In this paper a new sequential SAMPLING PLAN is introduced in which the acceptable quality level (AQL) and the lot tolerance percent defective (LTPD) are a fuzzy number. This PLAN is well defined, since, if the parameters are crisp, it changes to a classical PLAN. For such a PLAN, a particular table of rejection and acceptance is calculated and compared with the classical one.

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.

Binomial SAMPLING PLANs was developed for monitoring Metopolophium dirhodum population in wheat fields of Varamin region, Iran. Aphid population was sampled weekly during two growing seasons of 2001-2002. In each SAMPLING date, 50 wheat stems were chosen randomly and the number of aphids was counted and the data was used for developing binomial SAMPLING PLAN. The results indicated that the sample size estimated from the binomial method was larger than the enumerative method at the density lower than one aphid per tiller. However, a larger sample size was required in enumerative method at higher aphid densities. Analysis of the linear regression between the observed and estimated proportions of wheat tillers infested with M. dirhodum showed good fit between the binomial model and the data. Applying the model, it was possible to estimate the mean aphid population densities observed in this study (0.02-20.18 aphid/tiller). The results revealed that the developed binomial SAMPLING PLAN at precision levels of D=0.25 (acceptable precision level in IPM) could be applied to reduce SAMPLING time in monitoring programs of M. dirhodum in irrigated wheat fields of Varamin region.

In this paper, the effect of non-normality on SAMPLING PLAN using Yule’s model (second order auto regressive model {AR (2)}) represented by the Edgeworth series is studied for known s. The effect of using the normal theory SAMPLING PLAN in a non-normal situation using Yule’s model is studied by obtaining the distorted errors of the first and second kind. As one will be interested in having a suitable SAMPLING PLAN under Yule’s model for non-normal variables the values of n and k are determined.

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.

Introduction Acceptance SAMPLING PLANs (ASPs) are one of the statistical tools widely used by inspectors to evaluate the quality of productions. Depending on whether the desired quality characteristic of products can be measured on a numerical scale or not, the corresponding ASP is called variable and attribute ASP, respectively. Most ASPs only apply the current lot information to decide the quality of manufactured products. One of the drawbacks of such PLANs is that they need a large sample size to inspect the lot to judge its quality. To solve this problem, the methods of SAMPLING in ASPs were developed, and conditional PLANs were presented (Montgomery, 2020). In addition to the current information, past information on the process is also used in decision-making. Although the variable multiple dependent state SAMPLING (MDS) PLAN is preferred over the conditional PLANs due to the small sample size required, it is impossible to use it in a situation where the quality of manufactured products depends on more than one quality characteristic. In this study, to improve the performance of the mentioned method, ST pk-based MDS PLAN is proposed, which applies both current and past knowledge of the process and is applicable to inspect products with independent/dependent characteristics following a multivariate normal distribution. Material and Methods Let X = (X1,
,
,
, ,Xv) ′,be a random vector of independent quality characteristics and follow a multivariate normal distribution. The proposed variable MDS multivariate (VMDSM) PLAN, designed under the process capability index ST pk, has four parameters m,n,kr and ka. Applying a nonlinear optimization problem, optimal values of PLAN parameters are obtained. Also, to develop the application of the VMDSM PLAN in the presence of dependent variables, the principal component analysis technique is used. While comparing the performance of the proposed PLAN with variable single SAMPLING (VSS), variable repetitive group SAMPLING (VRGS) and modified VRGS (Modified-VRGS) PLANs based on the required sample size and operating characteristic (OC) curve. An industrial example is given to explain how to use the introduced PLAN. Results and Discussion To study the impact of the contracted values between customer and producer on the PLAN parameters, we consider several combinations of consumer’, s risk (, ) and manufacturer’, s risk (, ) as well as a different number of defective items in parts per million. The results demonstrate that the required sample size decreases when (, ) and (, ) become larger. Moreover, findings indicate that the OC curve of the proposed method is the best one among VSS, VRGS and Modified-VRGS PLANs. Also, compared to VSS and VRGS PLANs, the introduced PLAN needs a small sample size and is economical. Conclusion Today’, s, it is clear that production quality depends on many quality characteristics. So designing a multivariate ASP with small sample size, strong OC curve, and simple implementation is unavoidable. In this study, we proposed a PLAN suitable for a situation where the quality characteristics are mutually independent/dependent with multivariate normal distribution. The results showed that the introduced PLAN is better than the existing VSS and VRGS PLANs in terms of the required sample size and OC curve, and it is preferable to the Modified-VRGS method based on the OC curve.

In this paper, we develop an optimization model for the economic design of repetitive SAMPLING PLAN in the presence of two markets. The process under consideration produces a product with a normally distributed quality characteristic with unknown mean and known variance. The quality characteristic has a lower specification limit. The quality of the product is controlled via lot-by-lot acceptance SAMPLING PLAN. The objective function used in the model is maximizing profit and product conformity using the Taguchi loss function as a surrogate for product conformity. Risks of producer and consumer in two different markets are considered as constraints. We demonstrate the application of the model using a numerical example. Sensitivity analysis on model parameters shows that the result of the model is sensitive to changes in model parameters.