Bayesian stopping rule for normal distribution

Assume that x(1),x(2),...,x(n) are sequentially sampled from a normal distribution, N(mu,sigma(2))where sigma(2) is known. In order to have an economical quality control process; one is interested to know whether fewer observations can provide a similar reliability level, and what such a number can be. The Bayesian approach is used to construct a stopping rule involving two specified confidence levels: (1) the probability of the posterior estimate of the normal distribution with a mean value, mu, after m observations (m < n), and (2) the expectation of the probability of mu over the remaining s observations (s=n-m) when viewed pessimistically. To apply the proposed stopping rule, one should merely take the first M units and decide whether to accept the hypothesis H-o : mu = mu(0) or H-1 : mu = mu(1),mu(1) < mu(0). In addition, operating characteristic (OC) curves are commonly used to determine the number of samples required detecting the difference between products under certain acceptable risks. In this paper, the OC curves are also developed. Some examples are used to demonstrate the application of the proposed methodology.