Measurement Procedures for Improving the Variability Function

Abstract Stochastics investigates the relations between the determinate past and the indeterminate future, quantifies the structured connectivity of past and future and, thus, can be looked upon as a Science of Change . This reminds of the Book of Change , the ancient Chinese classics I Ging , which is considered as the oldest book of mankind. In the introduction of the 21st edition of Wilhelm Richard's famous translation [Ging, Text und Materialien, Eugen Diederichs Verlag, 1996], the late German sinologist Wolfgang Bauer writes: “The primary meaning of the word “I” is “exchange”, “change”, which corresponds to the basic character of the book. The non-static character constitutes its originality. Although a book of oracles it does not at all claim to predict the future as definite fate, but discloses the present situation, which, however, includes a “disposition” for the future development. And exactly this disposition is open to human actions by means of the permanently given advices. Not a single situation, but the tension between two situations is the topic of the I Ging , where the second emerges from the first.” In the view of Wolfgang Bauer's words the science of stochastics appears to be a modern quantitative fulfilment of ancient ideas of an acausal but structured stream of changes. In this paper one important aspect of the “disposition for the future development” is investigated namely the question which future developments are actually possible in a given situation. The proposed methods may be applied in so-called “zero-defects” situations arising in modern production environments, in cases where safety issues are of importance and in metrology.