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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 Received: 19 April
2013/Accepted: 5 February 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 REFERENCES Brook, D. & Evans, D.A. 1972. An approach to the probability distribution of CUSUM run length.
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*Corresponding author; email: tehsyin@usm.my
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