The ACCEPTANCE SAMPLING plan problem is an important topic in quality control and both the theory of probability and theory of fuzzy sets may be used to solve it. In this paper, we discuss the single ACCEPTANCE SAMPLING plan, when the proportion of nonconforming products is a fuzzy number. We show that the operating characteristic (OC) curve of the plan is a band having high and low bounds and that for fixed sample size and ACCEPTANCE number, the width of the band depends on the ambiguity proportion parameter in the lot. When the ACCEPTANCE number equals zero, this band is convex and the convexity increases with n Finally, we compare the OC bands for a given value of c.

In the present paper, the ACCEPTANCE single SAMPLING plan is developed by the generalized intuitionistic fuzzy numbers. The $\alpha_1$-cut and $\alpha_2$-cut sets of the generalized intuitionistic fuzzy numbers are applied to construct the ACCEPTANCE single SAMPLING plan. We also investigate the operating characteristic curve, where the parameter is considered the generalized intuitionistic fuzzy number. The $(\alpha_1,\alpha_2)$-cut set of generalized intuitionistic fuzzy operating characteristics is constructed. The bands are represented with upper and lower bounds instead of curves for operating characteristics and evaluated in detail. Finally, the numerical example is given to illustrate the proposed approach.

This paper questions some aspects of attributeACCEPTANCE SAMPLING in light of the original concepts ofhypothesis testing from Neyman and Pearson (NP). AttributeACCEPTANCE SAMPLING in industry, as developed byDodge and Romig (DR), generally follows the internationalstandards of ISO 2859, and similarly the Brazilian standardsNBR 5425 to NBR 5427 and the United StatesStandards ANSI/ASQC Z1. 4. The paper evaluates andextends the area of ACCEPTANCE SAMPLING in two directions. First, by suggesting the use of the hypergeometric distributionto calculate the parameters of SAMPLING plansavoiding the unnecessary use of approximations such as thebinomial or Poisson distributions. We show that, underusual conditions, discrepancies can be large. The conclusionis that the hypergeometric distribution, ubiquitouslyavailable in commonly used software, is more appropriatethan other distributions for ACCEPTANCE SAMPLING. Second, and more importantly, we elaborate the theory of ACCEPTANCESAMPLING in terms of hypothesis testing rigorouslyfollowing the original concepts of NP. By offering acommon theoretical structure, hypothesis testing from NPcan produce a better understanding of applications evenbeyond the usual areas of industry and commerce such aspublic 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 thenecessity of linking the acceptable quality limit (AQL)exclusively to the producer and the lot quality percentdefective (LTPD) exclusively to the consumer. In reality, the consumer should also be preoccupied with a value ofAQL, as should the producer with LTPD. Furthermore, wecan also question why type I error is always uniquelyassociated with the producer as producer risk, and likewise, the same question arises with consumer risk which isnecessarily associated with type II error. The resolution ofthese questions is new to the literature. The article presentsR code throughout.

The paper presents an economical model for double variable ACCEPTANCE SAMPLING with inspection errors. Taguchi cost function is used as ACCEPTANCE cost while quality specification functions are normal with known variance. An optimization model is developed for double variables ACCEPTANCE SAMPLING scheme at the presence of inspection errors with either constant or monotone value functions. The monotone value functions could be descending or ascending exponentially. In the case that inspection errors have exponentially functions, we can find the best value for inspection errors regarding to the sample number and other economical parameters. Finally sensitivity analysis has done on model parameters and some numerical examples are given to demonstrate how the developed model is applied.

ACCEPTANCE SAMPLING is one of the main parts of the statistical quality control. It is primarily used for the inspection of incoming or outgoing lots. ACCEPTANCE SAMPLING procedures can be used in an ACCEPTANCE control program to reach better quality with lower expenses, improved control, and increased efficiency. The aim of this paper is studying ACCEPTANCE SAMPLING based on non-parametric predictive inference in a fuzzy environment. In some cases, it may not be possible to define ACCEPTANCE SAMPLING parameters as crisp values. Especially in production environments, it may not be easy to define the number of parameters of conforming items or the size of the samples as crisp values. In these cases, these parameters can be expressed by linguistic variables. The fuzzy set theory can be used successfully to cope with the vagueness in these linguistic expressions for ACCEPTANCE SAMPLING based on non-parametric predictive inference. In other words, the aim of this paper is to present a new method titled fuzzy nonparametric predictive inference for single ACCEPTANCE SAMPLING plan.

