Stochastic Methods for Production Processes

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 is defined as the branch of science which deals with the aspect of “uncertainty”. As uncertainty constitutes a major problem in all area of life, the principles developed in stochastics are universally valid. This paper deals with production processes in the framework of stochastics. In the first part, the fundamental concept of stochastics, the Bernoulli-Space, is briefly introduced as an appropriate description of the real uncertainty aspect. Next two types of stochastic procedures are identified: The first consists of making statements concerning the indeterminate future, and the second deals with making statements concerning the determinate, but unknown past. The second part of this paper is devoted to production processes. It is shown that traditional SPC methods lost there significance within modern production environments which are characterized by an ever increasing degree of automation and by objectives which differ considerably from those during the pre-computerized times. The larger degree of complexity of the new process environment and the more demanding aims require new advanced means for dealing with uncertainty. By means of examples it is illustrated how stochastic methods comply with the needs of modern production processes.