Acceptance Sampling Procedures Research Articles

Reliability acceptance sampling procedures characterized with compound class of exponential–logarithmic distribution

Reliability acceptance sampling procedures characterized with compound class of exponential–logarithmic distribution

Determination of Optimum Sample Size for Lot Acceptance Attribute Sampling under Life Tests Based On Rayleigh Distribution Using Graphical Evaluation Review Technique (GERT)

This paper presents the graphical evaluation and review technique (GERT) exploration of performance measures for lot acceptance sampling procedures having attribute characteristics following life tests based on percentiles of Rayleigh Distribution and henceforth determining optimum sampling size. The advantageous implications of GERT analysis in this framework is primarily to visualize the dynamics of the sampling inspection system and secondly, critical analysis of sampling procedure characteristics. The formula of operating characteristics (OC) function and average sample number (ASN) function is derived and illustrated numerically. Lastly, tables have been provided to determine the optimum sample size assuring certain mean life or quality of the product.

Multistage acceptance sampling under nonparametric dependent sampling designs

The evaluation of a set of objects, e.g. items of a production lot, in terms of a random measurement, such that the decision is statistically designed to control the probability of false decisions considered as a function of the fraction of measurements falling below a threshold, can be conducted by acceptance sampling procedures. These methods are typically studied for the quality control problem to accept or reject a lot of produced items. This paper provides an extension of the acceptance sampling methodology to a multi-stage framework where a lot is inspected at several time points and only accepted if it passes all stages. The resulting sampling plans allow to specify both the stage-wise and overall error probabilities and can be calculated before inspections start. Going beyond the case of independent random samples drawn at each inspection time, we consider a panel type design resulting in a dependent sampling scheme. Based on asymptotic approximations we provide explicit formulas for the proposed sampling plans and an effective recursive algorithm for their calculation. The theoretical results cover consistency and asymptotic optimality of the sampling plans as well as a central limit theorem. The statistical properties of the approach are studied by simulations.

The role of inference in food safety

Author Summary: Concerned individuals have been trying to determine the safety of their food since ancient times. In ancient times, people themselves were the ultimate test of food safety, but as human evolution progressed, other techniques such as sensory perception and experimentation on animals were used. Today sophisticated analytical techniques and models are available to measure and predict food safety. These sophisticated techniques and models are dependent not only on the quality of samples that are collected and analyzed but also on how inferences are made from the analytical results to the food being sampled. Unfortunately, the Theory of Sampling and the role of inference have not been fully integrated into prediction of food safety.The basis for many "modern" food sampling protocols was developed prior to the development of the Theory of Sampling. Many of these sampling protocols were based on concepts of acceptance sampling procedures and associated inference. The Theory of Sampling enables the representative sampling of bulk materials and eliminates the reliance of acceptance sampling as the only method for the characterization of food and utilizes a different type of inference than for acceptance sampling. This contribution addresses the differences between inference for acceptance sampling and inference for the sampling of bulk materials and the implications of these differences for food safety.

Framework for Managing Mycotoxin Risks in the Food Industry

We propose a methodological framework for managing mycotoxin risks in the food processing industry. Mycotoxin contamination is a well-known threat to public health that has economic significance for the food processing industry; it is imperative to address mycotoxin risks holistically, at all points in the procurement, processing, and distribution pipeline, by tracking the relevant data, adopting best practices, and providing suitable adaptive controls. The proposed framework includes (i) an information and data repository, (ii) a collaborative infrastructure with analysis and simulation tools, (iii) standardized testing and acceptance sampling procedures, and (iv) processes that link the risk assessments and testing results to the sourcing, production, and product release steps. The implementation of suitable acceptance sampling protocols for mycotoxin testing is considered in some detail.

Exact inferences of the two-parameter exponential distribution and Pareto distribution with censored data

We develop an exact inference for the location and the scale parameters of the two-exponential distribution and the Pareto distribution based on their maximum-likelihood estimators from the doubly Type-II and the progressive Type-II censored sample. Based on some pivotal quantities, exact confidence intervals and tests of hypotheses are constructed. Exact distributions of the pivotal quantities are expressed as mixtures of linear combinations and of ratios of linear combinations of standard exponential random variables, which facilitates the computation of quantiles of these pivotal quantities. We also provide a bootstrap method for constructing a confidence interval. Some simulation studies are carried out to assess their performances. Using the exact distribution of the scale parameter, we establish an acceptance sampling procedure based on the lifetime of the unit. Some numerical results are tabulated for the illustration. One biometrical example is also given to illustrate the proposed methods.

