基于不完美检验的验收抽样方案经济设计

Economic Designing of Acceptance Sampling Plans Based on Imperfect Inspection

为降低抽样方案造成的风险及损失,利用误检概率和批产品不合格品率的先验分布,计算了生产方和使用方风险的后验概率.在综合考虑抽检成本、复检成本、误判损失的基础上,构建了一个基于不完美检验的整数非线性规划经济模型,提出了最佳抽样方案,并与无检验错误的抽样方案进行了比较.最后,讨论了模型参数对抽样方案和两类风险的影响.结果表明,在不合格品率较小时,有检验错误的平均检验量相对较大;两者的平均检出质量非常接近,但平均检出质量上限相较无检验错误时略低.

In actual production and sampling inspection,due to a variety of factors,the percentage of nonconforming products is often unknown and random,and inspection errors are also difficult to avoid.In order to reduce the risk and loss caused by sampling plans,the posterior risk probability of manufacturer and users is calculated by using the probability of inspection errors and the prior distribution of nonconforming product ratios in a batch.An integer nonlinear programming economic model based on imperfect inspection is established with a comprehensive consideration of sampling cost,reinspection cost and misjudgment loss.The optimal sampling plan is obtained and compared with the sampling plan without inspection errors.Finally,the effects of model parameters on the sampling plan and the two types of risks are discussed.Results show that the average total inspection with inspection errors is relatively large when defective rate of products is small;the average inspection quality of the two methods is very close,but the upper bound of the average outgoing quality with inspection errors is slightly lower than that without inspection errors.