Neutrosophic Statistical Interval Method Research Articles

Monitoring of production of blood components by attribute control chart under indeterminacy

The existing control chart for monitoring the blood components by attribute is designed using classical statistics. The existing attribute control chart can be applied only when the experimenter is sure about the proportion of defective or all the observations in the sample are determined. In this paper, new attribute control charts for monitoring the blood components under the neutrosophic statistics will be presented. The design of the proposed control chart is given under the neutrosophic statistical interval method. The applications of these control charts demonstrate that the proposed control charts are quite effective, adequate, flexible, and informative for monitoring the blood components under uncertain environment.

Single-stage and two-stage total failure-based group-sampling plans for the Weibull distribution under neutrosophic statistics

If the sample or population has vague, inaccurate, unidentified, deficient, indecisive, or fuzzy data, then the available sampling plans could not be suitable to use for decision-making. In this article, an improved group-sampling plan based on time truncated life tests for Weibull distribution under neutrosophic statistics (NS) has been developed. We developed improved single and double group-sampling plans based on the NS. The proposed design neutrosophic plan parameters are obtained by satisfying both producer’s and consumer’s risks simultaneously under neutrosophic optimization solution. Tables are constructed for the selected shape parameter of Weibull distribution and various combinations of neutrosophic group size. The efficiency of the proposed group-sampling plan under the neutrosophic statistical interval method is also compared with the crisp method grouped sampling plan under classical statistics.

Presenting post hoc multiple comparison tests under neutrosophic statistics

ObjectiveThe existing post hoc tests under classical statistics have been applied for analyzing the data having all determined, precise and exact observations. In practice, the data recorded from the complex situations or under uncertainty does not contain all determined observations in the data. MethodIn this case, the data is recorded in the indeterminacy interval and can be analyzed using neutrosophic statistics. ResultsIn this paper, we will modify the existing least significant difference Test, Bonferroni Test and Scheffe Test under the neutrosophic statistics. We will present some basic modified tests under neutrosophic statistical interval method (NSIM) and explained them with the help of real data. We will compare the performance of the proposed tests with the existing tests under uncertainty environment. ConclusionThe proposed post hoc tests are flexible and informative than the post hoc tests under classical statistics.

Introducing Grubbs’s test for detecting outliers under neutrosophic statistics – An application to medical data

ObjectiveIn this paper, we will introduce the designing of Grubbs’s test under neutrosophic statistics. The proposed test will be a generalization of Grubbs’s test under classical statistics. MethodWe will present the designing and the operational procedure of the proposed test under the neutrosophic statistical interval method. ResultsThe application of the proposed test will be given with the aid of real data from the medical field. ConclusionFrom the comparisons, it is concluded that the proposed test is more effective, informative and flexible than the existing Grubbs’s tests.

The W/S Test for Data Having Neutrosophic Numbers: An Application to USA Village Population

The W/S test under neutrosophic statistics is proposed in this paper. The Monte Carlo simulation under the neutrosophic statistical interval method is proposed and applied to study the sensitivity of various neutrosophic statistical distributions. The power of test curves for neutrosophic distributions is presented. The efficiency of the proposed W/S test under neutrosophic statistics is compared with that of the W/S test under classical statistics. The proposed test is explained with the aid of an example.

On detecting outliers in complex data using Dixon’s test under neutrosophic statistics

The existing Dixon’s test (DT) under classical statistics has been widely applied in a variety of fields. The main target of DT is to recognize the outlier or suspicious observation in the sample. The DT available in the literature is workable when all the observations in the sample or the population are precise, determined and certain. In practice, under the complex system, it may not possible that all observations in the data are determined. In such situations, the existing DT cannot be applied for the detection of the outlier value in the sample. In this paper, we will introduce a new Dixon’s test under the neutrosophic statistics is called (NDT). We will present the testing procedure for the proposed test using the neutrosophic statistical interval method. We will discuss its application with the help of an example.

Erlang Service Queueing Model with Neutrosophic Parameters

In this paper, we generalize the classical Erlang service queueing model, which has determined and crisp parameters to neutrosophic Erlang service queueing model which is more accurate because it opens the ability to deal with imprecise and incomplete knowledge of parameters. We have used the neutrosophic statistical interval method introduced by F. Smarandache to describe the parameters of the Erlang service queueing model and to find the neutrosophic performance measures.

Two-stage sampling plan using process loss index under neutrosophic statistics

This article develops the designing of two-stage process loss using neutrosophic statistics (NS). The neutrosophic operating characteristic for the two-stage sampling is developed under NS. Neutrosophic plan parameters are obtained using non-linear optimization using the neutrosophic statistical interval method for the constraints. A comparative study is carried out with the existing scheme. Some tables are provided and explained with an example under uncertainty.

