α-optimal sampling plans for lot-by-lot defects inspection

Investigations on acceptance sampling have attached rather few importance to defects inspection. For modern quality control, both the steadily increasing complexity of products and the need for differentiated cost calculation involve a clear demand for economic defects sampling in its practically most relevant form: lot-by-lot single sampling plans, where the OC (lot OC) is considered as a function of lot sizeN, sample sizen, acceptance numberc, number of defects in the lotK. Starting from an appropriate lot OC function, the present paper develops an economic cost and control model and an economic objective function for single defects sampling plans by adapting theα-optimal sampling scheme, introduced by E. von Collani for defectives inspection, to the purposes of defects inspection. A simple and accurate approximation ofα-optimal defects plans is derived by means of a Poisson approximation of the lot OC function.     

抽检国标路线图

本文将16个抽检国标，主要基于计数与计量、孤立与连续的分类，归纳成便于检索的路线图。对类似抽检问题，比较了众多不同抽检国标的方案，并举例说明百分比抽检不合理。     

TypeA operating characteristic functions of defects sampling plans

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.     

De statistische kwaliteitscontrôle als economisch probleem (I)

Summary  (Statistical quality control as an economic problem I).
A discussion is given about the application of 100 inspection and inspection by sampling. The choice between these two methods has to be based upon economic principles.     

Inferential Causal Models: Integrating Quality & Quantity

In-depth data analysis plus statistical modeling can produce inferentialcausal models. Their creation thus combines aspects of analysis by close inspection,that is, reason analysis and cross-tabular analysis, with statistical analysis procedures,especially those that are special cases of the generalized linear model (McCullaghand Nelder, 1989; Agresti, 1996; Lindsey, 1997). This paper explores some of the roots of this combined method and suggests some new directions. An exercise clarifies some limitations of classic reason analysis by showing how the cross tabulation of variables with controls for test factors may produce better inferences. Then, given the cross tabulation of several variables, by explicating Coleman effect parameters, logistic regressions, and Poisson log-linear models, it shows how generalized linear models provide appropriate measures of effects and tests of statistical significance. Finally, to address a weakness of reason analysis, a case-control design is proposed and an example is developed.     

Sampling inspection by variables: nonparametric setting

A classic statistical problem is the optimal construction of sampling plans to accept or reject a lot based on a small sample. We propose a new asymptotically optimal solution for acceptance sampling by variables setting where we allow for an arbitrary unknown underlying distribution. In the course of this, we assume that additional sampling information is available, which is often the case in real applications. That information is given by additional measurements which may be affected by a calibration error. Our results show that, first, the proposed decision rule is asymptotically valid under fairly general assumptions. Secondly, the estimated optimal sample size is asymptotically normal. Furthermore, we illustrate our method by a real data analysis and investigate to some extent its finite-sample properties and the sharpness of our assumptions by simulations.     

A note on acceptance sampling for variables

For 60 years acceptance sampling by variables has been recommended as an economic alternative to attribute sampling. Entry in the industrial practice happened after these plans were adopted in 1957 as Military Standard 414 by the US Army. Nowadays a slightly modified version of Mil-Std-414 is known as ANSI/ASQC Z1.9 or as International Standard ISO 3951. In this paper it is shown that the derivation of sampling plans by variables is based on assumptions which don’t hold, that acceptance sampling by variables is inappropriate, and that it doesn’t constitute an alternative to attribute sampling.     

The AQL and RQL of the attributes sampling plans in MIL-STD-1916

Since 1996, the Department of Defense-USA has adopted MIL-STD-1916 (Military Standard-1916) sampling plans instead of the traditional MIL-STD-105E (Military Standard-105E) sampling plans. MIL-STD-1916 emphasizes on an effective prevention-based strategy quality system. Its attributes sampling plans are based on “zero accept one reject” as criteria of judgment. In this paper, the lot sizes are regrouped from original 11 groups into 18 new groups such that 100% inspection and sampling plan could be clearly separated. The relationship between fraction nonconforming and probability of acceptance for each verification level (VL) and lot size is investigated. The acceptable quality level (AQL) and rejectabe quality level (RQL) for each VL and lot size are also investigated. The results of this research provide user friendly tables as guidance for both supplier and customer.     

