THE PHILOSOPHY OF SHEWHART'S THEORY OF PREDICTION

THE PHILOSOPHY OF <= /o:p>

SHEWHART'S<= /span> THEORY OF PREDICTION

Dr Mark Wilcox

Centre for Business Performance; Cranfield School of Management, Cranfield University, Cranfield, United Kingdom. MK430AL

email:mark.wilcox@cranfi= eld.ac.uk

(Note : This paper is a modified version of the author&= #8217;s presentation to the Proceedin= gs of the 9th Research Seminar: Deming Scholar's Program, Fordham University, New York, February, 2003.)

Abstract:

Shewhart's control charts are a fe= ature of statistical process control and linked to systems thinking. A system is a set of interconnected parts (processes) with a common purpose.&n= bsp; A systemic view of the universe suggests that nothing ever 'is' (e.g. substance or static), but always in a state of 'becoming' (e.g. in flux). In this paper I show how control c= harts are a semiotic device illustrating 'being,' 'becoming' and 'prediction'. Articulating his work, Shewhart developed a discourse of = flux as a means of describing the universe in motion.

Introduction

Shewhart's invention of the control chart in 1924 has been hailed as one of the greatest contributions to the philosophy of science (Deming:1986= ). For many it is a technique for plo= tting data derived from a process, service or product. Perhaps through complacency, we ac= cept its shape and form without question, choosing the various types of charts to suit our purpose. Because the majority of users of the charts, over the last 70 years or so, have been engineers, statisticians and mathematicians, it comes as no surprise that t= hey have seen it as a statistician's technique.

However, we also know that Shewhart read widely, and was greatly influenced by more than one philosopher. Now, well etched in the minds of t= he students of Shewhart's and Deming's work is tha= t they were both greatly influenced by the pragmatist philosopher and Harvard Professor; C.I. Lewis. It is equally well documented how Shewhart read Lewis' theory of knowledge 14 times, while Deming only read it 7 times (c.f. Blankenship and Petersen:1999; Mauléon and Bergman= :2002; Wilcox:2002). This empirical data is open to interpretation! Nevertheless,= the intriguing conundrum is that apparently, Shewhart did not read Lewis (1929) until after his major work was published in 1931 (or = at least, it was not referenced in his 1931 book). So, we are left with a search for = the root of Shewhart's ideas in order to understand= how he developed the control chart and his theory of prediction.

It would appear that Shewhart used Lewis= ' work as post-hoc rationalisation, because he is freq= uently referenced in the 1939 book of edited lectures (Wilcox= :2002). While, we can see certain influences from Lewis' work in the 1939 bo= ok, we have still to ascertain how he got where he did in 1931. Fortunately, = Shewhart was an excellent scholar and documented his sources in great detail. The extended (1931) bibliography is testimony to the research undertaken in developing his ideas. From this we can reliably trace the source of some of his ideas. =

The aim of this paper is to try to uncover some of the theories, ide= as and sources of information that helped Shewhart develop his theory of prediction and the control chart. While not wishing to shun the infl= uence of statistical theory, this paper will focus mainly on the philosophy of science and theory of knowledge. I will argue, that to fully understand Shewhart's work we have to have more than a grasp of = the philosophies that underpin his theories of prediction. I will try to show how Shewhart's work makes a unique contribution to the metaphysics of flux and substance (being and becoming).

Tracing the debates on flux and substance back to the pre-Socratic philosophers, I will describe how this concept was developed over the last = 2500 years. An important feature o= f this debate is the distinction between 'being' and 'becoming'. Being is the static state of what = 'is' (e.g. substance), and becoming is the state of 'flux' (e.g. process). Beginning with the now, well hackn= eyed problem, that Heracleitus had in = crossing the same river twice, I will try to show the relevance of these philosophical concepts to Shewhart's work. Time and space will not allow a fu= ll coverage of the history of this debate, so I will move quickly on to the wo= rk referenced by Shewhart in his 1931 and 1939 books.

I will show how the shape and structure of the control chart is an attempt to capture the 'being and becoming' of a process within a system. The two sides of a control chart, = are the scalar and the vector, which, when juxtaposed, provide a means to captu= re the here and now, while simultaneously representing times' arrow (Eddington:1929). Here, some of the well known, and = less well known scholars who influenced Shewhart, wi= ll be uncovered. While most people = are aware of Fisher's statistical theory, and Keynes' treatise on probability, = one rarely finds reference to the more peripheral authors in Shewhart's work. For instance, the data = point (the actual dot) on the control chart is underpinned by the theory of signs (semiotics) (Morris:1938) and "location of events" and being and becoming, past, present and future in (Eddington:1929). The design layout of the chart was= also subject to detailed consideration using the leading writer on this topic (<= span class=3DSpellE>Dwiggins:1928/48). These quite interesting facts, may come as a surprise, till one considers the = task that Shewhart had undertaken, which was to try = to make statistical theory and practice accessible to engineers and scientists. In the light of t= his, we can see how effective the control chart was, both, as a statistical technique, and means of communication.

