Inspection Error Adjustment in the Design of Single Sampling Attributes Plan

This article presents an approach for the design of single sampling attributes plans of given strength when inspection errors are present. The design criterion considered is the specification of two points of the Operating Characteristic curve. The design approach also recommends repeated testing of sampled nonconforming units for conformance in order to reduce the adverse effect of the inspection errors. It is shown that realistic sampling plan parameters can be obtained if the inspection error probabilities are taken into account in the design of sampling plans.     

基于过程能力指数的抽样风险研究

如果将生产过程中上一道工序的加工过程（设备）视为生产者,而紧邻的下一道工序的加工过程（设备）视为使用者,则上道工序加工的零部件在通过质量抽样检验进入下道工序的过程中．就将产生抽样风险。而由抽样风险确定的抽样方案直接关系到加工过程质量控制和检验成本控制等加工效率问题。考虑到许多大批量自动生产线的检验设备已经具备在线计算过程能力指数的能力．提出了一个基于过程能力指数的抽样风险分析方法,通过计算过程能力指数,得到相应的抽样风险．进而确定合理的抽样检验方案,从而将加工过程的重要指标——过程能力指数与抽样检验方案之间建立了联系。最后,以某汽车发动机曲轴生产线加工过程为例进行了抽样风险分析。     

定量包装中计量抽检方案的设计

从市场上抽取定量包装的商品进行检测时,经常碰到的问题是如何合理地抽取被检测的商品数量.文章将利用正态分布函数来讨论抽样方案的设计.     

配网重点物资采购抽检方案研究

针对现行配网物资采购抽检制度中存在的不同批量的产品事实上宽严程度不一致的问题,基于常用的MIL-STD-1916抽样标准,提出一种计数调整型的配网重点物资抽检方案。该抽检方案结合电网的抽检实际,在考虑科学性的基础上,兼顾电网抽检相关文件中规定的重点物资抽样检验4个“百分之百”的要求和(n|0)要求,且不加大现有抽检工作量。研究成果可以直接应用于配网物资采购抽检实际工作中。     

Run-Related Probability Functions Applied to Sampling Inspection

Run-related distributions are frequently encountered in sampling inspection in the application of stopping rules for different phases of sampling. In many cases the generating function of these distributions is known; nevertheless, it is too complicated to derive the pdf using the ordinary method, and only the expectation and variance are obtained. We present an approach, based on partial fraction expansion, to derive the exact pdf of several run-related variables from their generating function. Using efficient algorithms for finding roots of polynomials and simple recursive formulas, we complete the method presented by Feller. We derive and present exact probability functions of some run-related variables. An application to sampling inspection of attribute data in batches and for continuous production is suggested.     

浅议抽检产品平均检出质量的测算与控制

文章提出了所发现的多例企业使用抽样检验控制出厂产品返次率中存在的问题,通过对抽样方案的平均检出质量的测算分析,指出了所确定的抽样计划及其相关参数的不合理性,并给出解决的建议.     

Chain Sampling Scheme under Constant Inspection Errors

The primary aim of this paper is to extend the inspection error consideration to chain sampling schemes, an area that has not been dealt with in the literature. A mathematical model is developed to investigate the performance of chain sampling schemes under constant inspection errors. Expressions of performance measures, such as operating characteristic function, average total inspection and average outgoing quality, are derived to aid the analysis of a general chain sampling scheme, ChSP‐4A ( ) r, developed by Frishman. This study reveals that as Type I inspection error increases the probability of acceptance will decrease and as Type II inspection error increases the acceptance probability will increase. The effect of Type II error on the probability of acceptance is very marginal compared with that of Type I error, especially when the true fraction non‐conforming is small. In addition, the effects of inspection errors can be ‘eliminated’ by transforming to its equivalent perfect inspection counterpart, hence greatly reducing the complexity of the analysis. The effects of other sampling parameters are also studied to serve as a foundation for future plan designing purposes. Copyright © 2006 John Wiley & Sons, Ltd.     

Alternative Multi-level Continuous Sampling Plans

In this paper we consider certain continuous sampling plans for which the rules concerning partial inspection depend, in part, on the length of time it takes to decide that the process quality is good enough so that 100% inspection may be suspended (e.g. the time required to find i consecutive items free of defects). These plans are shown to be identical to various existing multi-level continuous plans with respect to many mathematical characterizations. In certain cases these plans may be more desirable or easier to administer in practice.     

The Average Sample Number for Truncated Single and Double Attributes Acceptance Sampling Plans

In attributes sampling acceptance plans the decision to reject the lot can often be made before inspection of a single sample is completed. In double sampling, the same decision may be possible before inspection of the first sample is completed or, if a second sample is required, before the second sample is completely inspected. Or, in double sampling one may always complete the inspection of the first sample, but if a second sample is required, terminate inspection of the second sample if the lot can be rejected before it is completely inspected. Using two formulas, believed to be new, it is shown how to compute the average sample number under these three hinds of truncation and tables of results for typical sampling plans are given.     

