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.

In this paper, the probability d istribution (Generalized Ray leigh) with t wo parameters (θ, σ 2), in case of outlier, is developed, where the probability density function (. .) is defined, and its mo ment generating function is derived, to help us in finding the moments, also its cumulative distribution function is found to be used, in obtaining the least squares estimator of the parameters σ 2 and θ. The parameters are estimated also by method of mo ments and method of least square, and also mixture of the estimators are derived, and explained, the estimators of maximu m likelihood for θ, σ 2 are also obtained.

This paper deals with constructing a new generated Marshal – Olkin Uniform family distribution which include finding the probability density function.

This research deals with constructing second order mixed model, from Exponential (θ), and Gamma (3,θ), where the mixing proportions are (αα+1),(1α+1). The p.d.f. is derived, and also CDF and reliability function. Then the parameters are estimated by method of moments and maximum likelihood as well as some proposed method. Where from Table 1 we find the first best fuzzy hazard rate is moment estimator with percentage and the second one proposed while the third best one is maximum likelihood estimation. We observe that the first best fuzzy hazard rate estimator is proposed one, and the second best one is maximum likelihood estimation and finally the moment estimator is best, according to the results of fuzzy hazard rate function, we find that the first best is the proposed one, while the second best one is moments estimator, and finally the third one is maximum likelihood estimation. All the derivation required are explained, and results of comparison are explained in tables.

In this paper ,we constructed a model for the total expected cost of quality control, which include four components, A1(inspection cost) and A2 represent cost of accepting defective units ,and the third component is A3(cost of rejecting good units) and finally A4 which is the loss due to stopping of production line. This model is modification for the model presented by Schmidt-Taylor [2]. The aim of model is to determine the three parameters of single sampling plan, were is the sample size, is acceptance number and is the time interval between inspections. The proposed model needs the multivariate search technique and enumeration procedure; to solve the expected cost quality model and then obtain the set of parameters that minimize this function the efficiency of proposed model was compared with this due to Schmidt-Taylor model .All notations and derivations are explained.Keyword: Acceptance sampling plan, proposed model for expected total cost of quality control, Multivariate search technique, enumeration procedure application.