Sequential estimation in generalized linear models when covariates are subject to errors

Sequential methods have been used for many applications; especially, when fixed sample procedures are not possible and/or when “early stopping” of sampling is beneficial for applications. At the same time, the issue of how to make correct inferences when measurement errors are present has drawn considerable attention from statisticians. In this paper, the problems of sequential estimation of generalized linear models when there are measurement errors in both adaptive and fixed design cases are studied. The proposed sequential procedure is proved to be asymptotically consistent and efficient in the sense of Chow and Robbins [Ann Math Stat 36(2):457–462, 1965] when measurement errors decay gradually as the number of sequentially selected design points increases. This assumption is useful in sequentially designed experiments, and can also be fulfilled in the case when replicate measurements are available. Some numerical studies based on a Rasch model and a logistic regression model are conducted to evaluate the performance of the proposed procedure.     

Polytomous logistic regression

In this paper a review will be given of some methods available for modelling relationships between categorical response variables and explanatory variables. These methods are all classed under the name polytomous logistic regression (PLR). Models for PLR will be presented and compared; model parameters will be tested and estimated by weighted least squares and by likelihood. Usually, software is needed for computation, and available statistical software is reported.
An industrial problem is solved to some extent as an example to illustrate the use of PLR. The paper is concluded by a discussion on the various PLR-methods and some topics that need a further study are mentioned.     

Latent variables in econometrics

Unobservable variables in econometrics are represented in one of three ways: by variables contaminated by measurement errors, by proxy variables, or by various manifest indicators and/or causes. This paper contains a discussion of models involving each of these representations, and highlights certain interesting implications that have been insufficiently emphasized or completely unrecognized in the literature.     

Confirmatory and Structural Categorical Latent Variables Models

The paper proposes a general framework for modeling multiple categorical latent variables (MCLV). The MCLV models extend latent class analysis or latent transition analysis to allow flexible measurement and structural components between endogenous categorical latent variables and exogenous covariates. Therefore, modeling frameworks in conventional structural equation models, for example, CFA and MIMIC models are feasible in the MCLV circumstances. Parameter estimations for the MCLV models are performed by using generalized expectation–maximization (E–M) algorithm. In addition, the adjusted Bayesian information criterion provides help for model selections. A substantive study of reading development is analyzed to illustrate the feasibility of MCLV models.     

水质监测中现场空白样影响因素研究

文章通过考察现场空白样采集过程的各个环节,研究出现分析结果随机性偏高的影响因素。结果表明,对于氨氮测定项目,现场暴露、运输过程以及现场加固定剂环节均会造成一定程度的空白偏高,但不是主要因素。F检验和t检验也表明采样环节不同的空白样,其分析结果精密度与准确度无显著差异。对于汞和镉测定项目,就所采集样本总体来说空白偏高主要来源于瓶子的清洁度,应建立和加强容器抽检制度,规范清洗操作。     

„Wahrscheinlichkeitslernen“ in der statistischen Lerntheorie

Zusammenfassung In diesem Beitrag zur statistischen Lerntheorie (Stimulus Sampling Theorie) wird einN-elementiges „Pattern“-Modell mitr verfügbaren Antworten und nichtkontingenter Verst?rkungsvorschrift diskutiert. Um von der lerntheoretischen Literatur nicht zu sehr abh?ngig zu sein, wird zun?chst ein kanpper überblick über die Grundbegriffe der Stimulus Sampling Theorie gegeben. Der Vorgang des „Wahrscheinlichkeitslernens“ wird mittels des Reiz-Antwort-Schemas der statistischen Lerntheorie erkl?rt. Durch die Einführung der sogenannten bedingenden Zust?nde gelangt die Theorie derMarkovketten zur Anwendung. Schlie?lich wird das Problem der übereinstimmung von empirischen Daten aus Lernexperimenten mit den aus der Theorie abgeleiteten anhand von Sequentialstatistiken studiert.

