Upper and Lower Control Limits for Monitoring Markoff’s Model and Non-Normal Variation with Known CV

Bhayare Unnati¹ , Singh Jais Raj²

1. School of Studies in Statistics, Vikram University, Ujjain, India.
2. School of Studies in Statistics, Vikram University, Ujjain, India.

Correspondence should be addressed to: unnati.b80@gmail.com .

Section:Research Paper, Product Type: Isroset-Journal
Vol.4 , Issue.6 , pp.35-42, Dec-2017

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v4i6.3542

Online published on Dec 31, 2017

Copyright © Bhayare Unnati, Singh Jais Raj . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
Control charts are essential tools for quality monitoring and construction of this charts were based on the assumption that observations were independent and normally distributed. The assumption of independence of quality characteristic is questionable, as autocorrelation among the observations becomes an inherent characteristic in quality control data. This phenomenon of inherent autocorrelation can cause significant deterioration of control charting performance. Autocorrelation had a substantial and detrimental effect on the statistical properties of control charts. The setting of control limits to utilize on a control chart assumes the assumption of normality. However, in many situation the condition does not hold. The objective of this paper is to investigate the upper and lower control limit properties of the control charts when the Markoff`s model and non-normality exists in the process.

Key-Words / Index Term :
Mean chart, Autocorrelation, Non-Normality, Markoff’s Model, Coefficient of Variation

