Using Decision Theory Approach to Bulid a Model for Bayesian Sampling Plans

The paper deals with constructing a model for Bayesian sampling plans for the system “Average out going quality level”, where the percentage of defectives is varied from lot to lot, so it considered to be a random variable, having a prior distribution , which must be fitted to represent the distribution of percentage of defectives efficiently. The parameters of this distribution must estimated, and then used in model construction. The aim of the model is to find the parameters of single Bayesian sampling plan (), the sample size, and the acceptance number (), from minimizing the total cost of the model, which comprises cost inspection and cost of repairing or replacement of defective units. In addition to cost of rejecting goo items, which is a penalty cost. Also the construction depend on decision rule[], for acceptance and decision rule for rejection[]. Finally the build model can be applied to another distribution like Gamma – Poisson, Normal – Beta, to find the sampling plan () necessary to test the product of the lot and to have a production with accepted to satisfy consumer's and producer's risk. All the derivation required to build this cost function are explained and all the results of obtained samples and applications are illustrated in tables.