In the classical statistics, for the inspection of a final lot of the product, a decision is made either the lot has good quality or not using an acceptance sampling plan. The acceptance of sampling using the classical statistics assumes that data are determinate. In some situations, the data may imprecise and even intermediate which leads to indecision about the quality of the submitted lot of the product. In this situation, neutrosophic statistics can be applied for the lot sentencing. In this paper, a new attribute sampling plan is proposed using the neutrosophic interval method. The lot acceptance, rejection, and indeterminate probabilities are computed using the neutrosophic binomial distribution at various specified parameters such as sample size and acceptance number. The efficiency of the proposed sampling plan is also discussed. A real example is also added to explain the proposed sampling plan.

In this paper, we originally proposed a new variable sampling plan using the neutrosophic interval statistical method. The neutrosophic operating characteristic (NOC) is derived using the neutrosophic normal distribution. The optimization solution is also presented for the proposed plan under the neutrosophic interval method.

The sampling plan using the classical statistics under the exponential distribution can be applied only when there are certainty and clearness and in observations and parameters. But, in practice, it is not necessary that under some circumstances all the observations/parameters are determined. So, we cannot analyze them using the classical statistics which provides results in the determined values.

The sampling plans have been widely used for the inspection of a lot of the product. In practice, the measurement data may be imprecise, uncertain, unclear or fuzzy. When there is uncertainty in the observations, the sampling plans designed using classical statistics cannot be applied for the inspection of a lot of the product. The neutrosophic statistic, which is the generalization of the classical statistics, can be used when data is not precise, uncertain, unclear or fuzzy. In this paper, we will design the variable sampling plan under the Pareto distribution using the neutrosophic statistics. We used the symmetry property of the normal distribution. We assume uncertainty in measurement data and sample size required for the inspection of a lot of the product. We will determine the neutrosophic plan parameters using the neutrosophic optimization problem. Some tables are given for practical use and are discussed with the help of an example.

In this paper, a new acceptance-sampling plan has been introduced for the two-stage process for multiple lines under the neutrosophic statistics. The parameters of the proposed sampling plan have been determined by satisfying the given risks using the optimization solution under the neutrosophic statistical interval method (NSIM) Using the specific producer’s and consumer’s risks, the parameters of the proposed plan have also been determined under neutrosophic operating function(NOF). The comparison based on the sample size of the proposed and the existing plans has been given at different plan parameters. The tables are provided, and an industrial example is illustrated for the practical use of the proposed sampling plan. The comparison reveals that the proposed plan is more efficient, flexible, and adequate to be used under uncertainty.

In this paper, we will introduce a neutrosophic regression estimator. We will design a new sampling plan using the neutrosophic regression estimator. The neutrosophic parameters of the proposed plan will be determined through the neutrosophic optimization solution.

In this manuscript, an attribute control chart using the repetitive sampling under the neutrosophic statistics system is discussed. The necessary measures of the proposed control chart under the neutrosophic statistics system are given. The control chart coefficients of the proposed control chart are determined using an algorithm under neutrosophic statistics system. The efficiency of the proposed control chart in terms of neutrosophic average run length (NARL) is discussed over the existing control chart under neutrosophic statistics system. From the comparison studies, it is found that the proposed control chart under neutrosophic statistics system is more sensitive in detecting a shift in the process as compared to existing control chart under neutrosophic statistics system. An industrial application of the proposed control chart under neutrosophic statistics system is also given.