Stochastic thinking may be looked upon as the opposite of causal thinking; however, the term stochastic thinking is rather ambiguous, because the meaning of stochastics is not clear. It can be looked upon as a branch of mathematics, or as "a cocktail of statistical ideas and probabilistic ideas", or in the sense of Bernoulli stochastics. Here stochastic thinking is explained in the sense of Bernoulli stochastics.
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Problem solving by stochastic thinking
Stochastic thinking for problem solving proceeds in three steps:
The main difference between stochastic thinking and the prevailing causal thinking is the focus: Stochastic thinking focuses on improving the whole, while causal thinking focus on improving parts. Stochastic thinking means to think in sets and structures, that is, to link the set representing the past and the sets representing the future by a set of probability distributions. Improving the system means to reduce the probabilities of the occurrence of problems.
Effect of stochastic thinking
Stochastic thinking focuses on the whole system and aims at improving it step by step. The steps are essentially triggered by the occurrence of problems which are considered as system faults necessitating changes of the system. In other words, stochastic thinking results in a continual examination and improvement of the whole to prevent the recurrence of problems. Thus, stochastic thinking results in proactive strategies in contrast to the reactive strategies which are the outcome of causal thinking.
System performance is modelled by a Bernoulli space which represents the basis for stochastic thinking. The Bernoulli space shows explicitly the existing ignorance by means of the ignorance space and the inherent randomness by the variability function and the random structure function. The ignorance space specifies the possible areas of learning, while the two random functions indicate the possibilities of future changes and their impacts.
Stochastic thinking is oriented towards long-term effects by means of continual improvement of the system, where improvement refers to the robustness of the system against disturbances or in other words improvements refer to the stability of the system.