Information about Special Cause Variation

	Alternative name
Common cause	Chance cause Non-assignable cause Noise
Special cause	Assignable cause Signal

Common- and special-causes are the two distinct origins of variation, in a process that features in the statistical thinking and methods of Walter A. Shewhart and W. Edwards Deming. However, it can be argued that they were recognised and discussed as early as 1703 by Gottfried Leibniz and are particularly important in the thinking of economists Frank Knight, John Maynard Keynes and G. L. S. Shackle. Several alternative names have been used over the years.

Origins and concepts

In 1703, Jacob Bernoulli wrote to Gottfried Leibniz to discuss their shared interest in applying mathematics and probability to games of chance. Bernoulli speculated whether it would be possible to gather mortality data from gravestones and thereby calculate, by their existing practice, the probability of a man currently aged 20 years outliving a man aged 60 years. Leibniz replied that he doubted this was possible as:

Nature has established patterns originating in the return of events but only for the most part. New illnesses flood the human race, so that no matter how many experiments you have done on corpses, you have not thereby imposed a limit on the nature of events so that in the future they could not vary.

This captures the central idea that some variation is predictable, at least approximately in frequency. This common-cause variation is evident from the experience base. However, new, unanticipated, emergent or previously neglected phenomena (e.g. "new diseases") result in variation outside the historical experience base. Shewhart and Deming argued that such special-cause variation is fundamentally unpredictable in frequency of occurrence or in severity.

John Maynard Keynes emphasised the importance of special-cause variation when he wrote:

By “uncertain” knowledge … I do not mean merely to distinguish what is known for certain from what is only probable. The game of roulette is not subject, in this sense, to uncertainty ... The sense in which I am using the term is that in which the prospect of a European war is uncertain, or the price of copper and the rate of interest twenty years hence, or the obsolescence of a new invention … About these matters there is no scientific basis on which to form any calculable probability whatever. We simply do not know!

Definitions

Common-cause variation

Common-cause variation is characterised by:

• Phenomena constantly active within the system;
• Variation predictable probabilistically;
• Irregular variation within an historical experience base; and
• Lack of significance in individual high or low values.

The outcomes of a roulette wheel are a good example of common-cause variation. Common-cause variation is the noise within the system.

Walter A. Shewhart originally used the term chance-cause. The term common-cause was coined by Harry Alpert in 1947. Shewhart called a process that features only common-cause variation as being in statistical control. This term is deprecated by some modern statisticians who prefer the phrase stable and predictable.

Special-cause variation

Special-cause variation is characterised by:

• New, unanticipated, emergent or previously neglected phenomena within the system;
• Variation inherently unpredictable, even probabilistically;
• Variation outside the historical experience base; and
• Evidence of some inherent change in the system or our knowledge of it.

Special-cause variation always arrives as a surprise. It is the signal within a system.

Walter A. Shewhart originally used the term assignable-cause. The term special-cause was coined by W. Edwards Deming.

Popular examples

Special causes

• High healthcare demand from elderly people
• Abnormal traffic (click-fraud) on web ads^[1]
• Extremely long lab testing turnover time due to switching to a new computer system
• Operator absent^[2]
• Poor adjustment of equipment
• Operator falls asleep
• Faulty controllers
• Machine malfunction
• Computer crashes
• Poor batch of raw material
• Power surges.

Common causes

• Inappropriate procedures
• Poor design
• Poor maintenance of machines
• Lack of clearly defined standing operating procedures
• Poor working conditions, e.g. lighting, noise, dirt, temperature, ventilation
• Machines not suited to the job
• Substandard raw materials
• Assurement error Quality control error
• Vibration in industrial processes
• Ambient temperature and humidity
• Insufficient training
• Normal wear and tear
• Variability in settings
• Computer response time
• Incompetent employee

Importance to economics

John Maynard Keynes and Frank Knight both discussed the inherent unpredictability of economic systems in their work and used it to criticise the mathematical approach to economics, in terms of expected utility, developed by Ludwig von Mises and others. Keynes in particular argued that economic systems did not automatically tend to the equilibrium of full employment owing to their agents' inability to predict the future. As he remarked in The General Theory of Employment, Interest and Money:

… as living and moving beings, we are forced to act … [even when] our existing knowledge does not provide a sufficient basis for a calculated mathematical expectation.

