Sains Malaysiana 44(7)(2015): 1067–1075

A Study on the S2-EWMA Chart for Monitoring the Process Variance based on the MRL Performance

(Suatu Kajian Carta S2-EWMA bagi Memantau Varians Proses Berdasarkan Prestasi MRL)

TEH SIN YIN1*, KHOO MICHAEL BOON CHONG2, ONG KER HSIN1, SOH KENG LIN1

& TEOH WEI LIN2,3

1School of Management, Universiti Sains Malaysia, 11800 Minden, Pulau Pinang, Malaysia

2School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Minden, Pulau Pinang

Malaysia

3Department of Physical and Mathematical Science, Faculty of Science, Universiti Tunku Abdul Rahman, 31900 Kampar, Perak Darul Ridzuan, Malaysia

Diserahkan: 19 April 2013/Diterima: 5 Februari 2015

ABSTRACT

The existing optimal design of the fixed sampling interval S2-EWMA control chart to monitor the sample variance of a process is based on the average run length (ARL) criterion. Since the shape of the run length distribution changes with the magnitude of the shift in the variance, the median run length (MRL) gives a more meaningful explanation about the in-control and out-of-control performances of a control chart. This paper proposes the optimal design of the S2-EWMA chart, based on the MRL. The Markov chain technique is employed to compute the MRLs. The performances of the S2-EWMA chart, double sampling (DS) S2 chart and S chart are evaluated and compared. The MRL results indicated that the S2-EWMA chart gives better performance for detecting small and moderate variance shifts, while maintaining almost the same sensitivity as the DS S2 and S charts toward large variance shifts, especially when the sample size increases.

Keywords: Exponentially weighted moving average (EWMA); Markov chain; median run length (MRL); sample variance

ABSTRAK

Reka bentuk optimum carta kawalan EWMA-S2 selang pensampelan tetap yang digunakan untuk memantau proses sampel varians adalah berdasarkan kriteria panjang larian purata (ARL). Oleh sebab bentuk taburan panjang larian berubah dengan magnitud anjakan dalam varians, maka panjang larian median (MRL) memberi penjelasan yang lebih bermakna tentang prestasi terkawal dan luar kawalan carta kawalan. Kertas kerja ini mencadangkan reka bentuk optimum untuk carta EWMA-S2 berdasarkan MRL. Teknik rantai Markov digunakan untuk mengira MRL. Prestasi carta-carta EWMA-S2, DS S2 dan S telah dinilai dan dibandingkan. Keputusan MRL menunjukkan bahawa carta EWMA-S2 memberikan prestasi yang lebih baik untuk mengesan anjakan varians yang kecil dan sederhana di samping mengekalkan kepekaan yang hampir sama dengan carta-carta DS S2 dan S terhadap anjakan varians yang besar, terutamanya apabila saiz sampel meningkat.

Kata kunci: Panjang larian median; purata bergerak berpemberat eksponen (EWMA); rantai Markov; varians sampel

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*Pengarang untuk surat-menyurat; email: tehsyin@usm.my

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