Attribute Acceptance Sampling Research Articles

Design of Fuzzy Sampling Plan Using the Birnbaum-Saunders Distribution

Acceptance sampling is one of the essential areas of quality control. In a conventional environment, probability theory is used to study acceptance sampling plans. In some situations, it is not possible to apply conventional techniques due to vagueness in the values emerging from the complexities of processor measurement methods. There are two types of acceptance sampling plans: attribute and variable. One of the important elements in attribute acceptance sampling is the proportion of defective items. In some situations, this proportion is not a precise value, but vague. In this case, it is suitable to apply flexible techniques to study the fuzzy proportion. Fuzzy set theory is used to investigate such concepts. It is observed there is no research available to apply Birnbaum-Saunders distribution in fuzzy acceptance sampling. In this article, it is assumed that the proportion of defective items is fuzzy and follows the Birnbaum-Saunders distribution. A single acceptance sampling plan, based on binomial distribution, is used to design the fuzzy operating characteristic (FOC) curve. Results are illustrated with examples. One real-life example is also presented in the article. The results show the behavior of curves with different combinations of parameters of Birnbaum-Saunders distribution. The novelty of this study is to use the probability distribution function of Birnbaum-Saunders distribution as a proportion of defective items and find the acceptance probability in a fuzzy environment. This is an application of Birnbaum-Saunders distribution in fuzzy acceptance sampling.

Acceptance sampling for attributes via hypothesis testing and the hypergeometric distribution

This paper questions some aspects of attribute acceptance sampling in light of the original concepts of hypothesis testing from Neyman and Pearson (NP). Attribute acceptance sampling in industry, as developed by Dodge and Romig (DR), generally follows the international standards of ISO 2859, and similarly the Brazilian standards NBR 5425 to NBR 5427 and the United States Standards ANSI/ASQC Z1.4. The paper evaluates and extends the area of acceptance sampling in two directions. First, by suggesting the use of the hypergeometric distribution to calculate the parameters of sampling plans avoiding the unnecessary use of approximations such as the binomial or Poisson distributions. We show that, under usual conditions, discrepancies can be large. The conclusion is that the hypergeometric distribution, ubiquitously available in commonly used software, is more appropriate than other distributions for acceptance sampling. Second, and more importantly, we elaborate the theory of acceptance sampling in terms of hypothesis testing rigorously following the original concepts of NP. By offering a common theoretical structure, hypothesis testing from NP can produce a better understanding of applications even beyond the usual areas of industry and commerce such as public health and political polling. With the new procedures, both sample size and sample error can be reduced. What is unclear in traditional acceptance sampling is the necessity of linking the acceptable quality limit (AQL) exclusively to the producer and the lot quality percent defective (LTPD) exclusively to the consumer. In reality, the consumer should also be preoccupied with a value of AQL, as should the producer with LTPD. Furthermore, we can also question why type I error is always uniquely associated with the producer as producer risk, and likewise, the same question arises with consumer risk which is necessarily associated with type II error. The resolution of these questions is new to the literature. The article presents R code throughout.

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.

Attribute Acceptance Sampling as a Tool for Verifying Requirements Using Monte Carlo Simulation

ABSTRACT Developed by quality engineers as an efficient statistical approach to verifying the acceptability of procured items within production environments, acceptance sampling can be generalized to other verification problems which similarly rely on the outcomes of stochastic sampling experiments. This article illustrates how the techniques and perspectives of attribute acceptance sampling can be adapted to the verification of probabilistic design requirements using Monte Carlo simulation. We consider requirements expressed as limit standards, specifying the performance indicator for conforming Monte Carlo trials; the minimum limiting proportion of conforming trials; and the maximum risk of accepting a nonconforming design. For such requirements, an attribute sampling plan prescribes the number of simulation replications that must be run and the number of nonconforming replications that can not be exceeded. The derivation and analysis of single-sample attribute acceptance plans for the mass-delivery requirement for NASA's Constellation Program (CxP) is provided as an example. More demanding (but potentially more efficient) alternatives to attribute acceptance sampling are suggested for applications with limited budgets for simulation trials.

An optimization‐based approach for designing attribute acceptance sampling plans

PurposeThis purpose of this paper is to present an optimization‐based approach to support the design of attribute sampling plans for lot acceptance purposes, with the fraction of non‐conforming items being modeled by a Poisson probability distribution function.Design/methodology/approachThe paper approach stands upon the minimization of the error of the probability of acceptance equalities in the controlled points of the operating curve (OC) with respect to sample size and acceptance number. It was applied to simple and double sampling plans, including several combinations of quality levels required by the producer and the consumer. Formulation of the design of acceptance sampling plans as an optimization problem, having as a goal the minimization of the squared error at the controlled points of the OC curve, and its subsequent solution employing GAMS.FindingsThe results are in strong agreement with acceptance sampling plans available in the open literature. The papers approach in some scenarios outperforms classical sampling plans and allows one to identify the lack of feasible solutions.Originality/valueAn optimization‐based approach to support the design of acceptance sampling plans for attributes was conceived and tested. It allows for a general treatment of these problems, including the identification of a lack of feasible solutions, as well as making possible the determination of feasible alternatives by relaxing some model constraints.

