Statistical process control (SPC) tools are used for the investigation and identification of unnatural variations in the manufacturing, industrial, and service processes. The control chart, the basic and the most famous tool of SPC, is used for process monitoring. Generally, control charts are constructed under normality assumption of the quality characteristic of interest, but in practice, it is quite hard to hold the normality assumption. In such situations, parametric charts tend to offer more frequent false alarms and invalid out-of-control performance. To rectify these problems, non-parametric control charts are used, as these have the same in-control run length properties for all the continuous distributions and are known as in-control robust. This study intends to develop a new non-parametric exponentially weighted moving average (NPEWMA) chart based on sign statistics under a ranked set sampling scheme that is hereafter named (NPREWMA-SN). The run-length profiles of the NPREWMA-SN chart are computed using the Monte Carlo simulation method. The proposed scheme is compared with NPEWMA-SN and classical EWMA-$\overline{X}$ charts, using different run length measures. The comparison reveals the in-control robustness and superiority of the proposed scheme over its competitors in detecting all kinds of shifts in the process location. A practical application related to the substrate manufacturing process is included to show the demonstration of the proposed chart.

Control charts may help keep industrial and manufacturing processes running smoothly and optimize their performance. In situations when it is uncertain how the data will be distributed, nonparametric control charts are more reliable and useful than parametric charts. The sign test statistic and arcsine transformation are rapidly used in designing the nonparametric control charts. This article has designed Exponentially weighted moving average and Cumulative sum control charts using sign test statistic and arcsine transformation under zero-state and steady-state at head-to-head optimal design parameter choices. The proposed study quantifies the effect of both tests for the in-control (IC) and out-of-control (OOC) processes. The run-length (RL) properties have been calculated by using the Monte Carlo simulation method to assess the performance of the designed schemes. The RL profiles show that all the nonparametric schemes have IC robust behavior against the non-normality of the distributions. The results of the study reveal that the sign test statistic reveals almost equal but quite better results at small shifts, if the actual shifts are medium to large then arcsine transformation may respond quite better. Application of the charts under sign and arcsine transformation has been executed using an artificial dataset.

The GARCH model is one of the most influential models for characterizing and predicting fluctuations in economic and financial studies. However, most traditional GARCH models commonly use daily frequency data to predict the return, correlation, and risk indicator of financial assets, without taking data with other frequencies into account. Hence, financial market information may not be sufficiently applied to the estimation of GARCH-type models. To partially solve this problem, this paper introduces intraday high-frequency data to improve estimation of the volatility function of a semiparametric GARCH model. To achieve this objective, a semiparametric volatility proxy model was proposed, which includes both symmetric and asymmetric cases. Under mild conditions, the asymptotic normality of estimators was established. Furthermore, we also discuss the impact of different volatility proxies on estimation precision. Both the simulation and empirical results showed that estimation of the volatility function could be improved by the introduction of high-frequency data.