In 1703, Jacob Bernoulli wrote to Gottfried Leibniz to discuss their shared interest in applying mathematics and probability to games of chance.
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.
However, new, unanticipated, emergent or previously neglected phenomena (e.g. "new diseases") result in variation outside the historical experience base.
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.
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' 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.
Alpert 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 ad hoc interventions 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.
The existence of special-cause variation led Keynes and Deming to an interest in Bayesian probability, but no formal synthesis emerged from their work.
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.
However, in practice, the probability of failure is much higher because they are not statistically independent; for example ionizing radiation or electromagnetic interference (EMI) may affect all the channels.
[7] The principle of redundancy states that, when events of failure of a component are statistically independent, the probabilities of their joint occurrence multiply.
Strategies for the avoidance of common mode failures include keeping redundant components physically isolated.