“An AQL System for Lot-By-Lot Acceptance Sampling By Attributes Selecting an O.C.Curve”

The choice among various possible types of acceptance inspection procedures is essentially an economic one. In making a decision regarding acceptance inspection for any particular purpose, it may be desirable to consider not only various possible systems or procedures of acceptance sampling by attributes but also the alternatives of (1) no inspection at all, but imposition of a requirement that statistical evidence of satisfactory quality be provided with each lot; (2) 100% inspection; and (3) possibilities of acceptance sampling by variables. It also is true that a satisfactory evaluation of all the pertinent economic factors is often quite difficult. For this reason, the choice of an acceptance procedure is commonly made on an intuitive basis. An important element of the selection of an acceptance inspection procedure should be the probable contribution of the procedure to quality improvement. The acceptance sampling systems and procedures described in this and the following chapters have often been strikingly successful in leading to such improvements.

Construction and Selection of Bayesian Chain Sampling Plan (BChSP-1) Using Quality Regions

Bayesian Acceptance Sampling Approach is associated with utilization of prior process history for the selection of Distributions (viz., Gamma Poisson, Beta Binomial) to describe the random fluctuations involved in Acceptance Sampling. The Acceptance sampling procedures are the practical tools for quality assurance applications involving product control. Acceptance sampling systems are advocated when small sample size are necessary or desirable towards costlier testing for product quality. The sampling plan which provides the vendor and buyer decision rules for product acceptance to meet the preset product quality requirement.The main thrust of this paper is to account for the possibility of dependence among the items of a sample. The development of new method for designing sampling plans based on range of quality instead of point- wise description of quality by invoking a novel approach called Quality Regions. This method seems to be versatile and can be adopted to the elementary production process where the stipulated quality level is advisable to fix at a later stage and provides a new procedure meant for designing Bayesian Chain Sampling Plan involving Quality Regions. Maximum Allowable Percent Defective (MAPD) is also considered for the selection of parameters for Bayesian Chain Sampling Plan. New quality descriptors called operating ratios are introduced to design the sampling plan.

New statistical distributions for group counting in Bernoulli and Poisson processes

Based on a sequential group sampling procedure, the authors introduce a new statistical distribution for group-by-group counting for Bernoulli processes. Suppose that a population contains an infinite number of items, each item having probability p for nonconformity and probability 1−p for conformity. Items are inspected group by group, where each group contains m items, and the number of nonconforming items are recorded only when inspection of a group is completed. The inspection procedure is terminated if the cumulative number of nonconforming items recorded is greater than or equal to a specified number r. The distribution introduced in this paper consists of two random variables: the number of groups inspected, K, and the cumulative number of nonconforming items observed, X. Statistical properties and inferences for the bivariate distribution of (K,X) are studied. The authors also discuss the limiting case as m→∞ and p→0 with mp fixed, and derive a new bivariate distribution for group-by-group counting for Poisson processes that approaches the gamma distribution in limit. A new type of control chart and an acceptance sampling procedure are developed based on (K,X), and examples are given to illustrate their applications.

Bayesian forecasting with the Holt–Winters model

Exponential smoothing methods are widely used as forecasting techniques in inventory systems and business planning, where reliable prediction intervals are also required for a large number of series. This paper describes a Bayesian forecasting approach based on the Holt–Winters model, which allows obtaining accurate prediction intervals. We show how to build them incorporating the uncertainty due to the smoothing unknowns using a linear heteroscedastic model. That linear formulation simplifies obtaining the posterior distribution on the unknowns; a random sample from such posterior, which is not analytical, is provided using an acceptance sampling procedure and a Monte Carlo approach gives the predictive distributions. On the basis of this scheme, point-wise forecasts and prediction intervals are obtained. The accuracy of the proposed Bayesian forecasting approach for building prediction intervals is tested using the 3003 time series from the M3-competition.