Studying the Effect of the Parameters of an Attribute Acceptance Sampling Plan on its Operating Characteristic Curve: A Visual Approach

In this article, a very simple and yet useful feature of Excel called the SPIN BUTTON is used to illustrate two concepts associated with attribute acceptance sampling plans. The first concept is calculating the probability of lot acceptance based on which the operating characteristic (OC) curve of an attribute sampling plan is drawn. The SPIN BUTTON can show, visually, that the exact probability of lot acceptance calculated using the Hypergeometric distribution can be approximated by the Binomial distribution. The second concept is how the probability of lot acceptance changes when either one of the three parameters N, n, c of a sampling plan changes. The SPIN BUTTON can also visually show us how the shape of the OC curve of a sampling plan changes when the parameters vary.

Improved attribute acceptance sampling plans in the presence of misclassification error

This paper considers an attribute acceptance sampling problem in which inspection errors can occur. Unlike many common situations, the source of the inspection errors is the uncertainty associated with statistical sampling. Consider a lot that consists of N containers, with each container including a large number of units. It is desired to sample some of the containers and inspect a sample of units from these selected containers to determine proper disposition of the entire lot. Results presented in the paper demonstrate significant shortcomings in traditional sampling plans when applied in this context. Alternative sampling plans designed to address the risk of statistical classification error are presented. These plans estimate the rate of classification errors and set plan parameters to reduce the potential impact of such errors. Results are provided comparing traditional plans with the proposed alternatives. Limitations of the new plans are also discussed.

Generalized Attribute Acceptance Sampling Plans

The imposition of acceptance criteria upon realizations of generalized sampling plans is described and shown to yield a large variety of new attribute acceptance sampling plans. The resulting generalized attribute acceptance sampling plans can be constr..

Joint Determination of Optimal Inventory and Quality Control Policy

Typically the operating policy for the inventory control system for a commodity is developed independent of the operating policy for the quality control system for that commodity and vice versa. In many circumstances, these systems are dependent on one another. A cost model that combines a fixed order quantity inventory control system with a Bayesian quality control system for a lot-by-lot attribute acceptance sampling plan is presented along with an algorithm to obtain the operating parameters for the combined systems. Behavior of the combined systems is investigated, and the costs and operating policy determined using this model are compared with the costs and operating policy determined when there is no integration of the two systems and when there is partial integration of the two systems. There are significant cost savings obtained by using the operating policy developed under the combined systems over the operating policy derived from the separate systems.

A Performance Approach to Attribute Sampling and Multiple Action Decisions

Abstract This paper describes the basic concepts and philosophies of an improved approach to attribute acceptance sampling, which has been tested successfully since 1971. The main measures of performance are expected outgoing quality and expected quality assurance cost. Boundary curves help portray feasibilities of quality-cost combinations, which leads to selections among Pareto optimal sampling plans. Quality and Cost effects are quantified by few parameters which represent situations such as: destructive or nondestructive sampling; effectiveness in finding and correcting defects; reworking vs. scrapping, etc. The model is structured as a Markov Decision Problem, with transition probabilities between sampling stages given by Bayesian estimates, with optimal solutions obtained through Dynamic Programming, with constraints to represent contractual restrictions, and with directed steps to evaluate given sampling plans. Practical applications require computer support.

The distribution of observed defectives in attribute acceptance sampling plans under inspection error : Collins, R.D., and Case, K.E.AIIE Transactions, Sep 1976, 8.3, 375–378

The distribution of observed defectives in attribute acceptance sampling plans under inspection error : Collins, R.D., and Case, K.E.AIIE Transactions, Sep 1976, 8.3, 375–378

The Distribution of Observed Defectives in Attribute Acceptance Sampling Plans Under Inspection Error

Abstract The Type B Operating Characteristic curve in attributes acceptance sampling is simply the probability of lot acceptance versus process fraction defective. The binomial mass function is appropriate for assessing this acceptance probability. Articles on inspection error in attributes acceptance sampling frequently assume the marginal distribution of the number of observed defectives in the sample is binomial with the true fraction defective replaced by the apparent fraction defective. This assumption, however, has been questioned and it is the object of this paper to show explicitly that the existing literature is quite correct. Following this development, additional results are presented which may be useful to others performing research in this area.

Acceptance sampling by exponential smoothing

Acceptance sampling by exponential smoothing presents a concept whereby each lot is accepted or rejected through interrogation of the current lot and all prior lots submitted. The number of defectives of a lot, in conjunction with historical results, is transformed to a quality index by simple exponential smoothing, utilizing larger values of the smoothing constant to lend more weight to the quality of current lots inspected. This quality index is compared with a predetermined threshold index to determine if the lot is to be accepted or rejected. This quality index is then retained to be used as the historical quality information to be applied to the quality index of the next lot. An important feature of the exponential smoothing technique is that an attribute quality can be transformed easily into a measurement quality. This allows the user to select an acceptance quality level at any producer's risk. Further, the OC curve can be forced through any other point by selecting the proper smoothing constant. The obvious limitation in the use of this technique is that the transformed variable—quality index—does not follow a known statistical distribution. This necessitates that simulation methods be used on the digital computer to derive OC curves for specified values of n and α. However, for the conditions of large n and large α, the transformed random variable is approximately normally distributed, giving an approximate normal solution for a plan of interest. It is anticipated that attribute acceptance sampling utilizing any quality index other than proportion defective will be viewed with suspicion by the average user. In this sense the exponential smoothing concept violates a basic precept of Dodge (1955) in that an effective plan must be a simple plan that the non-theoretician can understand and apply with reasonable confidence. However, the flexibility in the selection of OC curves, the utilization of prior lot information, and the ease of application dictate that the concept be given serious consideration as a cost reduction tool in acceptance sampling.