Sequential Bayes Solutions and Optimal Methods of Statistical Acceptance Control

Abstract

This paper gives a description of classes of sequential Bares solutions for the binomial family of distributions and for the Poisson process, if the weight function is monotonic and some of its zeros are points of increase for the a priori probability distribution. The corresponding Bares solutions are truncated with respect to n (or t). These solutions are determined by the process of trial and error between two bounds. A risk function for a Poisson process is proved to satisfy certain differential equations. It is possible to determine the bounds of Bares solutions with the help of these equations. The limiting theorem on the convergence of the boundaries of Bares solutions and the risk functions, when the corresponding binomial processes converge to a Poisson process, is proved. The results obtained are used in describing the class of optimum methods of statistical acceptance control.