TypeA operating characteristic functions of defects sampling plans
TypeA operating characteristic functions of defects sampling plans
复制标题
TypeA缺陷抽样方案操作特征函数
作者：
R. Göb
关于验收抽样的研究很少关注缺陷检验。关于单缺陷抽样方案的抽样模型和相应的操作特征函数，一般只考虑B型（过程模型）：从生产过程中抽样，其中操作特征函数被认为是样本量、验收数c和过程平均每项缺陷数λ的函数。对于现代质量控制，产品的稳定增加的复杂性和差异化成本计算的需要都涉及到对缺陷抽样的明确要求，其实际上最相关的形式是：逐批单次抽样计划，其中OC（类型A，批次OC）被认为是批量N，样本大小，验收数c，批次K中的缺陷数的函数。本文根据对缺陷总数K分布在N个单元上的适当假设，导出了两个单元的OC函数。这些OC函数的极限定理在一定程度上证明了泊松过程OC可以作为A型的近似的习惯假设。OC函数对样本大小、接受数c和批量K中缺陷总数的依赖关系用简单的公式描述。
Investigations on acceptance sampling have attached rather few attention to defects inspection. As to sampling models and the corresponding operating characteristic (OC) function of single defects sampling plans, generally only typeB (process model) has been considered: sampling from a production process where the OC is conceived as a function of sample sizen, acceptance numberc, and process average number of defects per itemλ. For modern quality control, both the steadily increasing complexity of products and the need for differentiated cost calculation involve a clear demand for defects sampling in its practically most relevant form: lot-by-lot single sampling plans, where the OC (typeA, lot OC) is considered as a function of lot sizeN, sample sizen, acceptance numberc, number of defects in the lotK. The present paper develops two lot OC functions from suitable assumptions on the arrangements of the total numberK of defects over theN elements of the lot. Limiting theorems on these OC functions are used to justify to some extent the customary assumption that the Poisson process OC can serve as an approximation for typeA. The dependence of the OC functions on sample sizen, acceptance numberc, total number of defects in the lotK is described by simple formulae.