Abstract
The EWMA charts are the well-known memory-type charts used for monitoring the small-to-intermediate shifts in the process parameters (location and/or dispersion). The hybrid EWMA (HEWMA) charts are enhanced version of the EWMA charts, which effectively monitor the process parameters. This paper aims to develop two new uppersided HEWMA charts for monitoring shifts in process variance, i.e., HEWMA1 and HEWMA2 charts. The design structures of the proposed HEWMA1 and HEWMA2 charts are based on the concept of integrating the features of two EWMA charts. The HEWMA1 and HEWMA2 charts plotting statistics are developed using one EWMA statistic as input for the other EWMA statistic. A Monte Carlo simulations method is used as a computational technique to determine the numerical results for the performance characteristics, such as average run length (ARL), median run length, and standard deviation run length (SDRL) for assessing the performance of the proposed HEWMA1 and HEWMA2 charts. In addition, to evaluate the overall performance of the proposed HEWMA1 and HEWMA2 charts, other numerical measures consisting of the extra quadratic loss (EQL), relative average run length (RARL), and performance comparison index (PCI) are also computed. The proposed HEWMA1 and HEWMA2 charts are compared to some existing charts, such as CH, CEWMA, HEWMA, AEWMA HHW1, HHW2, AIB-EWMA-I, and AIB-EWMA-II charts, on the basis aforementioned numerical measures. The comparison reveals that the proposed HEWMA1 and HEWMA2 charts achieve better detection ability against the existing charts. In the end, a real-life data application is also provided to enhance the implementation of the proposed HEWMA1 and HEWMA2 charts practically.
Highlights
Control charts are the essential tools of the statistical process monitoring (SPM) toolkit, used to detect the shifts in manufacturing and production processes parameter(s)
The memory-type charts, such as the exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts are sensitive in monitoring smallto-intermediate shifts in the process parameter(s)
The Monte Carlo simulations are employed to compute the numerical results associated with average run length (ARL), standard deviation run length (SDRL), extra quadratic loss (EQL), relative average run length (RARL), and performance comparison index (PCI) for the proposed HEWMA1 and HEWMA2 charts
Summary
Control charts are the essential tools of the statistical process monitoring (SPM) toolkit, used to detect the shifts in manufacturing and production processes parameter(s). Ali et al [23] suggested the generally weighted moving average (GWMA) and hybrid EWMA (HEWMA) chart to monitor process variance changes Both GWMA and HEWMA perform better than classical memory charts. The Monte Carlo simulations are employed to compute the numerical results associated with average run length (ARL), standard deviation run length (SDRL), extra quadratic loss (EQL), relative average run length (RARL), and performance comparison index (PCI) for the proposed HEWMA1 and HEWMA2 charts. Based on these measures, the proposed HEWMA1 and HEWMA2 charts are compared to the existing CH, CEWMA, HEWMA, AEWMA, HHW1, HHW2, AIBEWMA1, and AIBEWMA2 charts.
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