In the present paper, we propose a control chart based on extended exponentially weighted moving average (EEWMA) statistic to detect a quick shift in the mean. The mean and variance expression of the proposed EEWMA statistic are derived. The proposed EEWMA statistic is unbiased and simulation results show a smaller variance as compared to the traditional EWMA. The performance of the proposed control chart with the existing chart based on the EWMA statistic is evaluated in terms of average run length (ARL). Various tables were constructed for different values of parameters. The comparison of the EEWMA control chart with the traditional EWMA and Shewhart control charts illustrates that the proposed control chart performs better in terms of quick detection of the shift. The working procedure of the proposed control chart was also illustrated by simulated and application data.

Existing variance control charts are designed under the assumptions that no uncertain, fuzzy and imprecise observations or parameters are in the population or the sample. Neutrosophic statistics, which is the extension of classical statistics, has been widely used when there is uncertainty in the data. In this paper, we will originally design $S^2$ control chart under the neutrosophic interval methods. The complete structure of the neutrosophic $S^2$ control chart will be given. The necessary measures of neutrosophic $S^2$ will be given. The neutrosophic coefficient of $S^2$ control chart will be determined through the neutrosophic algorithm. Some tables are given for practical use. The efficiency of the proposed control chart is shown over the $S^2$ control chart designed under the classical statistics in neutrosophic average run length (NARL). A real example is also added to illustrate the proposed control chart. From the comparison in the simulation study and case study, it is concluded that the proposed control chart performs better than the existing control chart under uncertainty.

Existing control charts based on failure-censored (Type-II) reliability tests were designed using classical statistics. Classical statistics was applied for the monitoring of the process when observations in the sample or the population were determined. Neutrosophic statistics (NS) are applied when there is uncertainty in the sample or population. In this paper, a control chart for failure-censored (Type-II) reliability tests was designed using NS. The design of a control chart for the Weibull distribution, which is applied when there is a lack of symmetry using neutrosophic statistics, is given. The proposed control chart was used to monitor the neutrosophic mean and neutrosophic variance, which are related to the neutrosophic scale parameter. The advantages of the proposed control chart over the existing control chart are discussed.

In this manuscript, a control chart is designed when the quality characteristic of interest follows a gamma distribution using repetitive sampling. The Wilson-Hilferty approximation is used to transform the gamma distributed characteristic to a normal random variable. Two pairs of control limits are established and their control constants are determined by considering the specified in-control average run length (ARL). The out-of-control ARL is derived when the process is shifted in terms of the scale parameter of the Gamma distribution. The ARLs are presented for various values of the shape parameter according to process shift parameters. A simulated example is given to illustrate the proposed control chart.