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
RUJUKAN
Brook,
D. & Evans, D.A. 1972. An approach to the probability distribution
of CUSUM run length. Biometrika
59(3): 539- 549.
Castagliola, P. 2005. A new S2-EWMA
control chart for monitoring the process variance. Quality and
Reliability Engineering International 21: 781-794.
Castagliola, P., Celano,
G., Fichera, S. & Nunnari,
V. 2008. A variable sample size S2-EWMA control chart for monitoring
the process variance. International Journal of Reliability, Quality
and Safety Engineering 15(3): 181-201.
Castagliola, P., Celano,
G., Fichera, S. & Giuffrida,
F. 2007. A variable sampling interval S2-EWMA control chart for monitoring
the process variance. International Journal of Technology Management
37(1/2): 125-146.
Chakraborti, S. 2007. Run length distribution and
percentiles: The Shewhart X chart
with unknown parameters. Quality Engineering 19(2): 119-127.
Chang,
T.C. & Gan, F.F. 1994. Optimal designs
of one-sided EWMA charts for monitoring a process variance. Journal
of Statistical Computation and Simulation 49(1-2): 33-48.
Crowder,
S.V. & Hamilton, M.D. 1992. An EWMA for monitoring a process
standard deviation. Journal of Quality Technology 24(1):
12-21.
Di Bucchianico, A.A.D., Mooiweer, G.D. & Moonen, E.J.G.
2005. Monitoring infrequent failures of high-volume
production processes. Quality and Reliability Engineering
International 21(5): 521-528.
Eyvazian, M., Jalali
Naini, S.G. & Vaghefi, A. 2008.
Monitoring process variability using exponentially weighted moving
sample variance control charts. International Journal of Advanced
Manufacturing Technology 39(3/4): 261-270.
Gan, F.F. 1994. An optimal design of cumulative sum control chart based
on median run length. Communications in Statistics- Simulation
and Computation 23(2): 485-503.
Gan, F.F. 1993a. An optimal design of EWMA control charts based on median
run length. Journal of Statistical Computation and Simulation
45(3&4): 169-184.
Gan, F.F.
1993b. The run length distribution of a cumulative sum control chart.
Journal of Quality Technology 25(3): 205-215.
Gan, F.F. 1992. An Optimal Design of Cumulative Sum Control Charts
based on Median Run Length. Research Report No. 536, Lee Kong
Chian Center for Mathematical Research, Singapore.
Graham, M.A., Chakraborti, S. &
Human, S.W. 2011. A nonparametric exponentially weighted moving
average signed-rank chart for monitoring location. Computational
Statistics & Data Analysis 55(8): 2490-2503.
He, D. & Grigoryan, A. 2003. An improved double sampling S chart. International
Journal of Production Research 41(12): 2663-2679.
Khoo, M.B.C. 2004.
S2
control chart based on double sampling. International
Journal of Pure and Applied Mathematics 13(2): 249-258.
Li, S.Y., Tang,
L.C. & Ng, S.H. 2010. Nonparametric CUSUM and EWMA control charts
for detecting mean shifts. Journal of Quality Technology 42(2):
209-226.
Lucas, J.M. &
Saccucci, M.S. 1990. Exponentially weighted
moving average control schemes: Properties and enhancements. Technometrics 32(1): 1-12.
Montgomery, D.C.
2009. Statistical Quality Control: A Modern Introduction. 6th
ed. New Jersey: John Wiley & Sons (Asia) Pte. Ltd.
Radson, D. & Boyd,
A.H. 2005. Graphical representation of run length distributions.
Quality Engineering 17(2): 301-308.
Razmy, A.M. & Peiris, T.S.G. 2013. Design of exponentially weighted moving
average chart for monitoring standardized process variance. International
Journal of Engineering and Technology 13(5): 74-78.
Roberts, S.W. 1959.
Control charts tests based on geometric moving averages. Technometrics 1: 239-250.
Simões, B.F.T., Epprecht, E.K. & Costa, A.F.B. 2010. Performance comparisons
of EWMA control chart schemes. Quality Technology & Quantitative
Management 7(3): 249- 261.
Shu, L.J. 2008.
An adaptive exponentially weighted moving average control chart
for monitoring process variances. Journal of Statistical Computation
and Simulation 78(4): 367-384.
Teoh, W.L. &
Khoo, M.B.C. 2012. Optimal design of the
double sampling chart based on median run length. International
Journal of Chemical Engineering and Applications 3(5): 303-
306.
Thaga, K. 2003. Contributions
to statistical process control tools. PhD. Thesis, University of
Manitoba, Canada (unpublished).
Yang, S.F., Lin,
J.S. & Cheng, S.W. 2011. A new nonparametric EWMA sign control
chart. Expert Systems with Applications 38(5): 6239-6243.
*Pengarang untuk surat-menyurat; email: tehsyin@usm.my
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