This research work appertains to the acceptance sampling plan under the neutrosophic statistical interval method (ASP-NSIM) based on gamma distribution (GD), Burr type XII distribution (BXIID) and the Birnbaum-Saunders distribution (BSD). The plan parameters will be determined using the neutrosophic non-linear optimization problem. We will provide numerous tables for the three distributions using various values of shape parameters and degree of indeterminacy. The efficiency of the proposed ASP-NSIM will be discussed over the existing sampling plan in terms of sample size. The application of the proposed ASP-NSIM will be given with the aid of industrial data.

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.

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.

Sampling-based methods for uncertainty and sensitivity analysis are reviewed. The following topics are considered: (1) Definition of probability distributions to characterize epistemic uncertainty in analysis inputs, (2) Generation of samples from uncertain analysis inputs, (3) Propagation of sampled inputs through an analysis, (4) Presentation of uncertainty analysis results, and (5) Determination of sensitivity analysis results. Special attention is given to the determination of sensitivity analysis results, with brief descriptions and illustrations given for the following procedures/techniques: examination of scatterplots, correlation analysis, regression analysis, partial correlation analysis, rank transformations, statistical tests for patterns based on gridding, entropy tests for patterns based on gridding, nonparametric regression analysis, squared rank differences/rank correlation coefficient test, two dimensional Kolmogorov-Smirnov test, tests for patterns based on distance measures, top down coefficient of concordance, and variance decomposition.

The aim of reducing the inspection cost and time using acceptance sampling can be achieved by utilizing the features of allocating more than one sample item to a single tester. Therefore, group acceptance sampling plans are occupying an important place in the literature because they have the above-mentioned facility. In this paper, the designing of a group acceptance sampling plan is considered to provide assurance on the product’s mean life. We design the proposed plan based on neutrosophic statistics under the assumption that the product’s lifetime follows a Weibull distribution. We determine the optimal parameters using two specified points on the operating characteristic curve. The discussion on how to implement the proposed plan is provided by an illustrative example.

The aim of reducing the inspection cost and time using acceptance sampling can be achieved by utilizing the features of allocating more than one sample item to a single tester. Therefore, group acceptance sampling plans are occupying an important place in the literature because they have the above-mentioned facility. In this paper, the designing of a group acceptance sampling plan is considered to provide assurance on the product’s mean life. We design the proposed plan based on neutrosophic statistics under the assumption that the product’s lifetime follows aWeibull distribution. We determine the optimal parameters using two specified points on the operating characteristic curve. The discussion on how to implement the proposed plan is provided by an illustrative example.

This book systematically addresses the design and analysis of efficient techniques for independent random sampling. Both general-purpose approaches, which can be used to generate samples from arbitrary probability distributions, and tailored techniques, designed to efficiently address common real-world practical problems, are introduced and discussed in detail. In turn, the monograph presents fundamental results and methodologies in the field, elaborating and developing them into the latest techniques. The theory and methods are illustrated with a varied collection of examples, which are discussed in detail in the text and supplemented with ready-to-run computer code. The main problem addressed in the book is how to generate independent random samples from an arbitrary probability distribution with the weakest possible constraints or assumptions in a form suitable for practical implementation. The authors review the fundamental results and methods in the field, address the latest methods, and emphasize the links and interplay between ostensibly diverse techniques.