Simple random sample equivalent survey designs reducing undesirable units from a finite population

In this paper, we consider fixed size sampling plans for which the first order inclusion probabilities are identical for all units and the second order inclusion probabilities are constant for every pair-wise unit. The statistical conditions are identified under which these plans are equivalent to the usual simple random sampling plan. These sampling plans are constructed to reduce undesirable units.     

Relative efficienctes of sampling plans for selecting a small number of units from a rectangular region

We examine the efficiency of several sampling plans for use in certain agricultural, ecological and environmental studies. One concern for such studies is that plots that arephysically close might be more similar than distant plots. We considered sampling plansthat are designed to generate samples that represent the entire population while avoidingthe selection of units that provide essentially redundant information. All plans havethe property that they avoid the simultaneous selection of units that are, in some sense,neighboring units. By means of a simulation study, the efficiency of these plans iscompared to simple random Aampling Factors that influence the relative efficiencies areexamined. This is done for a number of different populations, representing variouspossible patterns for a response variable.     

Two-dimensional balanced sampling plans excluding adjacent units under sharing a border and island adjacency schemes

In Balanced Sampling Plans Excluding Adjacent Units (BSA plans) first order inclusion probabilities are equal and second order inclusion probabilities are zero for pairs of units at a distance less than or equal to m and are constant for pairs of units which are at a distance greater than m. These plans are useful when the adjacent units in the population provide similar information. In this paper, an algorithm based on linear programming approach has been developed for construction of two-dimensional BSA plans under sharing a border and island adjacency schemes for m ≤ 2. Some results on existence of such BSA plans have also been obtained for each adjacency scheme separately.     

Accuracy of approximate progressively censored reliability sampling plans for exponential models

Reliability sampling plans provide an efficient method to determine the acceptability of a product based upon the lifelengths of some test units. Usually, they depend on the producer and consumer’s quality requirements and do not admit closed form solutions. Acceptance sampling plans for one- and two-parameter exponential lifetime models, derived by approximating the operating characteristic curve, are presented in this paper. The accuracy of these approximate plans, which are explicitly expressible and valid for failure and progressive censoring, is assessed. The approximation proposed in the one-parameter case is found to be practically exact. Explicit lower and upper bounds on the smallest sample size are given in the two-parameter case. Some additional advantages are also pointed out.     

Two-dimensional balanced sampling plans excluding adjacent units

Hedayat et al. [Sampling plans excluding contiguous units. J. Statist. Plann. Inference 19, 159–170, Designs in survey sampling avoiding contiguous units. In: Krishnaiah, P.R., Rao, C.R. (Eds.), Handbook of Statistics, vol. 6. Elsevier, Amsterdam, pp. 575–583] first introduced balanced sampling plans for the exclusion of contiguous units. Sampling plans that excluded the selection of contiguous units within a given sample, while maintaining a constant second-order inclusion probability for non-contiguous units, were investigated for finite populations of N units arranged in a circular, one-dimensional ordering. While significant advancements have been made in the identification and generalizations of such plans—commonly referred to as BSA sampling plans—little is known concerning the extension of such sampling plans to multi-dimensional populations. This paper will present a review of the pertinent results of one-dimensional BSA sampling plans and a discussion concerning the properties of two-dimensional BSA sampling plans.     

Inference for a Linear Functional of Cumulative Hazard Function Via Empirical Likelihood

This article discusses sampling plans, that is, the allocation of sampling units, for computing tolerance limits in a balanced one--way random-effects model. The expected width of the tolerance interval is derived and used as the basis for comparing different sampling plans. A well-known cost function and examples are used to facilitate the discussion.     

Reliability sampling plans for the Weibull distribution under Type II progressive censoring with binomial removals

This paper presents reliability sampling plans for the Weibull distribution under Type II progressive censoring with random removals (PCR), where the number of units removed at each failure time follows a binomial distribution. To construct the sampling plans, the sample size n and the acceptance constant k are determined based on asymptotic distribution theory. The resulting sampling plans are tabulated for selected specifications under the proposed censoring scheme. Furthermore, a Monte Carlo simulation is conducted to validate the true probability of acceptance for the designed sampling plans.     

New balanced sampling plans excluding adjacent units

Hedayat et al. [1988a. Sampling plans excluding contiguous units. J. Statist. Plann. Inference 19, 159–170; 1988b. Designs in survey sampling avoiding contiguous units. In: Krishnaiah, P.R., Rao, C.R. (Eds.). Handbook of Statistics, vol. 6. Elsevier, Amsterdam, pp. 575–583] first introduced balanced sampling designs for the exclusion of contiguous units. Sampling plans that excluded the selection of contiguous units within a given sample, while maintaining a constant second-order inclusion probability for non-contiguous units, were investigated for finite populations of N units arranged in a circular, one-dimensional ordering. There remain many open questions about the existence of such plans and their extension to plans excluding adjacent units. We present new generation techniques and new balanced sampling plans for the exclusion of adjacent units under finite, one-dimensional, circularly and linearly ordered populations.     

Minimum Variance and VOQL Chain Sampling Plans–ChSP-4(c 1, c 2)

In this article the outgoing quality and the total inspection for the chain sampling plan ChSP-4(c ₁, c ₂) are introduced as well-defined random variables. The probability distributions of outgoing quality and total inspection are stated based on total rectification of non conforming units. The variances of these random variables are studied. The aim of this article is to develop procedures for minimum variance ChSP-4(c ₁, c ₂) sampling plans and their determination. In addition to minimum variance sampling plans, a procedure is developed for designing plans with a designated maximum variance, a VOQL (Variance of Outgoing Quality Limit) plan. The VOQL concept is analogous to the AOQL (Average Outgoing Quality Limit) except in the VOQL plan, it is the maximum variance which is established instead of the usual maximum AOQ.     

