The Study On Attributes Sampling Theory And Methods For Three-class Products

There are many needs in the application of sampling for multi- class products, for example, including food safety inspection, inspection and evaluation of apple export grade, quality control on the production line, product quality control and inspection in supply chain, Customs, industrial and commercial Bureau. Furthermore, international and national standards for the application of sampling also need the supporting of theories and methods to improve urgently, in order to formulate the appropriate stand ards. Sampling Plans for multi-class have stronger ability to identify qualified or unqualified lots, bringing more economical quality control, which provides a powerful tool for implementers of quality control and continual improvement. In this paper, attributes single and double sampling for three-class products are studied on the theory and methods. The main research parts of this dissertation are as follows.Firstly, owing to the fact that the existing sampling plans for three-class products can’t cover the actual needs, based on the classic two-class attributes sampling, six new three-class attributes single sampling plans are introduced and the corresponding operating characteristic(OC) functions are constructed separately. An important concept is introduced which is named non-conforming equivalent number and then all sampling plans can be considered as one kind sampling plan. Meanwhile, the geometry representation for sampling plans are established, the old and new sampling plans are compared using th is method. Moreover, general factors and suggestions on sampling plans for three-class products are given to choose a proper sampling plan.Secondly, an approach to design sampling plans for three-class products is proposed and several principles should be followed when using this approach. On the basis of the proposed sampling plans, propositions of OC function are summarized, and a three-dimesion OC surface is broken down into a number of OC curves. With some important points on the plane, an approach to design the sampling plans for three-class products is proposed, and several principles to design the sampling plans for are presented. At the same time, an approach to design the sampling plans is built, and an optimized model is established. Moreover, numerical examples and some discussions based on numerical computation results are given to illustrate the obtained results.Thirdly, attributes double sampling for three-class products is studied on the basis of the classical sampling theories and methods. A new attributes double sampling plan for three-class products(ADSPTP) is presented, and the probability of acceptance is derived, and then the corresponding operating characteristic function is constructed based o n the given procedure of performing ADSPTP, with which the 3-dimensional OC surface and sample contour plot are given. Meanwhile, general formulas for the average sample number(ASN) with complete and curtailed inspection of the second sample are derived and the 3-dimensional ASN surface is given, on which extreme points are discussed. Furthermore, differences are presented arising from different sampling plans parameters for the ASN surface. At the same time, sampling plans are solved by a nonlinear optimization model, and the performance of ADSPTP and the attributes single sampling plan for three-class products(ASSPTP) is compared in terms of the sampling size and the adjusted value of the producer’s risk and the comsumer’s risk. It is concluded that ADSPTP could have greater economic advantages comping with ASSPTP. Numerical examples and discussions are given to illustrate the obtained the theory and methods.Finally, taking hub products of Linhai Jufeng Machinery Co., Ltd. as an example, the designed ASSPTP and ADSPTP are given applying the theories and methods proposed in this paper. Considering the product features, the most appropriate sampling plan is chosen for the company. How to apply the proposed theory and methods for three-class products in this paper can refer to this.