Design of the Bartlett and Hartley tests for homogeneity of variances under indeterminacy environment

The existing Bartlett’s test and Hartley’s test under classical statistics can be applied only when all observations in the sample are determined, precise and determinate. In some complex situations, it may not possible to measure the exact observations. In this case, the neutrosophic statistics is applied for the decision. In this paper, we present Bartlett’s test and Hartley’s test under the neutrosophic statistics. We present the designing for the proposed tests under neutrosophic statistical interval method. We present an example and compare the proposed neutrosophic Bartlett’s test and Hartley’s test over the existing tests under classical statistics. From the comparative study, we conclude that the proposed tests are quite effective, informative and flexible to be applied under the indeterminate environment.

Design of a Control Chart Based on COM-Poisson Distribution for the Uncertainty Environment

This paper will introduce the neutrosophic COM-Poisson (NCOM-Poisson) distribution. Then, the design of the attribute control chart using the NCOM-Poisson distribution is given. The structure of the control chart under the neutrosophic statistical interval method will be given. The algorithm to determine the average run length under neutrosophic statistical interval system will be given. The performance of the proposed control chart is compared with the chart based on classical statistics in terms of neutrosophic average run length (NARL). A simulation study and a real example are also added. From the comparison of the proposed control chart with the existing chart, it is concluded that the proposed control chart is more efficient in detecting a shift in the process. Therefore, the proposed control chart will be helpful in minimizing the defective product. In addition, the proposed control chart is more adequate and effective to apply in uncertainty environment.

Design of Sampling Plan for Exponential Distribution under Neutrosophic Statistical Interval Method

Design of Sampling Plan for Exponential Distribution under Neutrosophic Statistical Interval Method

Design of a Control Chart for Gamma Distributed Variables Under the Indeterminate Environment

In this paper, the design of the control chart when the variable of interest follows the gamma distribution under the neutrosophic statistical interval method (NSIM) is proposed. The average run length, probability in-control, and probability of out-of-control will be derived using the NSIM. The neutrosophic control chart coefficient will be determined by the algorithm under the NSIM. The neutrosophic average run length for various shifts and specified parameters will be determined. The efficiency of the proposed control chart is discussed using the simulation study and a real example.

Design of X-Bar Control Chart for Resampling Under Uncertainty Environment

This paper presents the designing of the X-bar control chart using resampling scheme under the uncertainty environment. The necessary measures of the present chart are derived under the neutrosophic system. The neutrosophic average run length (NARL) when the process is in-control and out-of-control are derived under the neutrosophic statistical interval method (NSIM). The neutrosophic control chart coefficients are determined through the algorithm developed under NSIM. The comparative study shows that the proposed chart is better than the existing chart in NARL.

Sampling Plan Using Process Loss Index Using Multiple Dependent State Sampling Under Neutrosophic Statistics

This paper presents the designing of a sampling plan using the process loss consideration for the multiple dependent state sampling under the neutrosophic statistics. The operating characteristics under the neutrosophic statistical interval method (NSIM) are developed to find the neutrosophic plan parameters of the proposed sampling plan. A non-linear optimization under NSIM is used to find the optimal neutrosophic plan parameters under the given conditions. The advantages of the proposed sampling plan are discussed over the existing sampling plans. A real example having some uncertain observations is given for the illustration purpose.

Plan for Food Inspection for Inflated-Pareto Data Under Uncertainty Environment

The existing sampling plans for food inspection have been designed under classical statistics. These sampling plans are applied in the food industry under the assumption that all observations are determined, clear and certain. The neutrosophic statistics (NS) which is the generalization of classical statistics applied under uncertainty environment. In this paper, we propose one of the simplest acceptance sampling plans namely, a single sampling plan for inspecting the quality of the raw materials where the quality characteristic follows inflated Pareto distribution under the NS. The neutrosophic plan parameters are determined under the neutrosophic statistical interval method (NISM). We provide the range/interval of the sample sizes and acceptance criteria which satisfy both producer and consumer expectations. The advantages of the proposed plan are given. An example from the food industry is selected to explain the proposed plan.

Control Chart for Variance Using Repetitive Sampling Under Neutrosophic Statistical Interval System

In this paper, a control chart for variance using the repetitive sampling under the neutrosophic statistics is proposed. The proposed control chart can be applied for monitoring the variability in the process when some observations/parameters are unclear and indeterminate. The operational procedure of the proposed control chart and the necessary measures are given for the practical use of the proposed control chart. The control chart parameters are determined through the algorithm under neutrosophic statistical interval method. The efficiency of the proposed control chart is compared with the existing control chart in neutrosophic average run length. From the simulation study and a real example, it is concluded that the proposed control chart is more efficient in detecting a shift in the process and more adequate, effective, informative, and flexible under the uncertainty environment.

Design of a New Attribute Control Chart Under Neutrosophic Statistics

In this manuscript, we will originally design a Shewhart attribute control chart under the neutrosophic statistical interval method. The neutrosophic measures to study the performance of the proposed chart are given. The neutrosophic control chart coefficients are determined through the neutrosophic algorithm. A simulation study is also added to show the efficiency of the proposed control chart under the neutrosophic statistical interval method over the attribute control chart under the classical statistics. The comparison of the proposed chart with the existing chart is also given in terms of neutrosophic average run length (NARL). Some tables of NARL are given and explained using the real data from the company.