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The following is an excerpt on SPC implementation The Six Sigma Handbook: Fourth Edition by Paul Keller and Thomas Pyzdek (McGraw-Hill, 2014).
Shewhart (1931, 1980) defined control as follows:
A phenomenon will be said to be controlled when, through the use of past experience, we can predict, at least within limits, how the phenomenon may be expected to vary in the future. Here it is understood that prediction within limits means that we can state, at least approximately, the probability that the observed phenomenon will fall within the given limits.
The critical point in this definition is that control is not defined as the complete absence of variation. Control is simply a state where all variation is predictable. A controlled process is not necessarily a sign of good management, nor is an out-of-control process necessarily producing non-conforming product.
In all forms of prediction there is an element of chance. For our purposes, we will call any unknown random cause of variation a chance cause or a common cause, the terms are synonymous and will be used as such. If the influence of any particular chance cause is very small, and if the number of chance causes of variation are very large and relatively constant, we have a situation where the variation is predictable within limits. You can see from the definition above, that a system such as this qualifies as a controlled system. Where Dr. Shewhart used the term chance cause, Dr. W. Edwards Deming coined the term common cause to describe the same phenomenon. Both terms are encountered in practice.
Needless to say, not all phenomena arise from constant systems of common causes. At times, the variation is caused by a source of variation that is not part of the constant system. These sources of variation were called assignable causes by Shewhart, special causes of variation by Dr. Deming. Experience indicates that special causes of variation can usually be found without undue difficulty, especially with easy to use SPC software, leading to a process that is less variable.
Statistical tools are needed to help us effectively identify the effects of special causes of variation. This leads to another definition: Statistical Process Control
Learn more about the SPC principles and tools for process improvement in Statistical Process Control Demystified (2011, McGraw-Hill) by Paul Keller, in his online SPC Concepts short course, or his online SPC certification course.
Interpretation & Calculations