对产品抽样检验国家标准的探讨与研究

本文通过对抽样检验标准创立和我国统计抽样检验标准发展历程的深入探讨,以及对我国现行有效抽样检验国家标准主题内容和适用范围的综合分析,阐述了贯彻执行和正确使用抽样检验国家标准的重要性。     

Multilevel Continuous Sampling Procedure for Inspection by Attributes

In continuous production processes, where items are produced sequentially, the application of a continuous sampling inspection technique for the purpose of controlling or maintaining quality is sometimes more effective than the application of other types of techniques, such as lot-by-lot sampling inspection. In this article, a multilevel continuous sampling procedure is devised. Its long-run statistical properties, the AOQ function and AFI function, are derived by demonstrating the operation of the procedure as a finite Markov chain. This procedure is presented with the change in sampling rates in both geometric and arithmetic progression. Two initial sampling rates are given as 1/2 and 1/3. The flow process chart, some tables of AOQ and AFI functions, and the tables of the relevant parameters which yield a specified AOQL are presented to facilitate the application of these plans.     

The Dodge CSP-1 Continuous Sampling Plan Under Inspection Error1

This paper examines the results of Dodge's CSP-1 continuous sampling plan under inspection error. Both type I and II errors are explicitly included. Their effect on the average number of items inspected in a 100% screening sequence, average number of items passed during sampling inspection, average fraction of items inspected, proportion of items passed under sampling, and average outgoing quality are examined. Further, the relationships necessary to determine compensating sampling plans, considering inspection error, which yield the desired actual AOQL, are developed. Use of the compensating plan method is illustrated through an example.     

Inspector Errors and Sampling Plans

Expressions for the apparent fraction defective, average outgoing quality and average total inspected are developed for the case where inspection errors are assumed to be a linear function of the incoming quality. An example is presented to show how the actual performance measures of a single sampling plan depart from the theoretical values when inspection accuracy is assumed to follow the linearity assumption.     

Inspection Error Effects on Performance Measures of a Multistage Sampling Plan

The effects of inspection error on performance measures of single and double sampling by attributes are well known for certain combinations of sample by lot dispositions. This paper generalizes previous work on double sampling to multistage sampling. It provides expressions for the O.C. curves, average outgoing quality and average total inspection in the presence of inspection error for all combinations of sample by lot dispositions. Furthermore, the sensitivity analysis is carried out from a more general algebraic standpoint.     

Estimation of the Fraction Defective in Curtailed Sampling Plans by Attributes

In this paper we have obtained the maximum likelihood estimate of the fraction defective (p) under three different sampling plans. Plan 1 considers complete inspection of the sample, Plan 2 considers curtailing of the inspection at the rejection stage and Plan 3 considers curtailing of the inspection at both the acceptance and rejection stages.     

计量抽样检查程序设计

计量抽样检查是对产品质量特性进行检查,以确定一批产品是否接收的统计方法。本文论述了不合格品率计量抽样方案的原理。给出了国家标准GB6378的程序,通过计算机处理和示例分析,说明这种方法的应用。     

Multiobjective Decision Analysis for Acceptance Sampling Plans

In recent years there has been increased interest in the design and implementation of economically based sampling plans, especially those which consider a prior distribution of defectives in lots submitted for inspection. Sampling plans which are designed using this prior knowledge are often referred to as Bayesian sampling plans. This paper illustrates an approach to the design of Bayesian sampling plans which considers two criteria. The few previous attempts to design multiobjective Bayesian sampling plans have been based on expected values of the criteria. In this paper the authors present a design methodology which takes into consideration the distribution functions of the criteria after sampling inspection, and the utility function of the 'decision maker'. Illustrative examples of the use of the methodology are given as well as areas for further research.     

Tables for Determining Expected Cost Per Unit under MIL-STD-105D Single Sampling Schemes

When a MIL-STD-105D sampling scheme is used for a long period, some lots will be subjected to normal, some to reduced, and some to tightened inspection. This paper provides for several single sampling plans and various quality levels, the expected fraction of lots rejected, the expected sample size per lot, and the expected number of lots to be processed before sampling inspection must be discontinued. Equations are given to calculate the long term cost of sampling inspection using these expected values and appropriate cost parameters.     

Variables Sampling Plan for Resubmitted Lots in a Process with Linear Profiles

Acceptance sampling plans include a sampling scheme and a set of rules for determining whether an inspection lot from a supplier should be accepted or rejected. In some circumstances, the supplier is allowed to resubmit lots for further inspection when the original inspection result is unacceptable. In this study, two variables sampling plans based on the process‐yield index for a process with linear profiles are proposed to deal with lot sentencing. The single sampling plan is a special case of the resubmitted lots sampling plan. The plan parameters are determined using a nonlinear optimization method under the given values of producer's risk, consumer's risk, acceptable quality level, and lot tolerance percent defective. Numerous tables are provided to determine the plan parameters. One real example is used to illustrate our proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

Asymptotic Properties of the Restricted Bayesian Double Sampling Plan

We consider double sampling inspection plans for a given lot size, cost function, and prior distribution of the number of defectives. The restriction we impose on the sampling plan is that the size and acceptance number of the second sample do not depend on the outcome of the first sample. Hence, a double sampling plan is determined by five parameters: two sample sizes, two acceptance numbers, and one rejection number. The optimal plan is defined as the plan which minimizes the expected cost. Our results consist of finding optimal relations between the sample sizes, acceptance and rejection numbers and the lot size as the lot size tends to infinity. An asymptotic expansion of the regret function shows that for the optimal plan it increases as the lot size raised to the power 2/5 times the logarithm of the lot size raised to the power 1/5.