In conclusion, I will show how Shewhart's invention of the control chart is a multi-faceted concept and a major feat = of social construction, aiming to tackle the age-old problem of understanding = the universe when it is in a state of flux.&nb= sp; To help articulate his ideas, Shewhart (= 1939) distinguished scientific and emotive language (pp,84,85). I have called his style of writing a discourse of flux, weavi= ng a thesis out of engineering, physics, mathematical and philosophical texts. Shewhart was painfully aware of the consequences of using emotive language in the compan= y of engineers and scientists, warning his readers to tread carefully.

The roots of Shewhart'= s ideas.

Here, I define and deconstruct the ideas behind Shewhart's theories while using the debate on being and becoming as a focal theory. Whitehead (192= 9) states that there are two main metaphysical debates, one on substance, the other, on flux. This d= ebate is often referred to as "being and becoming". My aim is to show that Shewhart's work addressed this debate in a unique fas= hion, with his invention of the control chart, and unknown chance and assignable cause systems of variation.

We do not have to search far in Shewhart's work before we get to the heart of the problem. Opening up his 1931 book, he quote= s Pope saying " 'All chance is but action thou canst not = see', and we looked forward to the time when we would not see that direction. In other words, emphasis was place= d on the exactness of physical laws.&nbs= p; Today however the emphasis is placed elsewhere… 'Today the mathematical physicist seems more and more inclined to the opinion that eac= h of the so-called laws of nature is essentially statistical, and that all our equations and theories can do, is to provide us with a series of orbits of varying probabilities' " (Shewhart,1931:4-= 5).

At the time of writing, statistical methods were in their infancy, having been developed in the natural sciences. At the beginning of the 1939 book = he made the distinction more clear: "..whereas the concept of mass produ= ction of 1787 was born out of an exact science, the concept underlying the control chart technique of 1924 was born out of a probable science" (p4). Engineers were focusing on making = “exact” interchangeable parts, which were a feature of the early stages of mass-production which relied on inspection and detection to manage quality.=

Shewhart accepts the logical pri= nciple that: "It is conceivable that some time man will have a knowledge of a= ll the laws of nature so that he can predict the future quality of product with absolute certainty" (Shewhart, 1931:353).<= span style=3D'mso-spacerun:yes'> However, he was very good at teasi= ng his readers, and we have to read on, to find that this "is not merely a long way off but impossible" (op-cit). Indeed, we should also note th= at natural laws are subject to variation, and knowledge of all things in the past, is a logical impossibility.

My interpretation of this argument is that the engineers and scienti= sts were following a view of the universe based on a Parme= dian principle, that the world is one united whole, and knowable. Parmenides was one of the main exp= onents of the notion of 'being'. His argument was, that there was 'One Real Being'.

"He had declared that the whole of reality is a One Being or Existent Unity, having only such attributes as can be rigidly deduced from = the conceptions of Being and Unity. Each conception is taken with the utmost strictness. 'Being' implies complete reality; = 'Unity' excludes any plurality. There= is nothing but this One Real Thing" (Cornford's editorial commentary in Plato,1935= :220).

Lewis referred to Parmenides while criticising<= /span> the dogmatism of contemporary metaphysicians "…I am reluctant to= lay hands on that idealism which has played the role of Father Parmenides to all the present generation of philosophers" (Lewis,1929:9). Lewis had no time for dogma and loathed the sophistry of some of the metaphysical doctrines, that belittled common se= nse and experience. We shall see = the relevance of this point in due course, but first we must return to Shewhart's work.&nbs= p;

Shewhart's research project was to develop a more economic control of quality. He had to define the problem to his audience of engineers and scientists, which he did partly in the passage ab= ove. The nature of that part of the problem was that the engineers and scientist= s of the 18^th and 19^th century had adopted a flawed and unachievable strategy, in believing that they could know all the laws of na= ture.

With the advent of statistical theory in the natural sciences, a new epoch dawned. Shewhart, and others in the 1920s, started to apply statistical and probability theor= ies to mass production. But with = this approach, came a new set of problems. The epoch represented a relatively new way of thinking and was a paradigm shift in the extreme. To fully understand this shift, Shewhart read wide= ly, including many of the great philosophers of his time. He had to understand the consequen= ces of viewing the universe as non-static and in a state of flux. Hence, he was drawn to the philoso= phers of science for help and guidance.

