Probabilities of Failure in Mixed Acceptance Sampling Schemes

Mixed acceptance sampling schemes are commonly used for consumer protection. In a typical application, a sample is taken from a product lot and tested to check that the average value of the sample is not less than the labelled net content, and that there is no 'unreasonable' deficiency in any individual item. Exact and approximate expressions are obtained for the probabilities of failure or success under such schemes and under a variety of conditions.     

Two-Stage Variables Acceptance Sampling Plans Using Process Loss Functions

In this article, a variable two-stage acceptance sampling plan is developed when the quality characteristic is evaluated through a process loss function. The plan parameters of the proposed plan are determined by using the two-point approach and tabulated according to various quality levels. Two cases are discussed when the process mean lies at the target value and when it does not, respectively. Extensive tables are provided for both cases and the results are explained with examples. The advantage of the proposed plan is compared with the existing variable single acceptance sampling plan using the process loss function.     

A New Acceptance Sampling Policy Based on Number of Successive Conforming Items

In an acceptance-sampling plan, where items of an incoming batch of products are inspected one by one, if the number of conforming items between successive non conforming items falls below a lower control threshold, the batch is rejected. If it falls above an upper control threshold, the batch is accepted, and if it lies within the thresholds then the process of inspecting the items continues. The purpose of this article is to develop an optimization model to determine the optimum values of the thresholds such that constraints on the probability of Type I and Type II errors are satisfied. This article starts by developing a Markovian model to derive the expected total cost of the inspection problem containing the costs of acceptance, rejection, and inspection. Then, the optimum values of the thresholds are selected in order to minimize the expected cost. To demonstrate the application of the proposed methodology, perform sensitivity analysis, and compare the performance of the proposed procedure to the one of another method, a numerical example is given at the end and the results are reported.     

Optimal Design of Acceptance Sampling Plans by Variables for Nonconforming Proportions When the Standard Deviation Is Unknown

This article presents an optimization-based approach for the design of acceptance sampling plans by variables for controlling nonconforming proportions when the standard deviation is unknown. The variables are described by rigorous noncentral Student’s t-distributions. Single and double acceptance sampling (AS) plans are addressed. The optimal design results from minimizing the average sampling number (ASN), subject to conditions holding at producer’s and consumer’s required quality levels. The problem is then solved employing a nonlinear programming solver. The results obtained are in close agreement with previous sampling plans found in the literature, outperforming them regarding the feasibility.     

Two-Stage Cluster Sampling with Ranked Set Sampling in the Secondary Sampling Frame

Motivated by a real-life problem, we develop a Two-Stage Cluster Sampling with Ranked Set Sampling (TSCRSS) design in the second stage for which we derive an unbiased estimator of population mean and its variance. An unbiased estimator of the variance of mean estimator is also derived. It is proved that the TSCRSS is more efficient—in the sense of having smaller variance—than the conventional two-stage cluster simple random sampling in which the second-stage sampling is with replacement. Using a simulation study on a real-life population, we show that the TSCRSS is more efficient than the conventional two-stage cluster sampling when simple random sampling without replacement is used in both stages.     

A New Sampling Design for Systematic Sampling

A sampling design called “Modified Systematic Sampling (MSS)” is proposed. In this design each unit has an equal probability of selection. Moreover, it works for both situations: N = nk or N ≠ nk. Consequently, the Linear Systematic Sampling (LSS) and Circular Systematic Sampling (CSS) become special cases of the proposed MSS design.     

Pareto Sampling versus Sampford and Conditional Poisson Sampling

Abstract.  Pareto sampling was introduced by Rosén in the late 1990s. It is a simple method to get a fixed size π ps sample though with inclusion probabilities only approximately as desired. Sampford sampling, introduced by Sampford in 1967, gives the desired inclusion probabilities but it may take time to generate a sample. Using probability functions and Laplace approximations, we show that from a probabilistic point of view these two designs are very close to each other and asymptotically identical. A Sampford sample can rapidly be generated in all situations by letting a Pareto sample pass an acceptance–rejection filter. A new very efficient method to generate conditional Poisson ( CP ) samples appears as a byproduct. Further, it is shown how the inclusion probabilities of all orders for the Pareto design can be calculated from those of the CP design. A new explicit very accurate approximation of the second-order inclusion probabilities, valid for several designs, is presented and applied to get single sum type variance estimates of the Horvitz–Thompson estimator.     

Markov Sampling

A discrete parameter stochastic process is observed at epochs of visits to a specified state in an independent two-state Markov chain. It is established that the family of finite dimensional distributions of the process derived in this way, referred to as Markov sampling, uniquely determines the stochastic structure of the original process. Using this identifiability, it is shown that if the derived process is Markov, then the original process is also Markov and if the derived process is strictly stationary then so is the original.     

Layer Sampling

Layer sampling is an algorithm for generating variates from a non-normalized multidimensional distribution p( · ). It empirically constructs a majorizing function for p( · ) from a sequence of layers. The method first selects a layer based on the previous variate. Next, a sample is drawn from the selected layer, using a method such as Rejection Sampling. Layer sampling is regenerative. At regeneration times, the layers may be adapted to increase mixing of the Markov chain. Layer sampling may also be used to estimate arbitrary integrals, including normalizing constants.     