References :
[1]. Abraham, B. and Kartha, C.P. (1979). “Forecast stability and control Charts”, ASQC Technical Conference Transactions. American Society for Quality Control, Milwaukee, WI, pp 675–685
[2]. Alwan, L.C. (1991). “Autocorrelations: fixed and versus variable controlLimits”, Qual. Eng 4:167–188
[3]. Alwan, L.C. and Roberts, H.V. (1988). “Time-series modeling for statistical process control”, J Bus Econ Stat 6:87–95
[4]. Barton, D. E. and Dennis, K. E. (1952). “The condition under whichGram-Charlier and Edgeworth curve are positive definite and unimodel”, Biometrika, 39, 425-427.
[5]. Bennett, C. (1954) “Effect of measurement error on chemical process Control”, Industrial Quality Control 10:17–20
[6]. Berthouex, P.M., Hunter,W.G. and Pallesen, L. (1978). “Monitoring sewage treatment plants: some quality control aspects”, J Qual. Technol. 10:139–149
[7]. Box, G., Jenkins, G. and Reinsel, G. (1994). “Time Series Analysis, Forecasting and Control”, Prentis-Hall, Englewood Cliffs, New Jersey
[8]. Bhayare, U. and Singh, J. R. (2017). "The Effect of Measurement Error on the Power of X Charts with Known Coefficient of variation", International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.4, Issue.5, pp.33-39.
[9]. Delves, L.M. and Mohamed, J.L. (1985). “Computational methods for integral equations”, Cambridge University Press, New York, NY
[10]. Dooley, K.J., Kapoor, S.G., Dessouky, M.I. and Devor, R.E. (1986). “An integrated quality systems approach to quality and productivity improvement in continuous manufacturing processes”, Trans ASME J Eng Ind 108:322–327
[11]. Ermer, D.S. (1980). “A control chart for dependent data”, ASQC Technical Conference Transactions. American Society for Quality Control, Milwaukee, WI, pp 121–128
[12]. Harris, Y.J. and Ross, W.H. (1991). “Statistical process control procedures for correlated observations”, Can J Chem Eng 69:48–57
[13]. Kanazuka, T. (1986). “The effect of measurement error on the power of X-R charts”, Journal of Quality Technology 18:91–95
[14]. Kramer, H. and Schmid, W. (1997). “Control charts for time series”, Nonlinear Anal 30:4007–4016
[15]. Lin, W.S. and Adams, B.M. (1996). “Combined control charts for forecast based monitoring schemes”, J Qual. Technol. 28:289–301
[16]. Longnecker, M.T. and Ryan, T.P. (1992). “Charting correlated process data”, Technical report no. 166. Department of Statistics, Texas A&M University,College Station, Texas
[17]. Lu, C. and Reynolds, M. (1999). “EWMA control charts for monitoring the mean of autocorrelated processes”. J Qual. Technol. 31:166–188
[18]. Mittag, H. (1995). “Measurement error effect on control chart performance”, ASQC Annual Proceedings 49:66–73
[19]. Mittag, H. and Stemmann, D. (1998). “Gauge imprecision effect on the performance of the X-S chart”, Journal of Applied Statistics 25:307–
[20]. Mizuno, S. (1961). “Problems of measurement errors in process control”, Bulletin of the International Statistical Institute 38:405–415
[21]. Montgomery, D.C. (1996). “Introduction to statistical quality control”, 3rd edn. Wiley, New York
[22]. Montgomery, D.C. and Mastrangelo, C.M. (1991). “Some statistical process control methods for autocorrelated data”, J Qual. Technol. 23:179–193
[23]. Padgett, C.S., Thombs, L.A. and Padgett, W.J. (1992). “On the α-risks for Shewhart control charts”, Commun Stat Simul Comput 21:1125–1147
[24]. Rahim, A. (1985). “Economic model of X charts under non-normality and measurement errors”, Computer and Operations Research 12:291–299
[25]. Reynolds, M.R. JR., Arnold, J.C. and Baik, J.W. (1996). “Variable sampling interval in the presence of correlation”, Journal of Quality Technology 28:12–30
[26]. Runger, G.C., Willemain, T.R. and Prabhu, S. (1995). “Average run lengths for CUSUM control charts applied to residuals”, Commun Stat Theory Methods 24:273–282
[27]. Schmid, W. (1995). “On the run length of a Shewhart chart for correlated Data”, Stat Papers 36:111–130
[28]. Schmid, W. (1997). “CUSUM control schemes for Gaussian processes”, Stat Papers 38:191–217
[29]. Schmid, W. (1997b). “On EWMA charts for time series. In: Lenz HJ, Wilrich P-Th (eds) Frontiers of statistical quality control”, vol. 5, Physica-Verlag, Heidelberg
[30]. Schmid, W. and Schone, A. (1997). “Some properties of the EWMA control chart in the presence of autocorrelation”, Ann Stat 25:1277–1283
[31]. Searls, D. T. (1964). “The utilization of a known coefficient of variation in the estimation procedure”, Journal of the American Statistical Association, 59, 1225-1226.
[32]. Shewhart, W.A. (1931). “Economic control of quality of manufactured product”. Van Nostrand, New York.
[33]. Timmer, D.H., Pigantkiello, J. Jr. and Longnecker, M. (1998). “The development and evaluation of CUSUM-based control charts for an AR(1) process”, IIE Trans 30:525–534
[34]. Vander Weil, S.A. (1996). “Modeling processes that wander using movingaverage models”, Technometrics 38:139–151
[35]. Wade, R. and Woodall, W. (1993). “A review and analysis of cause-selecting control charts”, J Qual. Technol. 25:161–169
[36]. Wardell, D.G., Moskowitz, H. and Plante, R.D. RD (1992). “Control charts in the presence of data correlation”, Manage Sci 38:1084–1105
[37]. Wardell, D.G., Moskowitz, H. and Plante, R.D. (1994). “Run length distributions of special-cause control charts for correlated processes”, Technometrics 36:3–17
[38]. Yang, S. (2002). “The effects of imprecise measurement on the economicasymmetric X and S control charts”, The Asian Journal on Quality 3:46–56
[39]. Yashchin, E. (1993). “Performance of CUSUM control schemes for serially correlated observations”, Technometrics 35:37–52
[40]. Zhang, N.F. (1997). “Detection capability of residual control chart for stationary process data”, J Appl. Stat. 24:363–380
[41]. Zhang, G. (1984). “A new type of control charts and a theory of diagnosis with control charts”, World Quality Congress Transactions, AmericanSociety for Quality Control, Milwaukee, WI, pp 75–85