This paper introduced the neutrosophic uniform distribution and innovative simulation methods to generate random numbers from the neutrosophic uniform distribution and the neutrosophic Weibull distribution. We introduced simulation methods and algorithms designed to handle indeterminacy for both of these distributions. We provided random numbers generated from both distributions across a range of parameter values and degrees of indeterminacy. Furthermore, we conducted a comparative analysis between the classical simulation method in classical statistics and the neutrosophic simulation method. Our findings reveal that the proposed neutrosophic simulation method generates random numbers of smaller magnitudes compared to the classical simulation method under classical statistics. This observation forms the basis of our conclusion.

This paper presents a novel methodology aimed at generating chi-square variates within the framework of neutrosophic statistics. It introduces algorithms designed for the generation of neutrosophic random chi-square variates and illustrates the distribution of these variates across a spectrum of indeterminacy levels. The investigation delves into the influence of indeterminacy on random numbers, revealing a significant impact across various degrees of freedom. Notably, the analysis of random variate tables demonstrates a consistent decrease in neutrosophic random variates as the degree of indeterminacy escalates across all degrees of freedom values. These findings underscore the pronounced effect of uncertainty on chi-square data generation. The proposed algorithm offers a valuable tool for generating data under conditions of uncertainty, particularly in scenarios where capturing real data proves challenging. Furthermore, the data generated through this approach holds utility in goodness-of-fit tests and assessments of variance homogeneity.

Continuous monitoring and improving the production process is a crucial step for the entrepreneur to maintain its position in the market. A successful process monitoring scheme depends upon the specification of the quality being monitored. In this paper, the monitoring of temperature is addressed using the specification of moving average under uncertainty. We determined the coefficients of the proposed chart utilizing the Monte Carlo simulation for a different measure of indeterminacy. The efficiency of the proposed chart has been evaluated by determining the average run lengths using several shift values. A real example of weather-related situation is studied for the practical adoption of the given technique. A comparison study shows that the proposed chart outperforms the existing chart in monitoring temperature-related data.

The existing F-test of linearity cannot be applied when data has indeterminacy and uncertainty. The present paper introduces the F-test of testing linearity under neutrosophic statistics. We will develop F-test under neutrosophic statistics and neutrosophic analysis of the variance (NANOVA) table. The application of the proposed test will be given using the data of dry bulb temperature and relative humidity. From the analysis and comparison studies, it is found that the proposed F-test under neutrosophic statistics gives the results in indeterminate intervals and measures of indeterminacy. In addition, the proposed test is more flexible, adequate, and more informative than the F-test under classical statistics.

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.

This paper addresses neutrosophic statistics that will be used to design a double- acceptance sampling plan. We will design the sampling plans when the lifetime of the product follows the neutrosophic Weibull distribution. The plan parameters of the proposed double sampling plan will be determined using nonlinear optimization at various indeterminacy values and parameters. The productivity of the double sampling plan using neutrosophic statistics over the sampling plan under classical statistics will be given. The presentation of the proposed double sampling plan will be given with the help of industrial data.

The Weibull distribution has always been important in numerous areas because of its vast variety of applications. In this paper, basic properties of the neutrosophic Weibull distribution are derived. The effect of indeterminacy is studied on parameter estimation. The application of the neutrosophic Weibull distribution will be discussed with the help of two real-life datasets. From the analysis, it can be seen that the neutrosophic Weibull model is adequate, reasonable, and effective to apply in an uncertain environment.

This paper introduces the geometric distribution in the context of neutrosophic statistics. The research outlines the essential properties of this new distribution and introduces novel algorithms for generating imprecise geometric data. The study explores the practical applications of this distribution in the industry, highlighting differences in data generated under deterministic and indeterminate conditions using detailed tables, simulation studies, and real-world applications. The results indicate that the level of uncertainty has a substantial impact on data generation from the geometric distribution. These findings suggest updating classical statistical algorithms to better handle the generation of imprecise data. Therefore, decision-makers should exercise caution when using data from the geometric distribution in uncertain environments.