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.     

A Guide to Exact Simulation

Markov Chain Monte Carlo (MCMC) methods are used to sample from complicated multivariate distributions with normalizing constants that may not be computable in practice and from which direct sampling is not feasible. A fundamental problem is to determine convergence of the chains. Propp & Wilson (1996) devised a Markov chain algorithm called Coupling From The Past (CFTP) that solves this problem, as it produces exact samples from the target distribution and determines automatically how long it needs to run. Exact sampling by CFTP and other methods is currently a thriving research topic. This paper gives a review of some of these ideas, with emphasis on the CFTP algorithm. The concepts of coupling and monotone CFTP are introduced, and results on the running time of the algorithm presented. The interruptible method of Fill (1998) and the method of Murdoch & Green (1998) for exact sampling for continuous distributions are presented. Novel simulation experiments are reported for exact sampling from the Ising model in the setting of Bayesian image restoration, and the results are compared to standard MCMC. The results show that CFTP works at least as well as standard MCMC, with convergence monitored by the method of Raftery & Lewis (1992, 1996).     

An extension of Mohring's model for land rent distribution

In an early paper Herbert Mohring (J. Pol. Econ., 49 (1961)) presented a model for land rent distribution yielding the well-known result that the price of land must fall with the distance from the city center to offset transportation costs. Our paper is an extension of Mohring's model in which we relax some of his drastic simplifying assumptions. This extended model has been incorporated in a method for economic evaluation of city master plans which has been applied to a Swedish city. In this method the interdependence among housing, heating, and transportation, the durability of urban structures, and the uncertainty of future demand are explicitly considered within a cost-benefit approach. Some empirical results from this pilot study concerning land rent distributions are also presented here.     

Procedures to determine optimum two-stage sampling plans by attributes

Summary In order to compare two sampling plans we use the minimax regret principle, i.e. the minimax principle applied to regret functions. It is shown that among all two-stage sampling plans there exists an optimum sampling plan which can be computed with the aid of a procedure presented in this paper; furthermore another procedure is described how to obtain an approximately optimum two-stage sampling plan in a more direct way. Finally only those two-stage sampling plans are regarded which satisfy an additional condition; among these sampling plans an optimum one exists and is to be determined, too.     

Zur Bestimmung kostenoptimaler einfacher Stichprobenpläne bei abgebrochener Kontrolle

Summary The usefulness of curtailed and semicurtailed single sampling plans is described by their regret function, the expected avoidable costs of such plans. There always exists an optimal curtailed and semicurtailed single sampling plan which minimizes the maximum of the regret function. A procedure to determine optimal curtailed or semicurtailed single sampling plans is described and a numerical comparison of these optimal plans with the corresponding optimal single sampling plans is given for some chosen cost parameters.     

A general framework for approximate sampling with an application to generating points on the boundary of bounded convex regions

We consider the problem of generating a sample of points according to some given probability distribution over some region. We give a general framework for constructing approximate sampling algorithms based on the theory of Markov chains. In particular, we show how it can be proven that a Markov chain has a limiting distribution. We apply these results to prove convergence for a class of so-called Shake-and-Bake algorithms, which can be used to approximate any absolutely continuous distribution over the boundary of a full-dimensional convex body.     

Note on the generation of most probable frequency distributions

The most probable distribution of a stochastic variable is obtained by maximizing the entropy of its distribution under given constraints, by applying Lagrange's procedure.
The constraints then determine the type of frequency distribution. The above holds for continuous as well as for discrete distributions.
In this note we give a survey of various constraints and the corresponding frequency distributions.     

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.     

浅析二项分布、泊松分布和正态分布之间的关系

二项分布、泊松分布和正态分布一直是学习和研究概率统计的基础。在一定条件下,这三个分布之间存在着密切关系。文章通过求极限分布,研究了二项分布与泊松分布、二项分布与正态分布之间的关系,并利用特征函数和分布函数相互唯一确定这一性质,分析了泊松分布和正态分布之间的关系。     

A process control method based on five-parameter generalized lambda distribution

The use of control charts in statistical quality control, which are statistical measures of quality limits, is based on several assumptions. For instance, the process output distribution is assumed to follow a specified probability distribution (normal for continuous measurements and binomial or Poisson for attribute data) and the process supposed to be for large production runs. These assumptions are not always fulfilled in practice. This paper focuses on the problem when the process monitored has an output which has unknown distribution, or/and when the production run is short. The five-parameter generalized lambda distributions (GLD) which are subject to estimating data distributions, as a very flexible family of statistical distributions is presented and proposed as the base of control parameters estimation. The proposed chart is of the Shewhart type and simple equations are proposed for calculating the lower and upper control limits (LCL and UCL) for unknown distribution type of data. When the underlying distribution cannot be modeled sufficiently accurately, the presented control chart comes into the picture. We develop a computationally efficient method for accurate calculations of the control limits. As the vital measure of performance of SPC methods, we compute ARL’s and compare them to show the explicit excellence of the proposed method.     

