Abstract
Control charting is a graphical expression and operation of statistical hypothesis testing. In the present paper, we develop the economic design of the variable sampling intervals (VSI) exponentially weighted moving average (EWMA) charts to determine the values of the six test parameters of the charts (i.e., the sample size, the long sampling interval, the short sampling interval, the warning limit coefficient, the control limit coefficient, and exponential weight constant) such that the expected total cost is minimized. The genetic algorithm (GA) is applied to search for the optimal values of the six test parameters of the VSI EWMA chart, and an example is provided to illustrate the solution procedure. A sensitivity analysis is then carried out to investigate the effects of model parameters on the solution of the economic design.
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References
Amin, R. W. (1987). Variable Sampling Interval Control Charts, Ph.D. Dissertation, Virginia Tech, Blacksburg, VA, USA.
R.W. Amin R.W. Miller (1993) ArticleTitleA robustness study of X͡ charts with variable sampling Intervals Journal of Quality Technology 25 36–44
F. Aparisi C.L. Haro (2001) ArticleTitleHotelling’s T2 control chart with variable sampling intervals International Journal of Production Research 39 3127–3140 Occurrence Handle10.1080/00207540110054597
R.V. Baxley (1995) ArticleTitleAn application of variable sampling interval control charts Journal of Quality Technology 27 275–282
S. Bhattacharyya O.V. Pictet G. Zumbach (2002) ArticleTitleKnowledge-intensive genetic discovery in foreign exchange markets IEEE Transactions on Evolutionary Computation 6 IssueID2 169–181 Occurrence Handle10.1109/4235.996016
C.Y. Chou C.H. Chen C.H. Chen (2006) ArticleTitleEconomic design of variable sampling intervals T-square control charts using genetic algorithms Expert Systems with Applications 30 233–242 Occurrence Handle10.1016/j.eswa.2005.07.010
S.V. Crowder (1987) ArticleTitleA simple method for studying run length distributions of exponentially weight moving average control charts Technometrics 29 401–407 Occurrence Handle10.2307/1269450
A.J. Duncan (1956) ArticleTitleThe economic design of X͡ charts used to maintain current control of a process Journal of the American Statistical Association 52 228–242 Occurrence Handle10.2307/2281343
I.N. Gibra (1971) ArticleTitleEconomically optimal determination of the parameters of an X-bar control chart Management Science 17 635–646 Occurrence Handle10.1287/mnsc.17.9.635
A.L. Goel S.D. Jain S.M. Wu (1968) ArticleTitleAn algorithm for the determination of the economic design of X-bar charts based on Duncan’s model Journal of the American Statistical Association 63 304–320 Occurrence Handle10.2307/2283850
C. Ho K.E. Case (1994a) ArticleTitleEconomic design of control charts: a literature review for 1981–1991 Journal of Quality Technology 26 1–18
C. Ho K.E. Case (1994) ArticleTitleThe economically-based EWMA control chart International Journal of Production Research 32 2179–2186
J. H. Holland (1975) Adaptation in Nature and Artificial System The University of Michigan Press Ann Arbor, Michigan, USA
M.T. Jensen (2003) ArticleTitleGenerating robust and flexible job shop schedules using genetic algorithms IEEE Transactions on Evolutionary Computation 7 IssueID3 275–288 Occurrence Handle10.1109/TEVC.2003.810067
H.A. Knappenberger A.H. Grandage (1969) ArticleTitleMinimum cost quality control tests AIIE Transactions 1 24–32
Y.C. Lin C.Y. Chou (2005a) ArticleTitleAdaptive X͡ control charts with sampling at fixed times Quality and Reliability Engineering International 21 163–175 Occurrence Handle10.1002/qre.613
Y.C. Lin C.Y. Chou (2005) ArticleTitleOn the design of variable sample size and sampling intervals X-bar charts under non-normality International Journal of Production Economics 96 249–261 Occurrence Handle10.1016/j.ijpe.2004.05.001
T.J. Lorenzen L.C. Vance (1986) ArticleTitleThe economic design of control charts: a unified approach Technometrics 28 3–10 Occurrence Handle10.2307/1269598
D.C. Montgomery (1980) ArticleTitleThe economic design of control charts: a review and literature survey Journal of Quality Technology 12 75–87
M.R. Reynolds R.W. Amin J.C. Arnold J.A. Nachlas (1988) ArticleTitleX͡ charts with variable sampling intervals Technometrics 30 181–192 Occurrence Handle10.2307/1270164
S.W. Roberts (1959) ArticleTitleControl chart tests based on geometric moving averages Technometrics 1 239–250 Occurrence Handle10.2307/1266443
S.W. Roberts (1966) ArticleTitleA comparison of some control chart procedures Technometrics 8 411–430 Occurrence Handle10.2307/1266688
M.S. Saccucci J.M. Lucas (1990) ArticleTitleAverage run lengths for exponentially weighted moving average control schemes using the Markov chain approach Journal of Quality Technology 22 154–162
M.S. Saccucci R.W. Amin J.M. Lucas (1992) Exponentially weighted moving average control schemes with variable sampling intervals. Communications in Statistics – Simulation and Computation 21 IssueID3 627–657
J.C.C. Torng D.C. Montgomery J.K. Cochran (1994) ArticleTitleEconomic design of the EWMA control chart Economic Quality Control 9 3–23
L.C. Vance (1983) ArticleTitleA bibliography of statistical quality control chart techniques, 1970–1980 Journal of Quality Technology 15 59–62
K.H. Waldmann (1986) ArticleTitleBounds for the distribution of run length of geometric moving average charts Applied Statistics 35 151–158 Occurrence Handle10.2307/2347265
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Chou, CY., Chen, CH. & Liu, HR. Economic Design of EWMA Charts with Variable Sampling Intervals. Qual Quant 40, 879–896 (2006). https://doi.org/10.1007/s11135-005-8822-8
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DOI: https://doi.org/10.1007/s11135-005-8822-8