International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 1998 / Article

Open Access

Volume 11 |Article ID 745641 | 6 pages | https://doi.org/10.1155/S1048953398000197

Nonlinear filtering and optimal quality control

Received01 Oct 1997
Revised01 Jan 1998

Abstract

Some stochastic models of optimal decision processes in quality control problems are formulated, analyzed, and solved. It is assumed that costs, positive or negative, are assigned to various events in a simple manufacturing model, such as processing an item, producing a saleable item, discarding an item for salvage, selling a “lemon”, etc. and models are described by giving a sequence of events, some of which are decisions to process, to abandon, to accept, to restart, . All the models have the rather unrealistic classical information pattern of cumulative data. The object is then to find optimal procedures for minimizing the total cost incurred, first in dealing with a single item, and second, in operating until an item first passes all the tests. The policies that appear as optimal depend on such matters as whether a conditional probability given certain data exceeds a ratio of prices, and on more complex functionals of the conditional expectations in the problem. Special “sufficient” classes of policies are discerned, which reduce the decision problem to finding one number.

Copyright © 1998 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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