Keynes's thinking was at odds with the classical liberalism of the Austrian school of economists, but G. L. S. Shackle recognised the importance of Keynes's insight and sought to formalise it within a free-market philosophy.

Importance to industrial management

Harry Alpert observed:

A riot occurs in a certain prison. Officials and sociologists turn out a detailed report about the prison, with a full explanation of why and how it happened here, ignoring the fact that the causes were common to a majority of prisons, and that the riot could have happened anywhere.

The quote recognises that there is a temptation to react to an extreme outcome and to see it as significant, even where its causes are common to many situations and the distinctive circumstances surrounding its occurrence, the results of mere chance. Such behaviour has many implications within management, often leading to interventions in processes that merely increase the level of variation and frequency of undesirable outcomes.

Deming and Shewhart both advocated the control chart as a means of managing a business process in an economically efficient manner.

Importance to statistics

Deming and Shewhart

Within the frequency probability framework, there is no process whereby a probability can be attached to the future occurrence of special cause. However the Bayesian approach does allow such a probability to be specified. The existence of special-cause variation led Keynes and Deming to an interest in bayesian probability but no formal synthesis has ever been forthcoming. Most statisticians of the Shewhart-Deming school take the view that special causes are not embedded in either experience or in current thinking (that's why they come as a surprise) so that any subjective probability is doomed to be hopelessly badly calibrated in practice.

It is immediately apparent from the Leibniz quote above that there are implications for sampling. Deming observed that in any forecasting activity, the population is that of future events while the sampling frame is, inevitably, some subset of historical events. Deming held that the disjoint nature of population and sampling frame was inherently problematic once the existence of special-cause variation was admitted, rejecting the general use of probability and conventional statistics in such situations. He articulated the difficulty as the distinction between analytic and enumerative statistical studies.

Shewhart argued that, as processes subject to special-cause variation were inherently unpredictable, the usual techniques of probability could not be used to separate special-cause from common-cause variation. He developed the control chart as a statistical heuristic to distinguish the two types of variation. Both Deming and Shewhart advocated the control chart as a means of assessing a process's state of statistical control and as a foundation for forecasting.

Keynes

Keynes identified three domains of probability:

• Frequency probability;
• Subjective or Bayesian probability; and
• Events lying outside the possibility of any description in terms of probability (special causes)

- and sought to base a probability theory thereon.

References

Bibliography

• Deming, W E (1975) On probability as a basis for action, The American Statistician, 29(4), pp146-152
• Deming, W E (1982) Out of the Crisis: Quality, Productivity and Competitive Position ISBN 0-521-30553-5
• Keynes, J M (1921) A Treatise on Probability, ISBN 0-333-10733-0
• Keynes, J M (1936) The General Theory of Employment, Interest and Money ISBN 1-57392-139-4
• Knight, F H (1921) Risk, Uncertainty and Profit ISBN 1-58798-126-2
• Shackle, G L S (1972) Epistemics and Economics: A Critique of Economic Doctrines ISBN 1-56000-558-0
• Shewhart, W A (1931) Economic Control of Quality of Manufactured Product ISBN 0-87389-076-0
• Shewhart, W A (1939) Statistical Method from the Viewpoint of Quality Control ISBN 0-486-65232-7
• Wheeler, D J & Chambers, D S (1992) Understanding Statistical Process Control ISBN 0-945320-13-2

See also

• Common Cause Variation
• Special Cause Variation
• Corrective and Preventative Action (CAPA)