Shewhart and becoming=

Shewhart tried to explain how th= ere was variation in everything, which was a fundamentally different way of vie= wing the universe than the exact sciences had been doing. If there is variation in everythin= g, then …

"It follows, therefore, since we are thus willing to accept as axiomatic that we cannot do what we want to do and cannot hope to understand why we cannot, that we must also accept as axiomatic that a controlled qual= ity will not be a constant quality. Instead, a controlled quality must be a variable quality. This is the fi= rst characteristic" (Shewhart, 1931:6).=

This passage is an example of what I have called a discourse of f= lux which Shewhart developed in his work. A discourse of flux, is, as the na= me suggests, a way of communicating, consistent with the view of the world whe= re everything is in motion. This requires a special skill, for it is easy to lay a philosophical trap or par= adox with the careless use of words. I am suggesting that Shewhart was particularly effective at this style of writing, and we shall see more examples of the <= i>discourse of flux in this paper.

We should not underestimate the profound nature of content of the passage above, particularly when we consider that he was writing for an engineering audience, steeped in the practice of mass-production. While statistical theory was relat= ively new, the ideas of variation, flux and becoming had been around for 2500 yea= rs or more. These debates are at= the root of metaphysical and epistemological arguments going back to the pre-So= cratic philosophers.

Perhaps, one of the more enduring claims about the Universe was made= by Heracleitus 5^th Century BC, who suggested everything was in a state of flux or motion, as opposed to being static. Th= is debate has often been referred to as "being and becoming", with t= he proponents of flux in adopting the "becoming" argument. Heracleitus was probably the founder of the thesis of flux, in which he famously argued that, you cannot stand in the same river twice. One of his followers, Cratylus, took an extreme perspective and argued that= you cannot stand in the same river once, because both you and the river are constantly changing. Taking <= span class=3DSpellE>Heracleitus' work to the extreme,= can result in 'scepticism', where knowledge of = any kind becomes unlikely, and one is driven into a solipsist argument. So, for instance, the meaning of w= ords and concepts would be constantly changing, and a statement cannot remain tr= ue, or even the same statement (Plato, 1935:95-106).

Shewhart's control and prediction theory

While the theory of flux is quite seductive, with its emphasis on motion, it clearly brings its own problems, which Shew= hart had to address if he was going to use this concept to control quality. Quite adept at making a solid case= , Shewhart argued that there was variation in everythin= g, even the exact sciences. Here,= he demonstrated the semantic skills of a philosopher, while carefully construc= ting his thesis.

" a phenomenon will be said= to be in control when, through the use of past experience, we can predict, at lea= st within limits, how the phenomenon may be expected to vary in the future. Here it is understood that the prediction within limits means that we can state, at least approximately, t= he probability that the observed phenomenon will fall within given limits…" (Shewhart, 1931:6) (emphasis in original).

From this we can see how being able to predict is inextricably linke= d to control. Control reflects the present, or here and now, while prediction is what may happen in the future= . It is surprising how the emphasis = on prediction in Shewhart's work appeared to get l= ost in the passage of time. Only quite recently, has it reappeared in the literatu= re (c.f. Mauléon and Bergman: 2002; Wilcox:2002). Here, we see = Shewhart outlining a unique thesis, whereby engineers and scientists would be able to predict, product quality. His theory has many components whi= ch space will not allow a full exposition.&nb= sp; However, he lays down some rules, as in the following example.

"In fact a prediction of the type illustrated by forecasting the time of the eclipse of the sun is almost the exception rather than the rule= in scientific and industrial work.

In all forms of prediction an element of chance enters. The specific problem which concern= s us at the present moment is the formulation of a scientific basis for predicti= on, taking into account the element of chance, where for the purpose of our discussion, any unknown cause of a phenomenon will be termed a chance cause"(Shewhart,1931:7) (emphasis in original).

Shewhart's unknown ca= uses

The notion of an unknown cause is intriguing and we have to treat th= is cautiously. We can perhaps se= e the influence of Professor A.S. Eddington on this concept. In his Giffo= rd Lectures, Eddington (1928) talked about:

"Something unk= nown is doing something we don't know what- t= hat is the what our theory amounts to. It does not sound a = a particularly illuminating theory. I have read something like it elsewhere- The Sl= ithy toves. Did gyre and gimble in the wade (taken f= rom Jabberwocky). There is some suggestion of activity. There= is the same indefiniteness as to the nature of the activity and of what it is = that is acting. And yet from so unpromising a beginning we really do get somewhe= re. We bring into order a host of appa= rently unrelated phenomena; we make predictions, and our predictions come off. The reason - the sole reason- for = this progress is that our description is not limited to unknown agents executing unknown activities, but numbers are scattered freely in the descript= ion. … By admitting a few nu= mbers even 'Jabberwocky' may become scientific.&= nbsp; We can now venture on a prediction; if one of its toves escapes, oxygen will be masquerading in a garb properly belonging to nitrogen. In the stars and ne= bulae we do find such wolves in sheep's clothing which might otherwise have start= led us. It would not be a bad rem= inder to of the essential unknowness of the fundament= al entities of physics to translate it into "Jabberwocky"; provide all numbers - all metrical attributes - are unchanged, it does not suffer in the least. Out of the numbers pro= ceeds the that harmony of natural law which is the aim of sc= ience to disclose. We can grasp the= tune but not the player. Trinculo might have been referring to modern physics in the words, 'This is the tune of o= ur catch, played by the picture of nobody" (p.291-292).