In zero ACCEPTANCE number SAMPLING plans, the sample items of an incoming lot are inspected one by one. The proposed method in this research follows these rules: if the number of nonconforming items in the first sample is equal to zero, the lot is accepted but if the number of nonconforming items is equal to one, then second sample is taken and the policy of zero ACCEPTANCE number would be applied for the second sample. In this paper, a mathematical model is developed to design single stage and double stage SAMPLING plans. Proposed model can be used to determine the optimal tolerance limits and sample size. In addition, a sensitivity analysis is done to illustrate the effect of some important parameters on the objective function. The results show that the proposed two stage SAMPLING plan has better performance than single stage SAMPLING plan in terms of total loss function, sample size and robustness.

In this research, lifetime performance index (LPI) data are used to present a quick switching SAMPLING (QSS) plan based on a type‐II censoring life test and the assumption that the lifetime of units follows the Weibull distribution. In this proposed QSS plan, it is also assumed that the sample size (n) and the ACCEPTANCE criterion (k) are the same for both the normal and the tightened inspections of the QSS plan, but the failures (r) during the normal and tightened inspections are different in number. The equations needed to calculate the operating characteristic (OC) curve are presented for the proposed QSS along with an optimization model to minimize the average failure number (AFN). In this regard, the constraints of producer and consumers' risks are incorporated into the model. To show the performance of the proposed QSS plan, numerical analyses are performed and the studies conducted in this field are compared. The introduced QSS SAMPLING plan can significantly reduce the cost of manufacturers at the level of industrial organizations.

ACCEPTANCE of SAMPLING plans and trade credit has become increasingly common in today's business. These two issues should be considered simultaneously when determining an ordering decision. This paper uses EOQ to model the decision under the ACCEPTANCE SAMPLING plan and trade credit; meaning, how often it would be necessary to order to minimize the total related cost. We develop theorems based on optimum lemmas to solve the problem. Computational analyses are given to illustrate the solution procedures and we discuss the inuence of credit period, ACCEPTANCE SAMPLING plan, holding cost and ordering cost on the total cost, and the ordering decision. We conclude with a computational analysis that leads to a variety of managerial insights.

In ACCEPTANCE SAMPLING plans, the decisions on either accepting or rejecting a specific batch is still a challenging problem. In order to provide a desired level of protection for customers as well as manufacturers, in this paper, a new ACCEPTANCE SAMPLING design is proposed to accept or reject a batch based on Bayesian modeling to update the distribution function of the percentage of nonconforming items. Moreover, to determine the required sample size the backwards induction methodology of the decision tree approach is utilized. A sensitivity analysis that is carried out on the parameters of the proposed methodology shows the optimal solution is affected by initial values of the parameters. Furthermore, an optimal (n, c) design is determined when there is a limited time and budget available and hence the maximum sample size is specified in advance.

ACCEPTANCE SAMPLING (AS), as one of the main fields of statistical quality control (SQC), involves a system of principles and methods to make decisions about accepting or rejecting a lot or sample. For attributes, the design of a single AS plan generally requires determination of sample size, and ACCEPTANCE number. Numerous approaches have been developed for optimally selection of design parameters in last decades. We develop a multi-objective economic-statistical design (MOESD) of the single AS plan to reach a well-balanced compromise between cost and quality features. Moreover, a simple and efficient DEA-based algorithm for solving the model is proposed. Through a simulation study, the efficiency of proposed model is illustrated. Comparisons of optimal designs obtained using MOESD to economic model with statistical constraints reveals enhanced performance of the multi-objective model.