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In acceptance sampling, the hypergeometric operating characteristic (OC) function (so called type-A OC) is used to be approximated by the binomial or Poisson OC function, which actually reduce computational effort, but do not provide suffcient approximation results. The purpose of this paper is to examine binomial- and Poisson-type approximations to the hypergeometric distribution, in order to find a simple but accurate approximation that can be successfully applied in acceptance sampling.

The authors present a new binomial-type approximation for the type-A OC function, and derive its properties. Further, the authors compare this approximation via an extensive numerical study with other common approximations in terms of variation distance and relative efficiency under various conditions on the parameters including limiting cases.

The introduced approximation generates best numerical results over a wide range of parameter values, and ensures arithmetic simplicity of the binomial distribution and high accuracy to meet requirements regarding acceptance sampling problems. Additionally, it can considerably reduce the computational effort in relation to the type-A OC function and therefore is strongly recommended for calculating sampling plans.

The newly presented approximation provides a remarkably close fit to the type-A OC function, is discrete and needs no correction for continuity, and is skewed in the same direction by roughly the same amount as the exact OC. Due to less factorials, this OC in general involves lower powers than the type-A OC function. Moreover, the binomial-type approximation is easy to fit to the conventional statistical computing packages.

The red bead experiment (RBE) is very well‐known in total quality management. It was designed by Dr W.E. Deming to show managers several lessons in management and sampling. The RBE has evolved over several decades and now has an accepted standard format. The RBE also serves as an introduction to control charts which are an important tool in statistical quality control. Surprisingly very little is known about the statistical properties of the RBE. This is most likely due to the fact that the RBE involves mechanical sampling and so is much more complicated than probability sampling. New methods are given for statistical analysis when mechanical sampling is involved (e.g. mechanical sampling of non‐uniform output in a manufacturing environment). This approach has specific applications to control charts which are a major tool in quality control. In a rigorous analysis, it is shown that p, the sample proportion of red beads in the RBE, is an unbiased estimator of the RBE process defect rate. Expressions are also found for the variance of p, enabling the calculation of control chart limits. Some of the techniques used can be applied to other mechanical sampling situations which may at first viewing seem intractable.

The reduction of the time and resources spent inspecting product is critical to the success of Company L's continued resourcing efforts. The use of Mil‐Std and other sampling plans with acceptance numbers greater than zero usually results in increased inspection sizes and potential for controversy in inspection results between inspectors. The time and resources used to complete these outgoing inspections are directly related to the amount of product currently required to be inspected in order to determine the acceptance or rejection of a lot of finished goods. This paper proposes a new sampling policy that will allow Company L to reduce the size of outgoing inspections. The data used in the paper are from 2006 to 2007. It is a combination of Overseas Inspection reports from all suppliers as well as sales volumes for products sold to Company L's partner companies. There are currently over 80 suppliers that manufacture products for Company L. The major finding of this paper is that it is possible to reduce inspection size while still maintaining, or in most cases reducing, the risks associated with sample inspections. This will be accomplished by switching from the current Mil‐Std plan to a Zero acceptance number sampling plan.

This research aims to investigate the differences in designing the zero acceptance number single sampling plans using the apparent fraction of nonconforming and the binomial distribution against the exact convolute compound hypergeometric distribution when both types of inspection errors are present.

This research presents the derivation and uses the numerical study to compare the calculated probability of acceptance and the minimum sample size when using the present design concept of binomial distribution with true fraction of nonconforming replaced with the apparent one. Under the presences of inspection errors and zero acceptance number, the probability of acceptance is alternatively derived and presented in term of a function of the probability generating function. This research uses numerical method to determine the differences in the probability of acceptance. The computation of the minimum sample sizes are presented along with the numerical results and the comparison.

When the inspection errors are present, the probability of acceptance is extremely decreased even for 1 percent of inspection errors of Type I (rejecting good product) and Type II (accepting bad product). The binomial apparent nonconforming notions yields an over‐estimation of the probability of acceptance, comparing with the exact convolute compound hypergeometric notion under the zero acceptance single sampling plans especially at low fraction of nonconforming levels, the six sigma quality levels. The differences of the calculated probabilities of acceptance and the minimum sample sizes decrease as the inspection error of Type II increases given a fixed value of Type I error and consumer risk.

This research alternatively presents the mathematical derivation along with numerical study to assert the over‐estimation of the probability of acceptance and the minimum sample size if the existing methodology to design the zero acceptance number single sampling plans is used. This finding will help improve the sampling design strategy of the multistage production system.

Sampling plans for inspection by attributes contain rules for passing from normal to tightened inspection. Usually only the operating characteristic curve (O.C.) will apply but in tightened inspection, lots are unlikely to remain in tightened inspection and inspection will be terminated. This means that the normal and tightened O.C. curves are boundary curves and the true O.C. curve is a composite of both. This article presents a method for calculating the composite O.C. curve and proposes three criteria to compare switching rules.