A similarity between Eddington's and Shewhart's ideas appears quite transparent, as he articulated the problems of the unknown, and what may be described as chance and assignable causes. Also explicit are the notions of control and prediction. Clearly implicit, is that although= he accepted the theory of flux, he needed to develop a notion of control and prediction over the 'things' in flux. His novel idea of a chance cause, was his= first attempt to socially construct a discourse of flux, while avoiding the traps= of a static or exact discourse. = The idea that the variation in a 'thing' is caused by a chance cause is qualifi= ed by the assertion that the cause is 'unknown'. For 2,500 years philosophers have grappled with the concept of being and becoming, producing numerous explanations of how we make sense of the here and now, to avoid charges of solipsism, yet avoiding the equally flawed charge of knowing everything. The notion of variation and chance= and assignable causes, was Shewhart's attempt to ad= dress this problem.

Shewhart appeared to take some <= span class=3DGramE>advise from Eddington in h= is use of the Law of Large Numbers with which he provided four examples to show how the theory worked. From these examples he qualified his theory of unknown systems of chance causes to: Controlled or constant system of chance causes, which are of course variable in nature= (see Shewhart, 1931:Chapter X). He was then able to formu= late his ideas around the task of quality control and prediction with more certainty.

However, we find that prediction is a problematic concept, and one t= hat may get confused with other methodologies from forecasting for example. So, having defined his notion of a chance cause, he had to develop a scientific basis for control and predicti= on. Here he made a distinction between predicting the future price of stock in = 30 years time, and the result of tossing a coin 100 times, in 30 years time. Clearly, we would not bet on stock-market prices in 30 years time, for that type of prediction would be unreliable.&nb= sp; However, tossing a coin and predicting the result of a similar proce= ss, is quite plausible within the limits of probability. This example shows that not = all chance cause systems are the same, which lead hi= m to develop the first of three postulates for his thesis.

"Postulate 1- All chance systems of causes are not alike in the sense that they enable us to predict the future in terms of the past. Hence, if w= e are able to predict the quality of product even within limits, we must find some criterion to apply to observed variability in quality to determine whether = or not the cause system producing it is such as to make future predictions possible…

Postulate 2- Constant systems of chance causes do exist in nature. To say that such systems= exist in nature is one thing; to say that such systems exist in a production proc= ess is quite another thing. Today= we have abundant evidence of such systems of causes in the production of telep= hone equipment.

Postulate 3- Assignable causes of variation may be found and eliminated .<= /span> Hence to secure control, the manufacturer must seek to find and eliminate assignable causes. In practice however, he has the difficulty of judging from an observed set of data whether or not assignable causes are present… What we need is some yardstick to detect in such variations any evidence of the presence of assignable causes. Can we find such a yardstick? Experience of the kind soon to be considered indicates we can. = It leads us to conclude that it is feasible to establish criteria useful in detecting the presence of assignable causes of variation or, in other words, criteria which when applied to a set of observed values will indicate wheth= er or not it is reasonable to believe that the causes of variability should be left to chance." (ibid.:8,12,= 14)

Control limits, assignable causes and pragmatism

At this point in his thesis, he developed the concept of control lim= its to distinguish chance and assignable cause systems. Here we see how a table of data is re-presented on three control charts. Now with the use of control limits, the assignable causes could be f= ound and removed.

"Upon the basis of Postulate 3, it follows that we can find and remove causes of variability until the remaining system of causes is consta= nt or until we reach that state where the probability that the deviations in quality remain constant" And then on the final chart= he wrote the title: "Judgement Plus Modern Statistical Machinery Makes Possible The Establishment of Such Limits"= (ibid.:17).

The more observant, will have noticed the word 'judgement' in the passage above. The rea= son for this soon becomes apparent. For then, he argued that mathematical statistics did not give the desired criterion.

"What does this situation mean in plain English? Simply this: such criteria, if they exist, cann= ot be shown to exist by any theorizing alone, no matter how well equipped the theorist is in respect to probability or statistical theory. We see in this situation the long = recognised dividing line between theory and practice… the fact that= the criterion we happen to use has a fine ancestry of highbrow statistical theo= rems does not justify its use. Such justifications must come from empirical evidence that it works. As the practical engineer might sa= y, the proof of the pudding is in the eating" (ibid.:18)

This pragmatic use of theory and the role of mind in the process was clearly following Lewis’ ideas. Shewhart drove home the distinction between pure and applied statistics on several occasio= ns, on the basis that engineers or scientists had to make 'decisions' with 'rea= l' consequences, unlike those confined to the laboratory. Shewhart used trial and error to remove the causes till… "We assumed, therefor= e, upon the basis of the this test, that it was not feasible for research to go much further in eliminating causes of variability" (ibid.:21).