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.     

Community income distributions in a metropolitan area

We extend de Bartolome and Ross [C.A.M. de Bartolome, S.L. Ross, Equilibrium with local governments and commuting: Income sorting vs. income mixing, Journal of Urban Economics 54 (2003) 1–20] to the case when the income distribution in the metropolitan area is a continuous distribution. In particular, we consider a circular central city surrounded by a suburban community. All households must commute to the metropolitan center and public service levels differ in the two jurisdictions. There is intra-jurisdictional and inter-jurisdictional capitalization. Our model has an equilibrium in which the income distributions of the central city and of the suburban community do overlap. Our finding contrasts with the traditional finding of Alonso–Mills–Muth-type models of spatial sorting and of Tiebout-type models of fiscal sorting, both of which have been shown to predict that the income distributions of the two communities do not overlap. In addition, the model explains the fixedness in jurisdictional boundaries.     

Patterns and dynamics of population heterogeneity in mixtures models

Mixtures of distributions are a common modelling tool for durations of social phenomena, especially when the population is believed to be heterogeneous. We discuss heterogeneity patterns which can be captured by various mixing distributions in continuous and discrete time. Particular attention is given to recidivism data which Kaplan modeled by beta-mixtures of geometric distributions. We also investigate the dynamics of heterogeneity, measured via the variance of the mixing distribution, over the duration. It is shown that not all mixture models display decreasing heterogeneity over time.     

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.     

On the use of Markovian equilibrium distributions for land use policy evaluation

Using the Markov model of land use change as a framework for analyzing the impact of alternative land use policies, comparison of Markovian equilibrium distributions resulting from constrained simulations has been promoted as a means of evaluating the scope of land use policy impacts. Previous studies have not considered the question of measuring the confidence which can be placed in the predictions contained in the equilibrium distribution vector. This paper applies a method of assessing the levels of confidence in the predictions of the equilibrium distribution vector. Results suggest that use of equilibrium distributions of land use as a measure of policy impact has limited inferential value.     

Bayesian prediction with cointegrated vector autoregressions

A complete procedure for calculating the joint predictive distribution of future observations based on the cointegrated vector autoregression is presented. The large degree of uncertainty in the choice of cointegration vectors is incorporated into the analysis via the prior distribution. This prior has the effect of weighing the predictive distributions based on the models with different cointegration vectors into an overall predictive distribution. The ideas of Litterman [Mimeo, Massachusetts Institute of Technology, 1980] are adopted for the prior on the short run dynamics of the process resulting in a prior which only depends on a few hyperparameters. A straightforward numerical evaluation of the predictive distribution based on Gibbs sampling is proposed. The prediction procedure is applied to a seven-variable system with a focus on forecasting Swedish inflation.     

Imputing continuous data under some non-Gaussian distributions

There has been a growing interest regarding generalized classes of distributions in statistical theory and practice because of their flexibility in model formation. Multiple imputation under such distributions that span a broader area in the symmetry–kurtosis plane appears to have the potential of better capturing real incomplete data trends. In this article, we impute continuous univariate data that exhibit varying characteristics under two well-known distributions, assess the extent to which this procedure works properly, make comparisons with normal imputation models in terms of commonly accepted bias and precision measures, and discuss possible generalizations to the multivariate case and to larger families of distributions.     

果蔬农产品配送联盟的组织功能与利益分配研究

共同配送可以促进配送合理化已得到广泛认可,组建配送联盟开展共同配送能进一步发挥共同配送的规模化和集约化优势。文章针对果蔬农产品的配送特性分析了果蔬农产品配送联盟的组织功能,肯定了其在优化果蔬农产品共同配送中发挥的作用。利益分配的合理与否关系到联盟内部的团结稳定,是果蔬农产品配送联盟必须解决好的重大问题。用资源增加量、任务完成量、延迟送货时间三个可度量的指标建立分配模型,给出一种配送联盟中企业利益分配的方法并给出算例。     

Distributions characterized through conditional expectations

Using conditional expectations, we present results that lead to the characterization of several distributions. Both absolutely continuous random variables and discrete random variables are considered. In the case of absolutely continuous random variables, the results lead to the characterization of a family of distributions while in the case of discrete random variables, the distribution is almost uniquely determined under the stated conditions.