Duality is an important topic in informetrics, especially in connection with the classical informetric laws. Yet this concept is less studied in information retrieval. It deals with the unification or symmetry between queries and documents, search formulation versus indexing, and relevant versus retrieved documents. These ideas are elaborated in this note and the connection with the hypergeometric distribution is highlighted.

The purpose of this paper is to construct innovative exact and approximative sampling plans for acceptance sampling in statistical quality control. These sampling plans are determined for crisp and fuzzy formulation of quality limits, various lot sizes and common α- and β-levels.

The authors use generalized fuzzy hypothesis testing to determine sampling plans with fuzzified quality limits. This test method allows a consideration of the indifference zone related to expert opinion or user priorities. In addition to the exact sampling plans calculated with the hypergeometric operating characteristic function, the authors consider approximative sampling plans using a little known, but excellent operating characteristic function. Further, a comprehensive sensitivity analysis of calculated sampling plans is performed, in order to examine how the inspection effort depends on crisp and fuzzy formulation of quality limits, the lot size and specifications of the producer’s and consumer’s risks.

The results related the parametric sensitivity analysis of the calculated sampling plans and the conclusions regarding the approximation quality provide the user a comprehensive basis for a direct implementation of the sampling plans in practice.

The constructed sampling plans ensure the simultaneous control of producer’s and consumer’s risks with the smallest possible inspection effort on the one hand and a consideration of expert opinion or user priorities on the other hand.

This paper proposes a new inventory model with inspection policy because in practice the received orders may contain non- conforming (NC) items. So, a buyer who receive an order from a supplier should use an inspection policy.

The inspection policy is assumed to be zero-defect single sampling. Under this policy a lot is accepted only if no defect has been identified in the inspected sample. The fraction of NC is assumed to be a random variable following a Binomial distribution and the number of NC items detected by inspection assumed to be a random variable, which follows a hypergeometric distribution. Order quantity and sample size are the two decision variables. A solution procedure is presented for the proposed model. The proposed procedure presents the optimal solution.

Numerical examples presented to illustrate the procedure outlined for the proposed model and its applicability. The results of numerical examples and comparing them with traditional EOQ model reveal that by the proposed model, the buyer could reduce total cost that shows the efficiency and validity of the proposed model.

The novelty of this paper is the new proposed model that considers inspection policy in inventory management. The proposed model determines sample size as well as order quantity to consider both subject of inventory management and quality control, simultaneously.

As the complexity of the multi-component products increases the quality of these products becomes increasingly difficult to control throughout the supply chain. The first step to manufacturing a quality product is to ensure that the product components from suppliers meet specifications. Product quality can be controlled through sampling inspection of the components. The paper aims to discuss these issues.

The model presented in this paper was developed to determine the optimal sampling levels for incoming lots containing parts for production and assembly of multi-component systems. The main objective of the model is to minimize the expected cost that is associated with a nonconforming item reaching assembly.

In this research, the results showed that even with limited time available for inspection, performing sampling inspection significantly reduced the expected cost of a nonconforming item reaching assembly. The model, solved by the evolutionary algorithm, was able to provide a meaningful, near optimal solution to the problem.

In this model the time available for inspection is limited, the distribution of defects is assumed to follow the binomial distribution, and the distribution of accepting the lot with defects follows the hypergeometric distribution. In addition, the inspection is considered to be accurate and, if a nonconforming item is found in the inspected sample, the entire lot is rejected. An example is given with real world data and the results are discussed as they relate to supply chain management and quality.

The paper aims to estimates the limitations of a forced distribution performance appraisal system in identifying the highest performing individuals within an organization. Traditionally, manpower modeling allows organizations to develop plans that meet future human resource requirements by modeling the flow of personnel within an organization. The aim is to quantify the limitations of a performance appraisal system in identifying the best-qualified individuals to fill future requirements.

This paper describes an exploratory study using discrete event simulation based on the assignment, evaluation and promotion history of over 2,500 officers in the US Army. The obtained data provide a basis for estimating simulation inputs that include system structure, system dynamics, human behavior and policy constraints. The simulation approach facilitates modeling officers who receive evaluations as they move throughout the system over time.

The paper provides insights into the effect of system structure and system dynamics on the evaluation outcome of employees. It suggests that decreasing the number of a rater’s subordinates has a significant effect on the accuracy of performance appraisals. However, increasing the amount of time individuals spend on each assignment has little effect on system accuracy.

This research allows an organization’s leadership to evaluate the possible consequences associated with evaluation policy prior to policy implementation.

This work advances a framework in assessing the effect of system dynamics and structure, and the extent to which they limit or enhance the accuracy of an organization’s forced distribution performance appraisal system.