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

Abstract

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 fro m lot to lot, so it considered to be a rando m variable, having a prior d istribution (), wh ich 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 (), fro m minimizing the total cost of the model, which co mprises 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[1 − ()]. 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 exp lained and all the results of obtained samples and applications are illustrated in tables.

Comparing Different Estimators of Parameters and Reliability for Mixed Weibull by Simulation

“…The results for the estimator's of parameter's are explained in tables (1,2,3,4,12,13,14,15). Also the estimator's of reliability function are explained in tables (5,6,7,8,9,10,11,16,17,18,19,20,21,22).…”

“…The two subpopulation are represented in one function (1) as; (1) where; And the reliability function is; (6) Method of estimating parameter2.1-Maximum likelihood method ( ):It is the important method to find the estimator of mixed weibull which consist of two subpopulation ( ) and parameter of (mixing proportion parameter). If ( ) represents the time of failure of random sample ( ) taken randomly from Biweibull distribution, and we know when each unit belong to ( ), then we can determine the random variable T (time) of failure of ( ) units before (T) i.e ( ), then the data of sample here is called time censored sampling (Type I), and the conditional probability distribution for time failure from ( ) before time T is;…”