Sequential variable sampling plan for normal distribution

In this paper, a sequential variable sampling plan is studied. Suppose that the quality of an item in a batch is measured by a normally distributed random variable with a known variance, but the mean is unknown with a normal prior distribution. Then by using Bayesian approach and considering a Markov decision process, the optimality equations for the minimum total expected cost are formulated. We show that an optimal decision rule will have a control limit structure. An algorithm for a sequence of ε-optimal decisions is introduced. Then, the statistical procedure for conducting the sequential sampling plan is presented.