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.

Interval censored sampling plans for the gamma lifetime model

In this article, an acceptance sampling procedure for the gamma lifetime model is established under the interval censored test. Both producer and consumer risks are considered to develop the ordinary and approximate sampling plans with grouped data. Some of the proposed sampling plans are tabulated and the use of the tables is illustrated by an example. A sensitivity study is conducted to evaluate the influence of the length of the time interval on the proposed sampling plans.

Multivariate exponential smoothing: A Bayesian forecast approach based on simulation

This paper deals with the prediction of time series with correlated errors at each time point using a Bayesian forecast approach based on the multivariate Holt–Winters model. Assuming that each of the univariate time series comes from the univariate Holt–Winters model, all of them sharing a common structure, the multivariate Holt–Winters model can be formulated as a traditional multivariate regression model. This formulation facilitates obtaining the posterior distribution of the model parameters, which is not analytically tractable: simulation is needed. An acceptance sampling procedure is used in order to obtain a sample from this posterior distribution. Using Monte Carlo integration the predictive distribution is then approached. The forecasting performance of this procedure is illustrated using the hotel occupancy time series data from three provinces in Spain.

THE INSPECTION OF ACCEPTANCE SAMPLING FOR STEP-STRESS TESTS WITH AN EQUALLY-SPACED INTERVAL CENSORING SCHEME

For reducing the experimental time and considering the purpose of administrative convenience, the article establishes an acceptance sampling procedure for the Rayleigh lifetime distribution under a step-stress test with an equally-spaced interval censoring scheme. Both producer and consumer risks are considered and an algorithm is provided to develop the ordinary acceptance sampling plans. A numerical study is conducted for evaluating the performance of the proposed method. Moreover, a numerical example is used for illustration.

Acceptance Sampling Procedures for Ballistic Dispersion

The quality assurance testing of ammunition lots is a critical function of any ammunition procurement program. One important component of these procedures is a test for ballistic dispersion. In the case where dispersion is consistent with a circular normal distribution, this paper argues that the existing tests used by American and Canadian Departments of Defence are not as powerful as they could be. The increased power of the new test is measured using the example of 25mm APFSDS ammunition.

A Study on the Behavior of Operating Characteristic Curves of Sampling Plans Based on Polya Distribution

SYNOPTIC ABSTRACTAn implicit assumption that is made in the use of binomial distribution for number of non-conforming units under acceptance sampling procedures is that the dispersion about the process fraction non-conforming (p) or process average () is zero. When this assumption is violated or when an amount of dispersion around is present, the Polya distribution is an appropriate choice for assessing the performance of sampling plans. The Polya distribution is arrived by integrating the product of beta process distribution and the binomial sampling distribution over p. This paper presents the operating characteristic (OC) fonction of single sampling plans by attributes under the conditions of Polya distribution. An empirical study is also made on the behavior of Polya OC curves with respect to various sets of parameters.

Analysis of Operating Characteristic Curves of Gamma-Poisson Sampling Plans

SYNOPTIC ABSTRACTThe performance of acceptance sampling procedures is usually assessed through the operating characteristic (OC) curves based on the assumption that the number of defects per unit is modeled by the Poisson distribution. The Poisson distribution is defined with reference to the fixed parameter λ, representing the expected number of defects per unit. When λ is assumed to vary at random from lot-to-lot, the gamma distribution is a suitable prior distribution for λ. In this paper, the nature of OC curves of single sampling plans by attributes is analysed for various sets of plan parameters based on the gamma prior and Poisson sampling distributions.

Standards Column

This issue's Standards Column focuses on International Standards and associated supporting guidelines for acceptance sampling. These documents are developed within ISO by Subcommittee 5 on Acceptance Sampling of ISO Technical Committee 69 on Applications of Statistical Methods. In this issue will review: The three Technical Reports being developed as the ISO TR 8550 series to provide guidance selection and use of acceptance sampling systems Three of the documents that arte being developed in the ISO 3951 series on Acceptance sampling procedures for inspection by variables Finally, we will look at ISO/CD 8423, Sequential sampling plans for inspection by variables for percent nonconforming (known standard deviation), also a document of TC 69/SC5 but one that is designed for use outside the realm of acceptance inspections.