In 1939 he had included the notion of belief to his work. "The fact that we must depend= upon a human individual to choose successfully from his experience those conditi= ons that he believes will lead to valid conclusions through the use of probabil= ity theory indicates what appears to be a necessary human act of rational belie= ving and this act is always an attempt to relate past evidence E with a prediction P" (p.42).

So while statistical theory played a part, it was the role of human = judgment that determined the final limits on the chart. The significance of this research in terms of the philosophy of science should not be underestimated. Shewhart attempted to take the theory of flux and construct a discourse and method of illustration that would make it possible to understand and interpret flux i= n a process. Let us take a closer= look at what has now been achieved.

In this cas= e we have the number newspapers sold as the vertical axis, and the time series of daily intervals on the horizontal axis.&nb= sp; This simple juxtaposition challenges the critics of the theory of fl= ux by trying to know something, even if it is in flux. The chart illustrates the process = flux over time. It tries to illust= rate the being and becoming, where the being is in the data point, averaged out = on the mean. I will return to this later when we consider the chart as a semio= tic device.

Knowing what to measure

Shewhart's (1931) chapter on defin= ing quality ought to be a standard reference point for anyone defining quality. This chapter sets ou= t the problems of defining quality, and provides an operational definition for his research. It is also a master= -piece in the discourse of flux. We = have to consider whether the thing we are measuring 'has' an attribute called 'quality' as a form of goodness for example, or 'is' the thing a quality ob= ject per se. = Shewhart argued that the 'thing' consists of numerous quality criteria, e.g., colour, size, weight, and therefore if we change the = criteria, we change the thing. The alternative would be to perceive the thing as having an objective existence (substantive and static) upon which we confer the notion of quality. The fact that he chose this route = is quite significant, demonstrating his adherence to the metaphysics of flux.<= span style=3D'mso-spacerun:yes'>

Precise and Accurate Measurement

A data point on a chart is quite symbolic, trying to represent the h= ere and now. One on its own could be seen as a symbol of being, but when a few = are strung together, they illustrate becoming and flux. They are part of a social construc= tion of flux. Lewis (1929) used a = notion called an "instant mental reaction to experience" (p.358) constit= uting an 'island of knowledge'. Lew= is, like many others was attempting to avoid the solipsist traps and charges of= scepticism. Not surprisingly, we find that Shewhart took the measurement process very seriously.= He needed a precise and accurate m= ethod of measuring the 'things' in question.&nbs= p; Being quite pedantic on this point - he drew on the work of Goodwin (1908). Goodwin defined accurate, as meaning the methods of measuring, and precision, meaning reproducible in similar circumstances.&nbs= p; Leaving no stone unturned, Shewhart enga= ged with the theory of errors, thus demonstrating more variation for the discou= rse of flux. For the purpose of t= his paper, we only need to note whether the data was gained by methods in statistical control (e.g. accurate and precise) or not. If the data collection procedures<= /span> are in control then we m= ay place confidence in the prediction to be made from the data. The converse of this also applies.=

Shewhart's diagram for a data coll= ection procedure was quite simple, but equally poignant.

H¹ = C¹

(Shewhart,1939:89)

Here X =3D the values of the measurements; H. =3D the observer; and C.=3D the text describing t= he initial conditions. In essenc= e, this process occurs at every time data is collected. If either H. or C. = changes, then this should be noted as it may be cause of the measurement process goi= ng out of control. This diagram reappeared later, where it was shown as a series of measurements leading up= to the process of prediction. We should therefore think of this as the process behind each data point on a chart.

Prediction

We now have the means to gather data, which leads to Shewhart's theory of knowledge, and the basis for prediction. Lewis' influence on Shewhart's work becomes more transparent and we will soon see the pragmatism appearing= in the process of prediction. In essence this process may take place each time data is collected and present= ed on the chart.

<= span style=3D'mso-ignore:vglayout;position:absolute;z-index:2;left:0px;margin-le= ft: 174px;margin-top:5px;width:98px;height:2px'> Original data as evidence E = &nb= sp; = Prediction <= i>P

= &nb= sp; = &nb= sp; Degree of belief pb

        =             &nb= sp;            =           in prediction= P based on evidence E

(Shewhart, 1939:86) Figure 11

Using this model, we start at the left hand corner with original data. Sh= ewhart described various methods for predicting, based on best estimates, probabil= ity and Student range-type P¹ for example= . However, we also have to apply the= ories to interpret the data. Some o= f the theories will come from the laws outlined above. The concomitance of data a= nd theory lead to an interpretation using human judgement= .

