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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.

Zero acceptance number plans (c = 0 plans) are sometimes described as the only appropriate method of acceptance sampling in an environment in which zero defects is a meaningful concept. Considers the operating characteristic curves of such plans, and evaluates their effectiveness in the presence of low levels of defects. Suggests a confidence interval approach to establish sample size for c = 0 plans. Refers to alternative approaches.

A new plan is proposed for small‐sample situations using which a one‐third reduction in sample size can be achieved compared to the sample size of an equivalent zero acceptance number single sampling plan. This plan utilises the results of three successive samples for taking decision on acceptance of the lot under consideration. The plan is also robust to lot‐to‐lot quality trends.

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 determine single sampling plans (SSPs) by attributes when the number of nonconformities is distributed according to a zero-inflated Poisson (ZIP) distribution.

Manufacturing processes have now-a-days been aligned properly and are monitored well, so that the occurrence of nonconformities would be a rare phenomenon. The information related to number of nonconformities per product will have more number of zeros. Under such circumstances, the appropriate probability distribution of the number of nonconformities is a ZIP distribution. The operating characteristic function of the sampling plan is derived.

Parameters of the sampling plans are obtained for some sets of values of (p ₁, α, p ₂, β). Numerical examples are given to illustrate the selection of SSPs under ZIP distribution and to study its advantages over Poisson SSP.

Results obtained in this paper are original and has been done for the first time in this regard. Parameters of the sampling plans are essential to make decisions either to accept or reject the lots based on the inspection of the samples.

The purpose of this paper is to design a modified chain sampling plan for assuring the product percentile life where the lifetime follows Weibull or generalized exponential distributions (GEDs). In order to reduce the cost of inspection when implementing the proposed modified chain sampling plan, it is also considered the economic aspect of designing of proposed plan in this paper.

The authors have designed the proposed plan on the basis of two points on the operating characteristic (OC) curve approach. The optimization problem is used to determine the plan parameters of the proposed plan so that the specified values of producer’s risk and consumer’s risk are satisfied simultaneously.

The results we have obtained, confirm that the proposed plan will be very effective in reducing the sample size rather than other existing sampling plans. The OC curves of proposed plan, chain sampling plan and zero acceptance number single sampling plan show that the performance of proposed plan in discriminating the good and poor quality lots is better than other two plans. In this paper, it is proved that the value of number of preceding lots required for current lot disposition plays an important role.

The proposed modified chain sampling plan for assuring the percentile lifetime of the products under Weibull or GEDs is not available in the literature. The proposed plan can be used in all the manufacturing industries to assure the product percentile lifetime with minimum sample size as well as minimum cost.

The purpose of the paper is set to minimize the total cost of a manufacturing system when an acceptance sampling plan (ASP) is carried out in a fuzzy environment.

A fuzzy acceptance sampling plan (FASP) is employed for the inspection of the batch of products and a fuzzy cost optimization problem is formulated.

The extent of uncertainty determines an interval for the total cost function with upper and lower bounds. The effect of variation in the ambiguity of the proportion of defectives in the probability of acceptance is determined.

The proposed model is specifically designed for production and supply units with ASP for attributes. Still, the proportion of defectives in the inspection process is fuzzy.

Fuzzy probability distribution is used to model an optimal inspection plan for a general supply chain. Economic design of supply chain under fuzzy proportion of defectives is discussed for the first time.

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.

A procedure for designing chain sampling plans, ChSP‐1, is described for situations where one of the parameters, the sample size, is fixed. The procedure involves minimisation of the sum of the producer′s risk and consumer′s risk with due weights. Expressions have been derived under binomial and Poisson models, for the parameter i , using which one can obtain the plan for desired values of AQL/LQL weights and sample size. Examples are also given.

It is shown that the Quick Switching System, Tightened Normal Tightened Scheme and other switching systems emerge from the generalised two‐plan system involving normal and tightened inspection. The corresponding operating characteristic (OC) functions are also shown to emerge from generalised results. The performance of different systems is compared with reference to their OC curves. The possibility of being applied in a critical area of application (in which the single sampling plans are not possible to apply) is indicated.