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 ,...

Abstract Stochastic modelling has become a scientific catchword in many branches of science and in particular in quality theory. However, there are many misunderstandings concerning the term, and in many cases it is used wrongly. Therefore, this paper aims at introducing stochastic models, their...

Abstract Consider the following two situations which are characteristic for the application of statistical procedures. 1.) There is a deterministic variable of interest , whose actual value θ ∈ Θ is unknown. 2.) There is a random variable of interest with uncertain outcome . The aim in the...

Abstract Consider a product with quality characteristic X . Assume that the product is composed of n parts each with quality characteristic X i , and and let X = X 1 + . . . + X n Assume that there is a lower specification L and an upper specification U for X . Then the problem arises how to...

Abstract PISA stands for “Programme for International Student Assessment” performed, by the OECD and consisting of a cyclic evaluation of the new generations' basic competences. The first evaluation took place in 2000 and the results were published on 4 December 2001. According to the...

Abstract Considerable work has been done to investigate the sensitivity of explosive materials. Various methods are developed for determining statistically the “explosion characteristics”. Any statistical method is based on a stochastic model and, clearly, an inappropriate model yields...

Abstract Industrial quality control is necessary at least for two reasons: Monitoring product or process quality in order to perform interventions for assuring a desired quality level. Monitoring product or process quality in order to meet certain requirements (imposed by law or customers) for...

Abstract A rational selection of a probability distribution constitutes a major problem. Often a distribution function is selected which fits well to the observed data. In other cases the availability of statistical methods determines the model. Finally, in many fields of application there are...

Abstract Controlling uncertainty has an ever-increasing importance in all areas of industry. To meet the demand, the International Organisation of Standardization (ISO) developed and develops “statistical” standards. However, while success and failure of technical standards can be assessed...

Abstract In [v. Collani, Theoretical Stochastics, Heldermann Verlag, 2004] and [v. Collani, Empirical Stochastics, Heldermann Verlag, 2004] Stochastics, the Science of Prediction is re-established, its basic concepts are developed and fundamental stochastic procedures are introduced. Stochastics...