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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.

THE first part of this article, published in last month's issue of AIRCRAFT ENGINEERING, outlined the operation of the non‐statistical method of sampling inspection commonly met with in purchasing specifications, and explained the inability of such a sampling clause to discriminate effectively between good and bad quality product. The present issue describes the practical applications of statistically designed sampling inspection procedures, giving adequate quality assurance wherever 100 per cent inspection of the product is either inapplicable or uneconomic.

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.

This study investigates the repetitive mixed sampling (MRS) plan based on the Cpk index that was proposed by Aslam et al. (2013a). They were the first to study the MRS plan, but they did not pay attention to the fact that submitting to the variable inspection a sample that was first submitted to the attribute inspection, truncates the X observations. In addition, they did not work with an accurate expression to calculate the probabilities of the Cpk statistic.

The authors presented the results based on their original sampling plan through Monte Carlo simulation and defined the theoretical results of their plan when the sample submitted to the variable inspection is no longer the same one submitted to the attribute inspection.

The β risks of the optimum sampling plans presented by Aslam et al. (2013a) are pretty high, exceeding 46%, on average – this same problem was also observed in Saminathan and Mahalingam (2018), Balamurali (2020) and Balamurali et al. (2020), where the β risks of their proposed sampling plans are yet higher.

In terms of originality, the authors can declare the following. It is not a big deal to propose new sampling plans, if one does not know how to obtain their properties. The miscalculations of the sampling plans risks are dangerous; imagine the situation where the acceptance of bad lots exceeds 50% just because the sampling plan was incorrectly designed. Yes, it is a big deal to warn that this type of problem is arising in a growing number of papers. The authors of this study are the pioneers to discover that many studies focusing on the sampling plans need to be urgently revised.

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.

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.

Continuous Sampling Plans (CSP) are used where processes are continuous and products are not grouped into lots. The principal design criterion for these plans is the Average Outgoing Quality Limit (AOQL), which is the worst outgoing quality over all possible values of the incoming quality level. These are generally applicable to in‐process and final inspections and have been found to be most effective when administered in such a way as to provide an incentive to clear up the faults promptly. In applying the traditional continuous sampling plans, it is necessary to revert to 100 per cent inspection when the quality deteriorates. Therefore, the inspection rate must be larger than production rate and the unit inspection cost must be low. The plan presented in this article relaxes the 100 per cent inspection restriction while reaching the same AOQL quality assurance as traditional CSP‐1. The Markov chain process and numerical analysis will be used to formulate the plan. Its results are then evaluated against CSP‐2.

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.

Inspection error has been and continues to be an important area of research particularly in statistical quality control. While considerable work has been reported on the effect of inspection error on different sampling plans and the implications thereof, very little seems to have been done to assess the effects of such errors on MIL STD 105D plans. In this article some aspects related to inspection errors and operation of MIL STD 105D plans have been studied. Based on this study some observations have been made which have led to the development of a few subtle practical guidelines that may prove helpful to the operating manager in administering such plans effectively.

Selects one of Hamaker′s procedures for deriving a “σ” method (i.e. known process standard deviation) double sampling plan and exploits some of its properties to develop a system of “s” method (i.e. unknown process standard deviation) double sampling plans by variables that match the system of single specification limit “s” method single sampling plans of the current edition of the international standard on sampling by variables. ISO 3951: 1989. The new system is presented in two forms, the second of which may also be used for combined double specification limits and multivariate acceptance sampling.