While we acknowledge the influence of statistical = and probability theory, we should also be aware of the influence of the philoso= phy of science on Shewhart's work. Take the following lament:

"In general the problem of estimation presents the universal di= fficulties involved in all induction. If= one reads such a book as A Treatise on Probability , J.M.Ke= ynes, … he may feel at first very discouraged, because his attention will h= ave been directed to many of the serious difficulties involved in the applicati= on of probability theory. A usef= ul tonic in such a case is to read any one or more of the following books: The Nature of the Physical Worl= d, Eddington (1928) … The Logic of Modern Physi= cs Bridgman (1928),… The Analysis of Matter Rus= sell (1927) … At least these three books should provide a tonic, if it is true that misery loves company. Cer= tainly the serious difficulties involved in the interpretation of physical phenome= na are common to all fields, and the discussion in these books show how much we must rely upon the application of probability theory even in the 'exact' science (Shewhart, 1931:481) (underlining added= ).

Historically, induction carries its own problems, and these were inherent in the various doctrines of flux.= However, we shall have to leave the detail for another paper, and re= turn to Eddington's work. For instance his notion of 'Locati= on of Events' was developed around the past, present and future, showing how we m= ay locate ourselves in the flow of time, with the here and now. He described how the grand theorie= s of the universe were shaken in the 17^th century when the notion of 'Now' was perceived as 'the instantaneous state of the world' at that momen= t in time. This concept was dismis= sed by the astronomer Roemer who demonstrated that 'Now', cannot be an instant in = the global sense, because of the time, light, took to travel. "That was really= a blow to whole system of world wide instants, which were specially invented = to accommodate these events" (Eddington, 1928= :42,43).

Eddington developed some useful concepts on becoming, entropy and a new epistemology. In concluding the chapter on his epistemology, we find an amusing, but thought provoking paragraph, that may have caught Shewhart's attentio= n.

"It is only through a quantum action that the outside world can interact with ourselves and knowledge of it can = reach our minds. A quantum action m= ay be the means of revealing to us some fact about Nature, but simultaneously a f= resh unknown is implanted in the womb of Time.&= nbsp; An addition to knowledge is won at the expense of an addition to ignorance. It is hard to empty the well of Truth with a leaky bucket" (= Eddington,1928:229).

So we may return to Shewhart's work, and= how the process of interpretation required knowledge of the present. Equally, every interpretation invo= lved a prediction.   So, the sum= of knowledge is a 'leaky bucket', varying by the minute.

"Nonstatic char= acter of knowledge….we are forced to consider knowledge as something th= at changes as new evidence is approved by more data, or as soon as new predict= ions are made from the same data by new theories. Knowledge in this sense is somewha= t of a continuing process, or method, and differs fundamentally in this respect fr= om what it would be if it were possible to attain certainty in the making of predictions" (Shewhart, 1939: 104). <= /o:p>

We should also note how theories and laws were judged on their pract= ical value to interpret the present. They were also subject to variation as new data and interpretations either modified, or rendered them false.&n= bsp;

Past, Present and Future

To reinforce this argument, we are drawn to a quotation from Lewis (1934) "…knowing begins and ends in experience; but it does not = end in the experience in which it begins" (Quoted in Shewhart,1939:80). Shewhart was clearly fascinated with this riddle which he adopted in several ways to help form his ideas. Here we see h= is attempt to illustrate the riddle in a simple diagram. If we relate this to figure 11 abo= ve, we can imagine that this process occurs to the left of the centre, at the present. To see the full bene= fit of these two figures working together, we should think of the one below as mov= ing with time, with figure 11 acting as a wheel rotating on the present as time= 's arrow progresses forward. Data-interpretation (knowledge) - prediction - belief in prediction - ad infinitum. And so we see = Shewhart's epistemological techniques illustrating the notion of flux.

Previously observed   = ;        Practically verifiable=             O= nly theoretically verifiable   &= nbsp;

X^1,X²…X¹= ,…Xⁿ^&nb=
sp;Xⁿ⁺¹, Xⁿ⁺²= …X^n+fX^n+f+1, X^n+f+2…     = =

Past     &n= bsp;         =             &nb= sp;            =             &nb= sp;            =             &nb= sp;            =        Future     =             &nb= sp;

        =             &nb= sp;            =    Present

      =             &nb= sp;            =             &nb= sp;            =             &nb= sp;            =             &nb= sp;            =             &nb= sp;            =

(= Shewhart, 1939:133)

With care we can locate these two diagrams with the origins of the <= span class=3DSpellE>PDSA cycle; Shewhart's wheel. This took the three co= ncepts of specification, production and inspection from the 'exact' methods of mass-production, which he then formed into a circular spiral. "The thre= e steps constitute a dynamic scientific process of acquiring knowledge" (Shewhart, 1939:45). To fully understand how this works, Shewhart explains how scientists and statisticians join forces.&= nbsp; The scientists decide on the specification (ste= p1), and then join with the statisticians (step2) to eliminate assignable causes of variation to a point where predictions can be made. The statisticians need = the scientists' help to eliminate the causes, because of their knowledge of the process (the physics). When t= he state of statistical control has been attained the statistician can proceed without the scientist, (step 3) and "set up rules that lead to the most efficient prediction" (Shewhart, 1939: 119= ).

