Approximately optimum two-stage sampling plans

Summary In order to compare two-stage sampling plans we use the minimax regret principle i.e. the minimax principle applied to the corresponding regret functions. In this paper approximation formulas for optimum two-stage sampling plans are derived in the case of sampling by attributes as well as in the case of sampling by variables; furthermore a method is presented how to improve the approximate solution in the first case.     

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.     

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.     

α-Optimal sampling plans for large acceptance numbers

Acceptance sampling by attributes is an important tool of industrial quality control. In this paper the sampling plan is selected according to a given cost situation using the assumption that one knows the probability that the number of defective items in a lot does not exceed break even quality. An approximate solution is derived for the case that either the sampling cost is small or the lot sizeN large, which both imply a large acceptance numberc.     

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.     

Existence of balanced sampling plans avoiding cyclic distances

This article considers balanced sampling plans avoiding adjacent units. It is shown, using linear algebraic and design theoretic tools, that such plans exist for all sufficiently large populations. More generally, if any set of m circular distances is to be avoided in balanced sampling with subsets of size k, then such a plan exists, provided the population size N is at least mk ³. Research of the Peter J. Dukes is supported by NSERC.     

Estimation from two-stage unequal probability sampling with missing units

A formula is presented for an unbiased estimator for the variance of an unbiased estimator of a survey population total as well as for an unbiased estimator of its variance based on sampling in two-stages following Rao et al. J Roy Stat Soc B 24: 482–491 (1962) scheme in both stages when the originally selected units in both stages cannot be fully covered in the survey but are to be randomly sub-sampled. The development is helpful to tackle non-responses if assumed to have occurred at random in either or both the stages     

An optimum sampling design to base HT-method of estimating a finite population total

The problem of constructing a sampling design with the value of the sum of second order inclusion probabilities attaining its lower bound for non-integral values of the expected effective size of a sample in the design has been considered in this paper. If the values of the characteristic of interest on all the units in the population are non-negative the design is admissible (in the sense of variance) with respect to Horvitz-Thompson estimator in the class of designs with the same set of values of the first order inclusion probabilities of the units. Again such a design is best to use Horvitz-Thompson estimator of population total in the sense of smallest average variance of the estimator under a special superpopulatio model.     

Variables sampling plans for the Poisson and the binomial

Variables sampling plans based upon continuous distributions are well known. The usual assumption is that a measurable characteristic associated with a product has a normal distribution, a case which has been treated extensively in the literature. Other continuous distributions, particularly the exponential, have also been used as models. In this paper we discuss variables sampling plans for situations in which the measurable characteristic has either a Poisson or a binomial distribution.     

A two-stage sampling by unequal size samples from two normal populations with unknown variances

A two-stage procedure based on the statistic introduced by Scheffé (1943) to solve the Behrens-Fisher problem is considered in estimating the difference between the mean values of two normal distributions having unequal and unknown variances. Samples of unequal size are considered at each stage. A numerical example is given where the two-stage procedure is compared with the Satterthwaite (1946) approximate method.     

On Bayesian optimum allocation in some two phase sampling problems

Summary For estimating certain parametric functions, we consider the problem of allocatingN _i, the size of the sample from theith population,i=1,2,...,k, at the second phase of sampling of a two phase sampling procedure, given that we taken _i observations from the population at the first phase. We consider that the observations from theith population follow the exponential distribution with mean _i,i=1,2,...,k, and the functions to be estimated are (i) (d_i/_i) and (ii) (d_ii). When the total cost of sampling at the second phase is c _iN_i and is fixed, allocations using the Bayes approach are obtained so that the estimation is as precise as is possible.     

A simplified approach to M-estimation with application to two-stage estimators

This paper presents a simple version of the theory of M-estimation. It is argued that the theory is immediately applicable to almost all estimation schemes employed by econometricians. It is further argued that the great overlooked benefit of the theory is that is provides almost automatic asymptotic results, e.g., probability limits and asymptotic covariances. Thus one need not be a theoretical econometrician to invent and use specially tailored estimators. To illustrate its use the theory is applied to a variety of theoretical and applied problems. Particular attention is paid to two-stage estimators.     

Substance abuse coverage provided by employer medical plans

In summary, substance abuse is a serious problem in America. In fact, a Gallup poll ranked drug use as the Nation's number one problem. As a rapidly accelerating component of health care costs, charges for alcohol and drug abuse treatment are helping to drive up medical care expenses. The substance abuse crisis is also affecting employers, both public and private, who are struggling to provide needed health benefits while controlling spiraling plan costs. Despite the upward pressure on health costs, the problem is so serious that there has been a steady increase in the incidence of coverage for substance abuse treatment in employer-provided medical care plans, to the point that virtually all plans now provide some benefits. Nevertheless, health plans typically cover substance abuse treatment on a more restrictive basis than other illnesses. This may change, however, as the interest in, and the need for, comprehensive substance abuse treatment benefits grows.     

永恒力:立足中国布局亚洲

2011年3月9日,永恒力在上海和平饭店召开了以扩展亚洲业务为主题的新闻发布会。由永恒力集团销售董事Dr.Helmut Limberg(赫尔穆特·林伯格)、永恒力亚太区副总裁M r.Jan WillemJongert(荣延伟)、永恒力中国区总经理Mr.Alexander(O|¨)zbahadir(欧     

A two-stage model to forecast elections in new democracies

The purpose of this article is to propose a method to minimize the difference between electoral predictions and electoral results. It builds on findings that stem from established democracies, where most of the research has been carried out, but it focuses on filling the gap for developing nations, which have thus far been neglected by the literature. It proposes a two-stage model in which data are first collected, filtered and weighed according to biases, and then output using Bayesian algorithms and Markov chains. It tests the specification using data stemming from 11 Latin American countries. It shows that the model is remarkably accurate. In comparison to polls, not only does it produce more precise estimates for every election, but it also produces a more accurate forecast for nine out of every ten candidates. The article closes with a discussion on the limitations of the model and a proposal for future research.