The three statistical control charts using ranked set sampling

This article investigated the performance of the three common statistical control charts, the Shewhart x̅ chart, cumulative sum (CUSUM) chart, and exponentially weighted moving average (EWMA) chart for location using ranked set sampling (RSS) instead of the traditional simple random sampling (SRS). Considering a normal population, a Monte Carlo simulation is carried out for several shift values for each of the control chart. The average run length (ARL) showed that the control charts based on RSS data are superior to their corresponding SRS counterparts with no significant difference between CUSUM and EWMA charts. There is an interesting increase in the sensitivity of RSS based Shewhart x̅ chart relative to other charts

A new combined Shewhart-Cumulative Sum S chart for monitoring process standard deviation

The combined application of a Shewhart chart and cumulative sum (CUSUM) control chart is an effective tool for the detection of all sizes of process shifts as the scheme combines the advantages of a CUSUM at detecting small to moderate shifts and Shewhart for the quick detection of very large shifts. This article proposes new combined Shewhart-CUSUM S charts based on the extreme variations of ranked set sampling technique, for efficient monitoring of changes in the process dispersion. Using Monte Carlo simulations, the combined scheme is designed to minimize the average extra quadratic loss over the entire process shift domain. The results show that the combined Shewhart-CUSUM S charts uniformly outperform several other procedures for detecting increases and decreases in the process variability. Moreover, the proposed scheme can detect changes that are small enough to escape the Shewhart S chart or fairly large to escape detection by the CUSUM S chart. Numerical example is given to illustrate the practical application of the proposed scheme using real industrial data

An improved process monitoring by mixed multivariate memory control charts: an application in wind turbine field

Memory control chart such as multivariate CUSUM (MCUSUM) and multivariate EWMA (MEWMA) control charts are considered superior for the detection of small-to-moderate variation in the process mean vector. In this article, we have proposed two advanced forms of memory multivariate charts to identify the small amount of shifts in the process mean vector. The proposed control charts methodologies are based on the mixed features of the MCUSUM, MEWMA, classical EWMA chart, and chart based on principal component analysis. Monte Carlo simulation technique is used to simulate numerical results. To evaluate the performance of proposed control charts, we have used average run length for a single shift, extra quadratic loss function, relative average run length, and performance comparison index measures for certain range of shifts for overall performance. Results elaborate that proposed charts have outstanding performance for detection of small shifts in mean vector as compared to the various existing such as MCUSUM, MEWMA, etc. charts. For practical purpose, implementation of the proposed control charts with a real-life data in the field of wind turbine has included to make clear the advantages of proposed control chart(s) over other control charts for early detection of shifts

An adaptive EWMA scheme-based CUSUM accumulation error for efficient monitoring of process location

The examination of product characteristics using a statistical tool is an important step in a manufacturing environment to ensure product quality. Several methods are employed for maintaining product quality assurance. Quality control charts, which utilize statistical methods, are normally used to detect special causes. Shewhart control charts are popular; their only limitation is that they are effective in handling only large shifts. For handling small shifts, the cumulative sum (CUSUM) and the exponential weighted moving average (EWMA) are more practical. For handling both small and large shifts, adaptive control charts are used. In this study, we proposed a new adaptive EWMA scheme. This scheme is based on CUSUM accumulation error for detection of wide range of shifts in the process location. The CUSUM features in the proposed scheme help with identification of prior shifts. The proposed scheme uses Huber and Tukey bisquare functions for an efficient shift detection. We have used average run length (ARL) as performance indicator for comparison, and our proposed scheme outperformed some of the existing schemes. An example that uses real-life data is also provided to demonstrate the implementation of the proposed scheme