Now consider Shewhart's discourse of flux describing how he envisaged this working in practice: "In fact an econ= omic standard of quality is not a written finality, but is a dynamic process. It is not merely= the imprisonment of the past in the form of specification (step 1), but rather the un= folding of the future as revealed in the process of production (stepII) and inspection (step III), and made available in the running quality report " (Shewhart, 1939:119) (emphases added).

This control chart has been specially constructed to represent the future as an unknown, but predictable quantity. Now we can see the past present and future unfolding. It has been= said, the control chart is the voice of the process. Metaphorically they 'tell a story'= . We can, with experience, learn to = read the data points on the chart and detect process shifts (7points above or below the mean) or tampering manifest by zig-= zagging for example. The key to understanding this is in the notion of variation. We have to be able to interpret variation, to get the full story from a control chart. However, while understanding varia= tion is important, it must not detract from the real purpose of predicting the future. Indeed, I would sugge= st that control charts rarely gets used to their full potential as a predictive technique.

A theory of signs and the importance of display.

Statisticians use symbols to depict many aspects of their work, sometimes providing an index. However, few think of the symbolism of the control chart to portray flux and substance. Shewhart referred to Morris (1938) to acknowledge the importance of the way we prese= nt information with signs and symbols.

"The process in which something functions as a sign may be call= ed semiosis. This process, in a tradition which = goes back to the Greeks, has commonly been regarded as involving three (or four) factors: that which the sign refers to, and that effect on some interpreter= in virtue of which the thing in question is a sign to that interpreter. These three components in semiosis may be called respectively, the sign vehi= cle, the designatum, <= span style=3D'mso-spacerun:yes'> and the interpretant; the interpreter ma= y be included as a fourth factor. = These terms make explicit the factors left undesignated in the common statement t= hat a sign refers to something for someone" (Morris, 1938:3). <= /span>

Morris described the psychological, sociological and pragmatic use of signs and how different disciplines used them to convey meaning. Consider the imagery of the control chart, and how it functions as a means of communication. The vertical axis stands to project the scales of the variation in the thing being measured; straight line with symbols, probably numerical. The base of this line connects to = the vector, often representing time. The two lines form the axis of the chart on which the data may be plotted. Then we have the mea= n or median, drawn parallel to the vector, representing the 'heart' of the proce= ss being measured. The mean appe= ars static and could be thought of as the substance or 'being'.   However, we know it is not s= tatic, and subject to being moved when positive or negative shifts in performance = are recorded. <= /p>

Control limits, proudly guard their 3 sig= ma boundaries. Unknown but const= ant systems of chance causes reside safely in the limits. Their destiny unfolds before them. Present, predicted future, historical data, repeated - ad infinitum. Low betide the known assignable ca= uses which appear unwittingly outside the control limits, their fate now unknown.

An (almost) insignificant datum appears on a chart. A dot, a star or a square, it matt= ers not. Yet where the dot falls, determines the fate of the process' future, while relating to its past performance. Equally, the dot represents the precise and accurate measuring process that has taken place, determining its position on the chart.&nbs= p; The dots are connected, normally with straight lines. They represent connectedness, relationships and the spatial and temporal nature of the thing being measured. But more importantl= y, they are a symbol of being, in the flux of becoming.

The control chart is a sign conveying messages from a process. The chart had to be designed, so t= hat it would convey flux, constant systems of chance causes and known assignable causes. It had to be effectiv= e for engineers and scientists to use on a daily basis. Dwiggins (1928/48), a major contributor to advertising design, provided some interes= ting ideas for effective communication. For instance he described a concept called rhythm:… "the thing that puts life into design keeps= it from being dead and mechanical. In graphic space design it may be crudely defined as a living= ratio or size relation among various parts" (p.51). So a badly designed chart may not = convey the meaning of flux and assignable causes.= The mean and the control limits can be very effective in this respec= t.

Next we should consider what he called 'unity'. If we made both axis of a time ser= ies chart the same length, this would be unity. However, this might portray the va= riation and the time in unequal doses and convey the wrong image and message. It's about what catches the eye. "What happens at this critical instant may be called the question of 'primary contact and reaction'…= .the reader's eye is caught by the spots in the first flash of perception= and is attracted or repelled, and that he then takes cogni= sance of their meaning"(ibid.:69).   So, for instance, is a chart= that shows data rising to the far right corner, good, or bad? If the data on the scalar are pres= ented in inches instead of feet, the chart may be far more dramatic in appearance. So while we accep= t the notion of the control chart as an effective semiotic device, we should also= be aware that if it is designed badly it may convey the 'wrong' message.<= /o:p>

Conclusion

The aim of this paper was to uncover some of the ideas behind Shewhart's work.&nbs= p; For many, Shewhart is a reference point = to some distant past. Shewhart's work is clearly a major academic and pract= ical thesis, which has still to achieve universal acclaim. What this paper has shown, is a collection of some of the less well known sources of material, that Shewhart us= ed to construct his thesis. I have deliberately avoided the main stream texts of Fisher and Keynes for example, and tried to focus on the philosophy of science behind his work. Indeed, it is my contention, that = to fully understand Shewhart's work, one needs to understand the notions of being and becoming and the associated arguments behind these metaphysical concepts.

