Sampling Scheme Design With Detection Risk And Its Applicatio

The traditional counting sampling inspection usually assumes that the nonconforming rate is a fixed constant and there are no inspection errors.In actual production,the rate of unqualified products is often unknown and a random variable,and the inspection error is difficult to avoid.In order to reduce the risk and loss caused by the sampling scheme,the posterior probability of the risk of the producer and the user was calculated by using the prior distribution of the false detection probability and the unqualified product rate of the batch.Based on the comprehensive consideration of sampling cost,reinspection cost and misjudgment loss,an integer nonlinear programming economic model based on imperfect test is constructed.The optimal sampling scheme is proposed and compared with the sampling scheme without inspection errors.The results show that the average inspection quantity with inspection errors is relatively large when the rate of unqualified goods is small.The average detected quality was very close,but the average detected quality upper limit was slightly lower than in the case of no test error.Finally,the influence of model parameters on sampling scheme and two types of risks is discussed.The traditional sampling scheme design is based on off-line inspection,that is,the quality of the batch products is tested through sampling inspection to determine whether the quality of the batch products meets the requirements.This inspection mode is suitable for batch delivery of products.When the market has a continuous demand for the product,off-line inspection will affect the timely delivery of the product and cause losses to the interests of the producer and user.Therefore,it is necessary to study the optimization design of online sampling inspection scheme.In the initial stage of batch production,on-line inspection is used to judge the quality level of products according to the inspection results.If the inspection result is accepted,the production quality of the product is considered to meet the requirements,and the subsequent production of products will be exempted from inspection;If the inspection results are rejected,a full inspection shall be conducted on the lot.The products are first sold in the primary market.For the products that fail to pass the inspection or are returned by the market because of the unqualified inspection,they are sold in the secondary market through repair.Assuming that the demand rate of the primary market is a fixed constant,the average profit model is established on the basis of comprehensive consideration of sales profit,inspection cost,inventory cost,repair cost,production cost,etc.The optimal design method of batch and sampling schemes is studied,the influence of model parameters on batch and sampling schemes is discussed,and the validity of the proposed sampling schemes is verified.