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Summary In this contribution to the statistical learning theory (stimulus sampling theory) aN-element pattern model withr availables responses and noncontingent reinforcement schedule is discussed. First a short survey of the principles of the stimulus sampling theory is given. The process of „probability learning“ is explained by the stimulus-response model of the statistical theory of learning. By the introduction of the so-called conditioning states the theory ofMarkov chains may be applicated. Finaly, the goodness-of-fit between empirical data of learning experiments and predicted statistics is studied on the basis of sequential predictions.

     

自动装置采样检查替代短路试验中测量工作的探讨

本文就电气整套启动试验中发变组短路试验提出了改进方法,即在发变组短路试验中,利用各微机自动装置的采样进行电流回路的幅值相序检查,通过检测各自动装置无功测量的结果来判断方向性保护的正确性。     

Economic designs of single and double screening procedures

Summary Economic designs of single and double screening procedures for improving outgoing product quality based on two screening variables are presented for the case of one-sided specification limit. Two screening variables are observed simultaneously in single screening procedure and are observed sequentially in double screening procedure. It is assumed that the performance variable and the two screening variables are jointly normally distributed. Three quality cost functions — constant, linear, and quadratic — are considered. Cost models are constructed which involve screening inspection cost, and costs of accepted and rejected item. Methods of finding the optimal cutoff values are presented and a numerical example is given.     

Distortion in statistical inference: the distinction between data contamination and model deviation

The present work develops a basic classification scheme for distortion in the framework of classical statistical inference. In particular, it emphasizes the still outstanding and consequent distinction between data contamination and model deviation. It is explored when different implications on the performance of statistical inference procedures under the two types of distortion are possible and how these can be detected. A critical review of some important approaches in the robustness and diagnostics literature finally indicates which of them is aimed at data contamination and which at model deviation (independently from what has been claimed originally). The paper raises awareness of the above problem through a constructive discussion – it is not meant to introduce new methodology     

Air pollution-mortality models: A demonstration of the effects of random measurement error

Errors of measurement have long been recognized as a chronic problem in statistical analysis. Although there is a vast statistical literature of multiple regression models estimating the air pollution-mortality relationship, this problem has been largely ignored. It is well known that pollution measures contain error, but the consequences of this error for regression estimates is not known. We use Lave and Seskin's air pollution model to demonstrate the consequences of random measurement error. We assume a range of 0% to 50% of the variance of the pollution measures is due to error. We find large differences in the estimated effects on mortality of the pollution variables as well as the other explanatory variables once this measurement error is taken into account. These results cast doubt on the usual regression estimates of the mortality effects of air pollution. More generally our results demonstrate the consequences of random measurement error in the explanatory variable of a multiple regression analysis and the misleading conclusions that may result in policy research if this error is ignored.     

Economic designs of two-sided single and double screening procedures

Economic designs of single and double screening procedures for improving outgoing product quality based on two screening variables are presented for the case of two-sided specification limits. Two screening variables are observed simultaneously in the single screening procedure. In the double screening procedure, one variable is used first to make one of three decisions — accept, reject, or undecided — and after the first screening, the second variable is employed to screen the undecided items. It is assumed that the performance and the two screening variables are jointly normally distributed, and the deviation of the performance variable from the ‘ideal’ value causes dissatisfication to the consumers. Two quality cost functions — constant and quadratic — are considered. Cost models are constructed which involve screening inspection cost, and costs of accepted and rejected item. Methods of finding the optimal cutoff values are presented and a numerical example is given.     

On random fuzzy variables of second order and their application to linear statistical inference with fuzzy data

This paper summarizes some results on random fuzzy variables with existing expectation and variance, called random fuzzy variables of second order. Using the Frechét-principle and – via support functions – the embedding of convex fuzzy sets into a Banach space of functions it especially presents a unified view on expectation and variance of random fuzzy variables. These notions are applied in developing linear statistical inference with fuzzy data. Detailed investigations are presented concerning best linear unbiased estimation in linear regression models with fuzzy observations. Received: November 1999