the context of the organization's culture that the organization is unable to properly respond" (p.269). This chapter explores issues such as these. It starts with a discussion of the purpose and potential benefits of SPC/M. However, as we have seen, this is not the whole story; there are difficulties in practice. The section after gives a brief case study, based on a small manufacturing company, which illustrates many of the difficulties of trying to implement traditional SPC/M techniques, as well as some of the benefits. This leads on to a systematic discussion of these difficulties and how they might be resolved.