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 step is unquestionably to select
and/or compute the optimal type-I and type-II error probabilities,
namely the producer’s and consumer’s risks, or α & β errors,
respectively if the research hypothesis is set to be a good product vs
bad. This article is fundamentally opposed to conventionally and
judgmentally picking at best a subjective type-I error probability (α
error) and it therefore outlines a game theoretic approach, i.e. that of
von Neumann, to this historically century-old unresolved paradigm to
justify optimal choices when relevant market-centric factors such as
cost and utility are incorporated for input data. A game theory-based
algorithmic methodology and several detailed numerical examples of
practical nature with specific emphasis to company-specific acceptance
sampling plans (including a simple hospital scenario) for quality
control are studied. A side benefit of this method, in addition to
improving the enterprise acceptance sampling plans, is to transform the
traditional hypothesis testing procedure so as to make sound engineering
decisions from a “subjective” to an “objective” stance, provided
that the monetary cost and utility values as consequences to committing
error and non-error combinations are available.