Modified chain sampling plans for lot inspection by variables and attributes

The purpose of acceptance sampling is to develop decision rules to accept or reject production lots based on sample data. When testing is destructive or expensive, dependent sampling procedures cumulate results from several preceding lots. This chaining of past lot results reduces the required size of the samples. A large part of these procedures only chain past lot results when defects are found in the current sample. However, such selective use of past lot results only achieves a limited reduction of sample sizes. In this article, a modified approach for chaining past lot results is proposed that is less selective in its use of quality history and, as a result, requires a smaller sample size than the one required for commonly used dependent sampling procedures, such as multiple dependent sampling plans and chain sampling plans of Dodge. The proposed plans are applicable for inspection by attributes and inspection by variables. Several properties of their operating characteristic-curves are derived, and search procedures are given to select such modified chain sampling plans by using the two-point method.     

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.     

Link sampling for attributes

A few lot-by-lot acceptance sampling procedures for attributes are proposed as alternatives to the usual double sampling. In these schemes whenever a second sample is needed, the sample information from neighbouring lots is used. The new plans have the DC identical to that of the comparable double sampling plan. The primary advantage of these plans is a reduction in cost due to a smaller ASN. An empirical study which investigates the effect of sudden shifts in quality level on the probability of acceptance and ARL under the proposed plans is included     

Systematic and nonrandom sampling in the presence of linear trends

In the case of a finite population with a linear trend, improvements in estimation procedures are suggested for several well-known systematic samplingschemes. The use of the least squares regression estimator is examined and a sampling scheme which reduces its expected mean squared error is proposed.     

A procedure for selection of a gamma-Poisson single sampling plan by attributes

Design and evaluation of sampling plans by attributes and by variables are important aspects in the area of acceptance sampling research. Various procedures for the selection of conventional single sampling by attributes have been developed and are available in the literature. This paper presents a design methodology and tables for the selection of parameters of single sampling plans for specified requirements (strengths) under the conditions of a gamma prior and Poisson sampling distribution. The relative efficiency of gamma-Poisson single sampling plans over conventional plans is discussed through empirical illustrations.     

Hypothesis Testing in Two-Stage Cluster Sampling

Correlated observations often arise in complex sampling schemes such as two-stage cluster sampling. The resulting observations from this sampling scheme usually exhibit certain positive intracluster correlation, as a result of which the standard statistical procedures for testing hypotheses concerning linear combinations of the parameters may lack some of the optimal properties that these possess when the data are uncorrelated. The aim of this paper is to present exact methods for testing these hypotheses by combining within and between cluster information much as in Zhou & Mathew (1993).     

Variable sampling intervals for multiparameter shewhart charts

This paper considers the problem of using control charts to simultaneously monitor more than one parameter with emphasis on simultaneously monitoring the mean and variance. Fixed sampling interval control charts are modified to use variable sampling intervals depending on what is being observed from the data. Two basic strategies are investigated. One strategy uses separate control charts for each parameter, A second strategy uses a proposed single combined statistic which is sensitive to shifts in both the mean and variance. Each procedure is compared to corresponding fixed interval procedures. It is seen that for both strategies the variable sampling interval approach is substantially more efficient than fixed interval procedures.     

Small-sample performance of a modified least-failures sampling procedure for bernoulli subset selection

We describe two sequential sampling procedures for Bernoulli subset selection which were shown to exhibit desirable behavior for large-sample problems. These procedures have identical performance characteristics in terms of the number of observations taken from any one of the populations under investigation, but one of the procedures employs one-at-a-time sampling while theother allows observations to be taken in blocks during early stages of experimentation. In this paper, a simulation study of their behavior for small-sample cases (n > 25) reveals that they canresult in a savings (sometimes substantial) in the expected total number of observations requiredto terminate the experiment as compared to single-stage procedures. Hence they may be quite usefulto a practitioner for screening purposes when sampling is limited.     

Order Sampling Design with Prescribed Inclusion Probabilities

Order sampling with fixed distribution shape is a class of sampling schemes with inclusion probabilities approximately proportional to given size measures. In a recent article, methods were provided to compute the exact first and second order inclusion probabilities numerically when the distribution shape is of the Pareto type. In the same article, procedures were also provided for this case to adjust the parameters to get predetermined inclusion probabilities. In this paper we prove the existence and uniqueness of a solution for the latter problem, in general for any order sampling of fixed distribution shape.     

Empirical investigation about statistical properties of abundance estimates based on line-intercept and network sampling of tracks

Line-intercept sampling (Becker, 1991) and network sampling (Becker et al., 1998) seem to be the most appropriate procedures for estimating animal abundance in a study area on the basis of tracks. The purpose of this paper is to investigate the statistical properties of these alternative procedures by constructing confidence intervals for abundance and comparing the interval performances in terms of width and coverage.     

The Horvitz-Thompson Theorem as a Unifying Perspective for Probability Sampling: With Examples from Natural Resource Sampling

Courses in sampling often lack a coherent structure because many related sampling designs, estimators, variances, and variance estimators are presented as separate cases. The Horvitz-Thompson theorem offers a needed integrating perspective for teaching the methods and fundamental concepts of probability sampling. Development of basic concepts in sampling via this approach provides the student with tools to solve more complicated problems, and helps to avoid some common stumbling blocks of beginning students. Examples from natural resource sampling are provided to illustrate applications and insight gained from this approach.     

A perspective of composite sampling

Composite samples are formed by physically mixing samples. Usually, composite samples are used to reduce the overall cost associated with analytical procedures that must be performed on each sample, but they can also be used to protect the privacy of individuals.

