This paper aims to provide a multiple dependent state (MDS) sampling technique for light-emitting diode luminous intensities under indeterminacy by employing time truncated sampling schemes and the Weibull distribution. This indicates that ASN is significantly impacted by the indeterminacy parameter. Furthermore, a comparison is shown between the existing, indeterminate sampling plans and the recommended sample designs. The projected sampling technique is illustrated by calculating the luminous intensities of LEDs using the Weibull distribution. Based on the findings and practical example, we conclude that the suggested strategy needs a smaller sample size than SSP and the current MDS sampling plan.

Nitrogen dioxide (NO2) is the most active pollutant gas emitted in the industrial era and is highly correlated with human activities. Tracking NO2 emissions and predicting their concentrations represent important steps toward controlling pollution and setting rules to protect people\'s health indoors, such as in factories, and in outdoor environments. The concentration of NO2 was affected by the COVID-19 lockdown period and decreased because of restrictions on outdoor activities. In this study, the concentration of NO2 was predicted at 14 ground stations in the United Arab Emirates (UAE) during December 2020 based on training over a full time period of two years (2019-2020). Statistical and machine learning models, such as autoregressive integrated moving average (ARIMA), seasonal autoregressive integrated moving average (SARIMA), long short-term memory (LSTM), and nonlinear autoregressive neural network (NAR-NN), are used with both open- and closed-loop architectures. The mean absolute percentage error (MAPE) was used to evaluate the performance of the models, and the results ranged from \"very good\" (MAPE of 8.64% at the Liwa station with the closed loop) to \"acceptable\" (MAPE of 42.45% at the Khadejah School station with the open loop). The results show that the predictions based on the open loop are generally better than those based on the closed loop because they yield statistically significantly lower MAPE values. For both loop types, we selected stations exhibiting the lowest, medium, and highest MAPE values as representative cases. In addition, we demonstrated that the MAPE value is highly correlated with the relative standard deviation of NO2 concentration values.

The existing t-test of a correlation coefficient works under a determinate environment. In uncertainty, the existing t-test of a correlation coefficient is unable to investigate the significance of correlation. The study presents a modification of the existing t-test of a correlation coefficient using neutrosophic statistics. The test statistic is designed to investigate the significance of correlation when imprecise observations or uncertainties in the level of significance are presented. The test is applied to data obtained from patients with diabetes. From the data analysis, the proposed t-test of a correlation coefficient is found to be more effective than existing tests.

The purpose of this paper is to develop a multiple dependent state (MDS) sampling plan based on time-truncated sampling schemes for the daily number of cases of the coronavirus disease COVID-19 using gamma distribution under indeterminacy. The proposed sampling scheme parameters include average sample number (ASN) and accept and reject sample numbers when the indeterminacy parameter is known. In addition to the parameters of the proposed sampling schemes, the resultant tables are provided for different known indeterminacy parametric values. The outcomes resulting from various sampling schemes show that the ASN decreases as indeterminacy values increase. This shows that the indeterminacy parameter plays a vital role for the ASN. A comparative study between the proposed sampling schemes and existing sampling schemes based on indeterminacy is also discussed. The projected sampling scheme is illustrated with the help of the daily number of cases of COVID-19 data. From the results and real example, we conclude that the proposed MDS sampling scheme under indeterminacy requires a smaller sample size compared to the single sampling plan (SSP) and the existing MDS sampling plan.

To test the equality of several independent multinomial distributions, the chi-square test for count data is applied. The existing test can be applied when complete information about the data is available. The complex process, such as DNA count, the existing test under classical statistics may mislead. To overcome the issue, the modification of the chi-square test for multinomial distribution under neutrosophic statistics is presented in this paper. The modified form of the chi-square test statistic under indeterminacy/uncertainty is presented and applied using the DNA count data. From the DNA count data analysis, simulation, and comparative studies, the proposed test is found to be informative, springy, and good as compared with the existing tests.

The existing Z-test for uncertainty events does not give information about the measure of indeterminacy/uncertainty associated with the test.
This paper introduces the Z-test for uncertainty events under neutrosophic statistics. The test statistic of the existing test is modified under the philosophy of the Neutrosophy. The testing process is introduced and applied to the Covid-19 data.
Based on the information, the proposed test is interpreted as the probability that there is no reduction in uncertainty of Covid-19 is accepted with a probability of 0.95, committing a type-I error is 0.05 with the measure of an indeterminacy 0.10. Based on the analysis, it is concluded that the proposed test is informative than the existing test. The proposed test is also better than the Z-test for uncertainty under fuzzy-logic as the test using fuzz-logic gives the value of the statistic from 2.20 to 2.42 without any information about the measure of indeterminacy. The test under interval statistic only considers the values within the interval rather than the crisp value.
From the Covid-19 data analysis, it is found that the proposed Z-test for uncertainty events under the neutrosophic statistics is efficient than the existing tests under classical statistics, fuzzy approach, and interval statistics in terms of information, flexibility, power of the test, and adequacy.

In this paper, a new trimmed regression model under the neutrosophic environment is introduced. The mathematical model of the new regression model along with its neutrosophic form is given. The methods to find the error sum of square and trended values are also given. The trimmed neutrosophic correlation is also introduced in the paper. The proposed trimmed regression is applied to prostate cancer. From the analysis, it is concluded that the proposed model provides the minimum error sum of square as compared to the existing regression model under neutrosophic statistics. It is found that the proposed model is quite effective to forecast prostate cancer patients under an indeterminacy setting.

The uncertainty/indeterminate in control chart parameter/observations affects the performance of the control chart. This paper addresses the indeterminacy and its effect on the Shewhart X-bar control using multiple dependent state repetitive sampling. The probabilities and neutrosophic average run length for in-control and out-of-control processes are derived. The tables and figures of the proposed chart are presented when uncertainty/indeterminate is present in sample size and proceeding subgroups. The efficiency of the proposed chart is compared with the existing charts and the proposed chart is found to be efficient in terms of neutrosophic average run length.

The data obtained from the counting process is known as the count data. In practice, the counting can be done at the same time or the time of the count is not the same. To test either the K counts are differed significantly or not, the Chi-square test for K counts is applied.
The paper presents the Chi-square tests for K counts under neutrosophic statistics. The test statistic of the proposed test when K counts are recorded at the same time and different time are proposed. The testing procedure of the proposed test is explained with the help of pulse count data.
From the analysis of pulse count data, it can be concluded that the proposed test suggests the cardiologists use different treatment methods on patients. In addition, the proposed test gives more information than the traditional test under uncertainty.

The Spearman rank correlation test under classical statistics cannot be applied when the paired data is in interval or indeterminacy is presented in the paired data.
In this paper, the Spearman rank correlation test under neutrosophic statistics will be introduced. The proposed Spearman rank correlation test will be a generalization of the existing Spearman rank correlation test.
The proposed test is supposed to be more informative, flexible, and adequate to apply for the analysis of the measurement data. The application of the proposed test is given using the measurement of luteotropichormone data obtained from the clinical laboratory. Based on the information, the probability of accepting the null hypothesis H0N is 0.95, the chance of committing a type-I error is 0.05 and the chance of indeterminacy about the acceptance of H0N is 69%.
From the analysis, it is noted that the proposed test is more efficient in terms of the measure of indeterminacy as compared with the existing test. From the study, it is concluded that the proposed test is more informative, applicable and useable under an indeterminate environment as compared with the existing test under classical statistics. Therefore, it is recommended to apply the proposed test in clinical laboratories for testing the correlation between instruments.