What this paper has shown, is that Shewhart was a skilful writer, and he wove a very tight thesis, avoiding the paradox= es and solipsist traps, that await the less wary adventurers in this field. I have called his style of writing= a discourse of flux, providing a few of the numerous examples of this composition. = It would seem logical to focus on Shewhart's style= of writing in the teaching of his theories, for they are part and parcel of understanding the philosophical concepts behind his ideas. By combining the theories from the philosophy of science, statistical and probability theory, he broke new ground. More significantly he= made his work accessible to engineers and scientists who could use their 'judgement pragmatically' with his inventions of the c= ontrol chart and chance and assignable cause systems.

Bibliography

Blankenship, B. and Petersen, P.B., (1999) W.Edwards Deming's Mentor and Others Who= Made an Impact on His Views During the 1920s and 1930s. Journal of Management History. Vol 5,= No 8, pp 454-467. MCB University Press.

Deming, W.E., (1986) Out of The Crisis, MIT Press, Cambridge, Massachusetts.

Deming, W.E. (1991) "A Tribute to Walter A. Shewhart On the Occasion o= f the 100^th Anniversary = of His Birth" SPC INK Newsletter Winter 1991. SPC Press, Inc.=

Deming, W.E., (1993) (= 2^nd edition) The New Economics, MIT Press, Cambridge, Massachusetts.=

Dukich, T. (2002) Alfred North Whitehead's "Philosophy of Organism" as the Foundation of W.Edwards Deming's "New Philosophy". Adventure of Whitehead's Metaphysics in 21^s=
t Century Reality. Proceedings of the 8^th Annual Researc= h Seminar Fordham Universi= ty, New York. (February: 2002)

Dwiggins, W.A., (1928/48) Revised ed= ition. Layout in Advertising. Harper and Brothers. USA.

=

Eddington, A.S. (1928/9) The Nature of the Physical World. Cambridge University Press. London

Fisher, R.A. (1925/48) Statistical Methods for Resea= rch Workers. Oliv= er Boyd and Son, Edinburgh

Goodwin, H.M., (1908/1920 edition) Elements of The Precision of Measurements and Graphical Methods. McGraw-Hill Book Company, New= York.

Guthrie, W.K.C., (1971) A History of Greek Philosophy= . Volume 1: = The Earlier Presocratics and the Pythagoreans, Cambridge University Press, Cambridge

Keynes, J.M. (1921) A Treatise on Probability. Macmillan Company: New York.

Lewis, C.I., (1929/1956) Mind and The = World Order: Outline of a Theory of Knowledge.&n= bsp; Dover publications: New York.

Lowe, V. (1990)= Alfred North Whitehead, The Man and His Work, Vol II.

Mauléon, C. and Bergman, B. (2002) On the Theory of Knowledge in the Quality Movemen= t- C.I. Lewis' Contribution to Quality Pioneers. Proceedings of the 8^{th
Annual Research Seminar Fordham} Universi= ty, New York. (pp 156-164: February: 2002)

Morris, C.W., (1938) Foundations for the Theory of Signs. = Internationa= l Encyclopaedia of Unified Science. Volume 1.<= /span> Number 2. The University of Chicag= o Press, Chicago, Illinois.

Plato, (1934)( Edited by Cornford, F.M) Plato's Theory of Knowledge: The Theaetetus and the Sop= hist translated with a running commentary. Routledge &Keegan Paul, London.

Shewhart, W= .A., (1931/1980) Economic Control of Quality of Manufactured Product ASQC: Milwaukee.

Shewhart, W= .A., Deming= , W.E., (ed) (1939/1986) Statistical Method from The Viewpoint of Quality Control. Dover Publications: New York.<= /span>

Stebbing, L.S. (1930/45) A Modern Introduction to Logi= c. Methuen and Company. London.

Whitehead, A.N. (1929/60) Process and Reali= ty The MacMillan Company. New York.

Wilcox, M. (2002) Whither the Pragmatism? Proceedings of the 8^th Annual Rese= arch Seminar. Fordham University, New York (pp 258-269: February:2002)<= /span>

Wilcox, M. (2003) Prediction and Pragmatism in = Shewhart's Theory of Statistical Control Management Decisi= on (Focus on Management History) (forthcoming)

=

=

=