Combining Process and Product Control for Reducing Sampling Costs

In this paper mixed acceptance sampling procedures are analyzed which combine methods of process control and acceptance sampling for arriving at an efficient and cost-reduced way of performing the control of outgoing or incoming lots of product. The resulting plans are called mixed sampling plans.

Cuthbert Daniel: Industrial Statistician

Cuthbert died in New York City on August 8, 1997, at age 92. All professions have outstanding individuals. The entertainment business calls them stars. Certainly Cuthbert was a star among statisticians: original in his contributions, unique in personality, well known and popular throughout the profession. If you ever met Cuthbert Daniel, however tangentially, you remembered. His speech was crisp, witty, and occasionally devastating. His seminars were always well attended and he enjoyed teaching. Conversations with his sister, Maude Corser, suggest he was always lively and self-confident. As a young man in high school he found joy in countering conventional dress codes by wearing khaki woolen shirts with white ties. He would not conform. He was then, and clearly remained, a singular person. Two excellent personal interviews of Cuthbert are available: the first, An Interview with Cuithbert Daniel, is a videotape in the Distinguished Statistician Series of the ASA (1987) hosted by J. S. Hunter, sponsored by IBM, and introduced by Herman Friedman. The second interview, Conversation with Cuthbert Daniel by Ed Tufte appears in Statistical Science, (1988). To honor Cuthbert's 80th birthday in 1984 Colin Mallows edited a book of papers contributed by his many friends: Design, Data & Analysis (Mallows 1987). It contains an excellent biography and a bibliography complete to that date. An appreciation of Cuthbert's contributions to applied statistics and the design of experiments evokes the need to describe the world of industrial statistics near the end of WWII. Waging war required masses of quality equipment, and American industry quickly took up the challenge. As part of the war effort W. Edwards Deming, in a letter to W. Allen Wallis at Stanford University in April 1942, suggested establishing a broad educational effort to teach Shewhart methods. Soon an extensive educational program was started and by the end of the war Shewhart charts and Dodge-Romig acceptance sampling procedures were in wide use throughout industry. During the war period very little is found descriptive of the industrial applications of experimental design. L. H. C. Tippett's book Statistical Methods in Industty was published by the British Iron and Steel Federation in 1943, and K. A. Brownlee's pamphlet Indutstrial Experimen?tation, used during the war, was published by His Majesty's Stationery Office in 1946. In the final traumatic year of WWII Walter Shewhart was President of the ASA, the first industrial statistician to so serve. It is interesting to read in his Presidential address, statistics is not simply a tool as is so often stated but a scientific way of looking at the universe: statistical method is not something apart from the scientific method but is the scientific method.. . (The italics are Dr. Shewhart's.) Of course, an essential part of the scientific method is the planning of experiments, and it was here that Cuthbert was about to make his many contributions. An early interest in the sciences led Cuthbert to MIT as an undergraduate. A maverick, he took heavy concentrations in English and history to go along with the usual engineering requirements. He received both a BS and MS in chemical engineering (1925, 1926). An interest in physics led him to the University of Berlin for a year but he soon abandoned physics to return to the U.S. as an instructor at Cambridge School, Kendall Green, MA. Later, for four years, he taught physics and the sciences to teachers in New York City. A concern with good teaching led to an appointment as a research associate in Evaluation of School Broadcasts at Ohio State 1939-1940, and later in New York City at the Office of Radio Research, Columbia University. His very first paper appears in the Journal of Applied Psychology and deals with a problem of comparisons of popular songs. His first book, Radio Listener Panels, co-authored with H. Gaudet, was published by the Federal Radio Education Committee in 1941. In the early 1940s Cuthbert's wife, Janet, a PhD biochemist, happened to bring home R. A. Fisher's Statistical Methods for Research Workers. That event led to a reading of Fisher's Design of Experiments and a career in statistics was catalyzed. He found a focus for his education in mathematics, physics, and engineering. From then forward he be-