On Bayesian Sampling Inspection Plans with Multiple Criteria

[[abstract]]In this paper, we consider a Bayes approach for the sampling inspection problem. To keep both the prior and the posterior distributions in the same distribution family, the conjugate prior distributions are often chosen for the relevant parameters in a problem. As the result, many calculation difficulties can be overcome. In 1988, Lam Yeh derived an approximation of the Bayes risk in a relevant problem and found the optimal sample size. Instead of selecting a conjugate prior, in this research we choose uniform and symmetrically triangular distribution as the prior distribution to reflect the differences in subjective cognition among decision makers about the parameters in concerns. Obviously, under the same parameter space, concerning the subjective cognition about relevant parameters, symmetrically triangular prior is deeper than uniform prior, and this just reflect the facts that different decision makers have different thoughts to the problem. In this paper, we find that for the different prior, the optimal sample size corresponding to the minimum Bayes risk reflects the decision maker's cognition about the relevant parameters