Composite sampling can reduce the cost of identifying individual cases that have a certain trait, such as those with a rare disease or those exceeding pollution-level standards. Not much is lost by applying this method as long as the trait is relatively rare.

Composite sampling can reduce the cost of estimating the mean of some process. When samples are composited, the ability to estimate the variance is lost. In spite of this, the potential savings are so great that composite samples have been used.

Much of this paper deasl with the variance of estimators based on composite sampling when the porportions of hte original samples comprising the composite sample are actually random. Taking repeated samples and measurements on several composite samples complicates the prodcedure, but allows the estimation of between and within variation as well as measurement error.     

A characteristic function approach to the biased sampling model,with application to robust logistic regression

Many sampling problems from multiple populations can be considered under the semiparametric framework of the biased, or weighted, sampling model. Included under this framework is logistic regression under case–control sampling. For any model, atypical observations can greatly influence the maximum likelihood estimate of the parameters. Several robust alternatives have been proposed for the special case of logistic regression. However, some current techniques can exhibit poor behavior in many common situations. In this paper a new family of procedures are constructed to estimate the parameters in the semiparametric biased sampling model. The procedures incorporate a minimum distance approach, but are instead based on characteristic functions. The estimators can also be represented as the minimizers of quadratic forms in simple residuals, thus yielding straightforward computation. For the case of logistic regression, the resulting estimators are shown to be competitive with the existing robust approaches in terms of both robustness and efficiency, while maintaining affine equivariance. The approach is developed under the case–control sampling scheme, yet is shown to be applicable under prospective sampling logistic regression as well.     

Survey sampling in graphs

The Horvitz-Thompson estimation theory is applied to snowball sampling and some other sampling procedures using a known or unknown graph structure in the survey population. In particular, simple graph-parameter estimators and variance estimators are obtained which are based on various kinds of partial information about the graph.     

Design and analysis of two-phase studies with binary outcome applied to Wilms tumour prognosis

Two-phase stratified sampling is used to select subjects for the collection of additional data, e.g. validation data in measurement error problems. Stratification jointly by outcome and covariates, with sampling fractions chosen to achieve approximately equal numbers per stratum at the second phase of sampling, enhances efficiency compared with stratification based on the outcome or covariates alone. Nonparametric maximum likelihood may result in substantially more efficient estimates of logistic regression coefficients than weighted or pseudolikelihood procedures. Software to implement all three procedures is available. We demonstrate the practical importance of these design and analysis principles by an analysis of, and simulations based on, data from the US National Wilms Tumor Study.     

Estimation of a rare sensitive attribute in a stratified two-stage unrelated randomized response model by using Poisson probability distribution

The present article deals with the estimation of mean number of respondents who possess a rare sensitive character in presence of known and unknown proportion of a rare unrelated non-sensitive attribute by using the Poisson probability distribution in stratified random sampling as well as in stratified random double sampling. The variance of rare sensitive character is also derived under proportional and optimal allocation methods in stratified random sampling when stratum sizes are known and unknown. The properties of the suggested estimation procedures have been deeply examined. The proposed model is found to be dominant over Lee et al. [Estimation of a rare sensitive attribute in a stratified sample using Poisson distribution. Statistics. 2013;47:575–589] model. Numerical illustrations are presented to support the theoretical results. Results are analysed and suitable recommendations are put forward to the survey practitioners.     

Lower bounds for confidence coefficients for confidence intervals for finite population quantiles

Assuming stratified simple random sampling, a confidence interval for a finite population quantile may be desired. Using a confidence interval with endpoints given by order statistics from the combined stratified sample, several procedures to obtain lower bounds (and approximations for the lower bounds) for the confidence coefficients are presented. The procedures differ with respect to the amount of prior information assumed about the var-iate values in the finite population, and the extent to which sample data is used to estimate the lower bounds.     

Bayesian Design of Special Type of Double Sampling Plans for Compliance Testing

Bayesian acceptance sampling plans, which utilize prior information on the process variation, can be employed as an alternative to conventional types of plans for taking decisions on the disposition of submitted lots. A special type of double sampling inspection plans by attributes with small acceptance numbers using Bayesian methodology is presented in this paper emphasizing its significance over small acceptance number single sampling plans. The procedures for designing such sampling plans for specified degree of discrimination which would ensure protection to the producer and consumer are discussed with illustrations under the conditions for the application of gamma-Poisson distribution.     

Simulation algorithms for integrals of a class of sampling distributions arising in population genetics

Efficient stochastic algorithms are presented in order to simulate allele configurations distributed according to a family π _A , 0<A<∞, of exchangeable sampling distributions arising in population genetics. Each distribution π _A has two parameters n and k, the sample size and the number of alleles, respectively. For A→0, the distribution π _A is induced from neutral sampling, whereas for A→∞, it is induced from Maxwell–Boltzmann sampling. Three different Monte Carlo methods (independent sampling procedures) are provided, based on conditioning, sequential methods and a generalization of Pitmans ‘Chinese restaurant process’. Moreover, an efficient Markov chain Monte Carlo method is provided. The algorithms are applied to the homozygosity test and to the Ewens–Watterson–Slatkin test in order to test the hypothesis of selective neutrality.     

Numerical techniques for estimating probabilities

In this article we consider the pioblem of finding the maximum likelihood estimate for a certain class of discrete sampling models. Methods are adapted from parts of convex optimization theory, includiug aspects of equivalence theory, duality theorv and iterative procedures Their application is illustrated through example.