双重抽样

本世纪六十年代以来,各国在抽样调查领域内有了新的发展,尤其在应用于经济和社会调查方面取得了许多重要的进展,诸如关于抽样比例和百分比估计,决策问题中的样本含量,由于分层而得益的估计,分层抽样中的比率和回归估计,系统抽样(或称等距抽样),双重抽样(或称二相抽样),以及调查中关于误差来源的研究等等,都是较为新颖的技术,引起各国特别是发展中国家有关人员的广泛兴趣。本文试就其中的双重抽样作简略介绍。     

A List Sequential Sampling Method Suitable for Real-Time Sampling

Abstract.  A flexible list sequential π ps sampling method is introduced and studied. It can reproduce any given sampling design without replacement, of fixed or random sample size. The method is a splitting method and uses successive updating of inclusion probabilities. The main advantage of the method is in real-time sampling situations where it can be used as a powerful alternative to Bernoulli and Poisson sampling and can give any desired second-order inclusion probabilities and thus considerably reduce the variability of the sample size.     

序贯抽样检验检索表的改进

序贯抽样检验方法由于每检验完一个样品都要做出一次记录与判断,并且其判断规则还比较复杂,因而实施起来并不容易.文章在简化判断规则的基础上,改进了检索表,并对其科学性进行了检验,旨在使序贯抽样检验更加简便易行.     

分层累计抽样技术中抽样框图的绘制

对称等距抽样是我国社会经济抽样凋查中的一种主要方法。但其确定样本点的计算公式比较复杂难记,从而限制了这种方法的推广和应用。用分层累计抽样技术来实施对称等距抽样,技术简便,容易操作。抽样框图是分层累计抽样技术的关键一步,笔者在实践中摸索出了一种绘制抽样框图的简便方法,并由计算机来完成,使得分层累计抽样技术更完善,易于推广、应用。一、分层累计抽样技术设总体有N个单位,分别用A_1,A_2,…,A_N表示,各单位的有关标志值分别用X_1,X_2,…,X_N表示,辅助标志值分别用     

Adaptive Cluster Sampling in Two‐stage Sampling

Adaptive cluster sampling can be a useful design for surveying rare and clustered populations. Here we present a new development in adaptive cluster sampling where we use a two‐stage design and extend the complete allocation sampling method. In the proposed new design the primary sample units are selected and, depending on the value of a preset condition, the entire primary unit is surveyed, as in complete allocation sampling. In the next step, if a second condition is met, the surrounding primary sample units are selected. We review the efficiency of the proposed design for sampling the New Zealand Castle Hill buttercups and provide unbiased estimators for the population total and sampling variance.     

Matching Performance of Continuous Sampling Plans with Single Sampling Plans

Single sampling plans are widely used for appraising incoming product quality. However, for situations where a continuous product flow exists, lot-by-lot demarcations may not exist, and it may be necessary to use alternate procedures, such as CSP-1, for continuous processes. In this case, one would like to be able to understand how average performance of the continuous sampling procedures compares to the more commonly used single sampling plans.

In this study, a model is devised which can be used to relate plan performance between single sample lot acceptance procedures and Dodge's(1943) CSP-1 continuous sampling plan. It is shown that it is generally not possible to match up performance based upon operating characteristic curve expressions for the two plans. Instead, the plans are matched by equating expressions for π(p), the long run proportion of product which is accepted, under both procedures. This is shown to be equivalent to matching up properties on an average outgoing quality basis. The methodology may be extended for any derivative plan under MIL-STD-1235B (1982), the military standard for continuous acceptance sampling.     

基于双重抽样框的抽样估计方法研究

 随着经济社会的快速发展,抽样调查中调查对象的流动日益频繁,传统的单一抽样框很难完整覆盖流动性的目标总体,如果一定要使单一抽样框实现完整覆盖,成本必定是高昂的,甚至由于编制过程漫长使抽样调查失去其时效性。有时采用两个不完整抽样框的组合可以实现对目标总体的完整覆盖。基于双重抽样框进行抽样调查,其抽样设计工作不难,但是由于样本在两个抽样框中存在交叉,致使抽样估计甚是困难。基于此,本文将系统评述目前国外已有的各种双重抽样框估计方法,将这些方法分为分离抽样框估计和组合抽样框估计两类,并按照统一的模式比较各估计方法的功效,文章最后对我国采用双重抽样框调查进行展望。     

Teaching Survey Sampling

In recent years the focus of research in survey sampling has changed to include a number of nontraditional topics such as nonsampling errors. In addition, the availability of data from large-scale sample surveys, along with computers and software to analyze the data, have changed the tools needed by survey sampling statisticians. It has also resulted in a diverse group of secondary data users who wish to learn how to analyze data from a complex survey. Thus it is time to reassess what we should be teaching students about survey sampling. This article brings together a panel of experts on survey sampling and teaching to discuss their views on what should be taught in survey sampling classes and how it should be taught.