THE POWER OF X-CHART IN PRESENCE OF DATA CORRELATION
Keywords:
Control Chart, Correlation, Power of X-Chart.Abstract
A fundamental assumption in the development of X control chart is that the underlying distribution of the quality characteristic is normal and the process data is normally distributed. However we may have certain situations where the assumption of independence and normality are either fully or partially violated. In this paper an attempt has been made to examine the power of X chart when the assumption of independence of the data is violated. Expressions for the power of X-chart are derived for different values of correlation coefficient.
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References
Box, G.E.P., Jenkins, G.M. and Rinsel, S.M. (1994). Time series analysis:
Forecasting and control, 2nd ed. Holden-Day, San Francisco, CA.
Chou, C.Y. , Chen, C.H and Liu, H.R. (2005). Acceptance control charts for
non-normal data, Journal of Applied Statistics, 32, p. 25–36.
Kanazura, T. (1986). The effect of measurement error on the power of X R−
chart, J. of Quality Technology,18(2), p. 91-95.
Maragah,H.D, and Woodall, W.H.(1992). The effect of autocorrelation on the
retrospective X chart, Journal of Statistical Computation and Simulation, 40,
p. 29-42.
Montgomery, D.C. (1991). Introduction to Statistical Quality Control, 2nd ed.
J. Wiley & Sons, New York, NY.
Montgomery, D.C., and Mastrangelo, C.M. (1991). Some statistical process
control methods for auto-correlated data (with discussion), Journal of Quality
Technology, 23, p. 179-204.
Neuhardt, J.B. (1987). Effect of correlated sub-samples in statistical process
control, .IIE transactions, 19, p. 208-214.
Padgett, C. S., Tombs, L. A. and Padgett, W. J. (1992). On the α-risks for
Shewart control, Comm. Statist. Simulation and Computation, 21, p. 1125-
Rossoul,N., Abbas, S. and Mehdi,D. (2010). Linear profile monitoring in the
presence of non-normality and autocorrelation, International journal of
Industrial Engineering and Production Research, 21(4), p. 221-230.
Singh, H.R. and Singh, J. R. (1982). Variable Sampling Plan under second
order Auto-regressive model. Indian Association of Products, Quality and
Reliability Transactions , 7(2), p. 97-104.
Singh, J. R. and Kulkarni, K. (2009). The effect of Yule’s process on the
power of X chart, Varahmihir, J. Math. Sci., 9(1), p. 123-126..
Wardell,D.G., Moskowitz,H. and Plante, R.D.(1994). Run length distribution
of special- cause control charts for correlated processes (with discussion),
Technometrics, 36(1), p. 3-27.
Yang,K. and Hancock, W.M.(1990). Non-normality and design of control
charts for averages, Decision Sciences, 23, 1099-1113.