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All Journal Parameter: Jurnal Matematika, Statistika dan Terapannya
Samin Radjid
Institut Teknologi Sepuluh Nopember
Mathematics

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EWMA Robust Max-M Control Chart for Synthetic and Real Data Samin Radjid; Wibawati Wibawati; Muhammad Ahsan
Parameter: Jurnal Matematika, Statistika dan Terapannya Vol 5 No 1 (2026): Parameter: Jurnal Matematika, Statistika dan Terapannya
Publisher : Jurusan Matematika FMIPA Universitas Pattimura

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/parameterv5i1pp219-232

Abstract

Quality monitoring in multivariate industrial processes requires a control chart that can simultaneously evaluate changes in the process mean and variability. This study applies the Exponentially Weighted Moving Average Robust Max-M Control Chart (ERMM-Chart) to synthetic data and real cement clinker quality data. The ERMM-Chart is constructed from a robust Max-M statistic that monitors the mean and variability components, followed by an Exponentially Weighted Moving Average (EWMA) smoothing mechanism. Phase I parameters are estimated using the Fast Minimum Covariance Determinant (Fast-MCD) method to obtain robust estimates of the process center and covariance matrix. The synthetic data are used to illustrate the response of the ERMM-Chart under no-shift, mean-shift, variability-shift, and simultaneous mean-variability shift conditions. Meanwhile, the real clinker data are analyzed using two quality characteristics, namely free lime (FCaO) and tetracalcium aluminoferrite (C4AF). The results show that the ERMM-Chart can distinguish the reference phase from the monitoring phase through statistic points exceeding the upper control limit. The chart also provides early detection of process changes based on the Run Length value. Thus, the ERMM-Chart can be used as a robust simultaneous multivariate control chart for individual observations.
Co-Authors Muhammad Ahsan Wibawati Wibawati