Common mode failure

Random effects

Random error

Systematic effects

Systematic error

Common and special causes are the two distinct origins of variation in a process, as defined in the statistical thinking and methods of Walter A. Shewhart and W. Edwards Deming. Briefly, "common causes", also called Natural patterns, are the usual, historical, quantifiable variation in a system, while "special causes" are unusual, not previously observed, non-quantifiable variation.

The distinction is fundamental in philosophy of statistics and philosophy of probability, with different treatment of these issues being a classic issue of probability interpretations, being recognised and discussed as early as 1703 by Gottfried Leibniz; various alternative names have been used over the years.

The distinction has been particularly important in the thinking of economists Frank Knight, John Maynard Keynes and G. L. S. Shackle.

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.

...
Wikipedia