EMBEDDED POLYNOMIAL PLANS OF RANDOM WALKS AND THEIR APPLICATIONS

摘要

Consequent plans of random walks are a good model for plans of the statistical control of quality and reliability (see), and also for the regulation of sports matches. In this article, we consider embedded plans of random walks, which were first offered in report with reference to binomial plans of the statistical control of reliability. For simplicity, first two-level embedded plans of random walks of the form Ⅱ_(nes) [ Ⅱ~G ∣ Ⅱ~W], consisting of two levels (steps) (Ⅱ~G is a plan of random walks of the first level, Ⅱ~w is a plan of random walks of the second level) are studied. The embedded plans of random walks Ⅱ_(nes) [ Ⅱ~G∣ ∣~W]and others offered by us in this article are a generalization of noble models of group tests (see, for example,) of schemes of a continuous control (see) of a two-level regulation of sports matches (in particular, in the game of tennis). The choice of the description of embedded plans of polynomial random walks is due to the relative simplicity of parities obtained here and by the widespread possibilities of their application for the solution of applied tasks. However, it is possible to construct embedded plans using multidimensional Polya walks, multidimensional Poisson walks , and others (see). Below we obtain the main probability characteristics of embedded polynomial plans. The construction of embedded polynomial and binomial plans of random walks for the solution of the following tasks is considered in detail: (1) a statistical control of quality and reliability; (2) a statistical continuous control; (3) a description of a regulation of chess matches.