Cyclic Polygonal Designs with Block Size 3 and Joint Distance α = 2

Polygonal designs are useful in survey sampling in terms of balanced sampling plans excluding contiguous units (BSECs) and balanced sampling plans excluding adjacent units (BSAs). In this article, the method of cyclic shifts has been used for the construction of cyclic polygonal designs (in terms of BSAs) with block size k = 3 and λ = 1, 2, 3, 4, 6, 12 for joint distance α = 2 and 51 new designs for treatments v ≤ 100 are given.     

Determination of single sampling attributes plans for given (aql. aoql)

This paper presents tables and a computer program for determining single sampling plans for given AQL, producer's risk and AOQL for the case of nonconforming units and nonconformities. Comparison with Soundararajan's (1981) procedures for selection of single sampling plans for given (AQL, AOQL) is also given     

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     

Bayesian acceptance sampling plans following economic criteria: An application to paper pulp manufacturing

The main purposes of this paper are to derive Bayesian acceptance sampling plans regarding the number of defects per unit of product, and to illustrate how to apply the methodology to the paper pulp industry. The sampling plans are obtained following an economic criterion: minimize the expected total cost of quality. It has been assumed that the number of defects per unit of product follows a Poisson distribution with process average 5 , whose prior information is described either for a gamma or for a non- informative distribution. The expected total cost of quality is composed of three independent components: inspection, acceptance and rejection. Both quadratic and step-loss functions have been used to quantify the cost incurred for the acceptance of a lot containing units with defects. Combining the prior information on 5 with the loss functions, four different sampling plans are obtained. When the quadratic-loss function is used, an analytical relation between the optimum settings of the sample size and the acceptance number is derived. The robustness analysis indicates that the sampling plans obtained are robust with respect to the prior distribution of the process average as well as to the misspecification of its mean and variance.     

Acceptance Sampling Plans from Truncated Life Tests Based on the Generalized Birnbaum–Saunders Distribution

In this article, we develop acceptance sampling plans when the life test is truncated at a pre-fixed time. The minimum sample size necessary to ensure the specified median life is obtained by assuming that the lifetimes of the test units follow a generalized Birnbaum–Saunders distribution. The operating characteristic values of the sampling plans as well as producer's risk are presented. Two examples are also given to illustrate the procedure developed here, with one of them being based on a real data from software reliability.     

On the performance of a sampling scheme in statistical quality control using incomplete prior information

Assume that a lower bound is known for the probability that the fraction defective of incoming lots does not exceed a certain level. Sampling plans which incorporate this information have been developed by Krumbholz and Schröder. Taking a linear cost model, the range of the gains that may be achieved using these plans instead of the minimax sampling plan is discussed. Some technical results concerning existence and uniqueness of sampling plans based on incomplete prior information are proved.     

Interval censored sampling plans for the log-logistic lifetime distribution

The log-logistic distribution is one of the popular distributions in life-testing applications. This article develops an acceptance sampling procedure for the log-logistic lifetime distribution based on grouped data when the shape parameter is given. Both producer and consumer risks are considered to develop the ordinary, approximate and simulated sampling plans. Some of the proposed sampling plans are tabulated; moreover, those three types of sampling plans are compared with each other under the same censoring rates. The use of these tables is illustrated by an example.     

Reliability sampling plans for the two-parameter exponential distribution under progressive censoring

This paper presents reliability sampling plans for the two-parameter exponential distribution under progressive censoring. These sampling plans are quite useful to practitioners, because they provide savings in resources and in total test time. Furthermore, they off er the flexibility to remove functioning test specimens from further testing at various stages of the experimentation. In the construction of these sampling plans, the operating characteristic curve is derived using the exact distributional properties of maximum likelihood estimators. An example is given to illustrate the application of the proposed sampling plans.     

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.     

Partial groups ranked set sampling and mean estimation

Ranked set sampling (RSS) is an advanced sampling method which is very effective for estimating mean of the population when exact measurement of observation is difficult and/or expensive. Balanced Groups RSS (BGRSS) is one of the modification of RSS where only the lowest, the median and the largest ranked units are taken into account. Although BGRSS is advantageous and useful for some specific cases, it has strict restrictions regarding the set size which could be problematic for sampling plans. In this study, we make an improvement on BGRSS and propose a new design called Partial Groups RSS which offers a more flexible sampling plan providing the independence of the set size and sample size. Partial Groups RSS also has a cost advantage over BGRSS. We construct a Monte Carlo simulation study comparing the performance of the mean estimators of the proposed sampling design and BGRSS according to their sampling costs and mean squared errors for various type of distributions. In addition, we give a biometric data application for investigating the efficiency of Partial Groups RSS in real life applications.     

Improved attribute acceptance sampling plans based on maxima nomination sampling

This paper demonstrates the use of maxima nomination sampling (MNS) technique in design and evaluation of single AQL, LTPD, and EQL acceptance sampling plans for attributes. We exploit the effect of sample size and acceptance number on the performance of our proposed MNS plans using operating characteristic (OC) curve. Among other results, we show that MNS acceptance sampling plans with smaller sample size and bigger acceptance number perform better than commonly used acceptance sampling plans for attributes based on simple random sampling (SRS) technique. Indeed, MNS acceptance sampling plans result in OC curves which, compared to their SRS counterparts, are much closer to the ideal OC curve. A computer program is designed which can be used to specify the optimum MNS acceptance sampling plan and to show, visually, how the shape of the OC curve changes when parameters of the acceptance sampling plan vary. Theoretical results and numerical evaluations are given.