Summary: 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. L. Yeh [Biometrika 75, No. 2, 387-391 (1988; Zbl 0638.62098)] derived an approximation of the Bayes risk in a relevant problem and found the optimal sample size. Instead of selecting a conjugate prior, we choose uniform and symmetrically triangular distributions as the prior distribution to reflect the differences in subjective cognition among decision makers about the parameters of concerns.
Obviously, under the same parameter space, concerning the subjective cognition about relevant parameters, the symmetrically triangular prior is deeper than the uniform prior, and this just reflects the fact that different decision makers have different thoughts to the problem. We find that for different priors the optimal sample size corresponding to the minimum Bayes risk just reflects the decision maker’s cognition about the relevant parameters.