Game theoretic computing of producer’s and consumer’s risks, α & β, for
acceptance sampling using cost and utility
Abstract
When establishing a hypothesis testing procedure to ensure its
credibility, the most significant of all is unquestionably to select
and/or compute the optimal Type-I and the Type-II error probabilities,
namely Producer’s and Consumer’s Risks, α & β respectively. This
article as opposed to the conventionally and judgmentally picking at
best a subjective Type-I error probability, outlines a Game theoretic
approach, i.e. that of von Neumann, to this historically unresolved
paradigm to justify optimal choices for Type-I error probability (α) and
Type-II error probability (β) when cost, utility and other
market-centric factors are incorporated as input data. A game
theory-based algorithmic methodology and several numerical examples of
practical nature with specific emphasis to company-specific Acceptance
Sampling plans for Quality Assurance are illustrated. A side benefit of
this method in addition to improving the Acceptance Sampling plans is to
transform the traditional Hypothesis Testing process in making sound
engineering decisions from a “subjective” to “objective” stance,
provided that the monetary cost and utility consequences of committing
error and non-error combinations are available.