Selecting a quality control attribute sample: An information-economics method

The information-economics approach to assessing the value of information is different from the statistical approach. The statistical approach focuses on determining the probabilities of type I and II errors, while the information-economics approach focuses on maximizing the expected monetary value of the whole process. This attitude is the basis for the models of sequential decision processes, especially Markov decision processes (MDP) or partially observed Markov decision processes (POMDP). However, as in traditional single-sampling models, the sample size and sampling costs are not treated as decision variables in a cost-effective manner. This paper uses a well-known information-economics model - the Information Structure Model - to determine the optimal sample size and decision rule in QC single-sampling problems. The method uses rough information about the costs of types I and II errors and other parameters of the sampling problem. That method can be applied by decision makers to decide whether to use a QC sample and to determine the optimal QC plan in order to maximize the long-range expected monetary value of sampling gained by the firm. An algorithm for single-sampling plan determination is presented toward the end of the paper. Applications to double-sampling or sequential-sampling problems need further research.