Abstract—A critical step in hypothesis testing at the computer theory and/or engineering decision-making stage is to optimally compute and use type-I (
α) and type-II (
β) error probabilities. The article’s first research objective is to optimize α and β errors, or producer’s and consumer’s risks, or risks of false positives (
FP) and false negatives (
FN) by employing the merits of a game-theoretical framework. To achieve this goal, the cross-products of errors and non-errors model is proposed. The second objective is to apply the proposed model to an industrial manufacturing quality control mechanism, i.e. sequential sampling plans (
SSP). The article proposes an alternative technique compared to prematurely selecting the conventionally pre-specified type-I and type-II error probabilities. One studies mixed strategy, two-players and zero-sum games’ minimax rule derived by von Neumann and executed by Dantzig’s linear programming (
LP) algorithm. Further, one equation for one unknown scenario yielding simple algebraic roots validate the computationally-intensive LP optimal solutions. The cost and utility constants are elicited through company-specific input data management. The contrasts between conventional and proposed results are favorably illustrated by tables, figures, individual and comparative plots, and Venn diagrams in order to modify and improve the traditionally executed SSP’s final decisions.
Index Terms—Cross-products of errors, minimax rule, accept-reject-continue-terminate, cost and utility.
Mehmet Sahinoglu is with the Faculty at Computer Science Dept., Troy University, USA (e-mail: mesa@troy.edu). Sedat Capar is with Faculty of Science, Dokuz Eylul University, Turkey (e-mail: sedat.capar@deu.edu.tr).
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Cite:Mehmet Sahinoglu and Sedat Capar, "Optimizing Type-I (α) and Type-II (β) Error Probabilities by Game-Theoretic Linear Programming for Sequential Sampling Plans in Quality Control ," International Journal of Computer Theory and Engineering vol. 14, no. 1, pp. 27-38, 2022.
Copyright © 2022 by the authors. 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 (CC BY 4.0).
