In this paper, a new Nonparametric Control Chart based on two EWMA statistics is proposed for monitoring process deviation from the target value. The performance comparison of the proposed Chart with the existing Nonparametric EWMA sign Control Chart and a Nonparametric CUSUM mean Control Chart are made by using out-of-Control average run length. The simulation study showed the superiority of the suggested Chart over the four other parametric and Nonparametric Charts. An empirical illustration is also provided for performance evaluation of the proposed Chart. By comparing the proposed Chart with the existing Charts, it is concluded that the proposed Chart is more sensitive in detecting a small shift in the process.

Nonparametric Control Chart based on signed-rank statistic is used for detecting changes in mean (median). Although the Sign-Rank (SR) Chart is more efficient under heavy-tailed distributions (double exponential and Cauchy) but the performance of this Chart is very inappropriate in light-tailed distributions (uniform and normal). In this paper, signed-rank Chart is developed with variable sampling interval. The performance of signed-rank Chart with variable sampling interval (VSI-SR) is compared to signed-rank Chart with fixed sampling interval (FSI-SR) and `X Chart. The numerical results demonstrated the VSI-SR Chart is better from the FSI-SR Chart. Also the VSI-SR Chart is more efficient from `X Chart in heavy-tailed distributions and some of changes under normal light-tailed distribution.

This study proposed a dual ExponentiallyWeighted Moving Average (EWMA) statistics based Nonparametric sign Control Chart to monitor the process deviation from the targeted value. The performance of the proposed Chart is compared with the existing Nonparametric version of the EWMA sign and Cumulative Sum (CUSUM) mean Control Charts by using out-of-Control average run length for various shifts in the process. The simulation study showed the superiority of the suggested Chart over the existing counterparts. A real dataset is also considered for the application of the proposed Chart.

Control Charts are one of the most effective tools used in quality Control to monitor various quality characteristics in a process with the aim to improve quality of the product. Usually, in Shewhart Control Charts, the normality assumption met for the data, but sometimes there is lack of information regarding the statistical distribution of the observations. For this reason, non-parametric Control Charts are used in this situation. In this research, non-parametric sign Charts are introduced to deal with the lack of information regarding observations’ statistical distribution. Nonparametric Generalized Weighted Moving Average Sign Control Chart (NS GWMA) designed using statistical design and average run length (ARL) and its statistical performance was studied. But statistical design is not enough to ensure the performance of a Control Chart, so in the next steps, economic design (ED) and economic-statistical design (ESD) were applied using cost model of Lorenzen and Vance, in order to optimize both statistical and economical characteristics of the Control Chart. The results show that the non-parametric sign-generalized weighted moving average sign Control Chart performed well in detecting small shifts in the process and also had optimized cost and time to perform.

Control Charts are widely used to identify changes in the production process, and when it comes to identifying small changes in the process, non-Shewhart Control Charts such as exponential weighted moving average (EWMA) and generalized weighted moving average (GWMA) are better alternatives to Control Charts than Shewhart 𝑋 Control Chart. In this context, Nonparametric Control Charts are used when the distribution of quality characteristic of the process is unknown, in which the Sign Control Chart is one of the most popular Nonparametric Control Charts. In this paper, for the first time, a generalized weighted moving average sign Control Chart using a ranked set sampling (RSS) design is introduced. The performance of the proposed Control Chart is evaluated using simulated data according to the average run length evaluation criterion, and simulation studies showed that the GWMA sign Control Chart under the RSS design is better at detecting small process changes than the EWMA sign Control Chart under the RSS design. The performance of the proposed Control Chart has been evaluated using simulated data according to the average execution length evaluation criteria in Julia software, and the simulation studies show that due to changes in the regulatory parameter α, the 𝐺𝑊𝑀𝐴𝑆𝑅𝑆𝑆 + Control Chart is more sensitive than the 𝐸𝑊𝑀𝐴𝑆𝑅𝑆𝑆 + Control Chart in discovering small process changes, also the 𝐺𝑊𝑀𝐴𝑆𝑅𝑆𝑆 + Control Chart is more sensitive than the 𝐺𝑊𝑀𝐴𝑆𝑆𝑅𝑆 + and 𝐷𝐺𝑊𝑀𝐴𝑆𝑆𝑅𝑆 + Control Charts are more efficient and sensitive in identifying small process changes, which shows the advantage of RSS scheme over SRS scheme. In addition, it was proved that increasing k and the number of cycles and large values of q decrease 𝐴𝑅𝐿1 and increase the power of the Control Chart in identifying process changes.

Multivariate Control Charts such as Hotelling's T2 and X2 are commonly used for monitoring several related quality characteristics. These Control Charts use correlation structure that exists between quality characteristics in an attempt to improve monitoring. The purpose of this article is to discuss some issues related to the G Chart proposed by Levinson et al. [9] for detecting shifts in the process variance-covariance matrix. They use a G statistic which is distributed as a chi-square with p(p+1)/2 degrees of freedom where p denotes the number of variables under study. The authors show through simulation that the chi-square distribution only holds for certain cases. The results could be important to practitioners who use G Chart for monitoring purposes.

The two most significant sources of uncertainty are randomness and incomplete information. In real systems, we wish to monitor processes in the presence of these two kinds of uncertainty. This paper aims to construct a fuzzy statistical Control Chart that can explain existing fuzziness in data while considering the essential variability between observations. The proposed Control Chart avoids defuzzification methods such as fuzzy mean, fuzzy mode, fuzzy midrange, and fuzzy median. The out-of-Control states are determined based on a fuzzy in-Control region and a simple and precise graded exclusion measure that determines the degree to which fuzzy subgroups are excluded from the fuzzy in-Control region. The proposed Chart is illustrated with a numerical example.