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Robustness to Non-Normality and Ar (2) Process of Control Charts

Singh D.P1 , Singh J.R2

Section:Research Paper, Product Type: Isroset-Journal
Vol.1 , Issue.1 , pp.8-17, Feb-2014


Online published on Dec 17, 2014


Copyright © Singh D.P , Singh J.R . 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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IEEE Style Citation: Singh D.P , Singh J.R, “Robustness to Non-Normality and Ar (2) Process of Control Charts,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.1, Issue.1, pp.8-17, 2014.

MLA Style Citation: Singh D.P , Singh J.R "Robustness to Non-Normality and Ar (2) Process of Control Charts." International Journal of Scientific Research in Mathematical and Statistical Sciences 1.1 (2014): 8-17.

APA Style Citation: Singh D.P , Singh J.R, (2014). Robustness to Non-Normality and Ar (2) Process of Control Charts. International Journal of Scientific Research in Mathematical and Statistical Sciences, 1(1), 8-17.

BibTex Style Citation:
@article{D.P_2014,
author = {Singh D.P , Singh J.R},
title = {Robustness to Non-Normality and Ar (2) Process of Control Charts},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {2 2014},
volume = {1},
Issue = {1},
month = {2},
year = {2014},
issn = {2347-2693},
pages = {8-17},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=93},
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=93
TI - Robustness to Non-Normality and Ar (2) Process of Control Charts
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - Singh D.P , Singh J.R
PY - 2014
DA - 2013/12/17
PB - IJCSE, Indore, INDIA
SP - 8-17
IS - 1
VL - 1
SN - 2347-2693
ER -

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Abstract :
In this paper we investigate the effect of non-normality and auto-correlation on the OC function of mean chart with known coefficient of variation. We synthesize the second order auto-correlation process by its three different roots. In particular, the shift in the auto-correlation structure from independent data to a random walk, this is a special case of the structural shift occurring in the process. For various values of roots the values of OC functions are tabulated with known coefficient of variation.

Key-Words / Index Term :
Mean chart, non-normality, OC function, auto-correlation, coefficient of variation

References :
[1]. Albin, S. L., Kang, L., Shea, G. (1997). An X and EWMA chart for individual observations, Journal of quality Technology. 29:41–48.
[2]. Amin,R.W. and Ethridge,R.A.(1998). A note on Individual and Moving Range Control Vhart, Journal of Quality Technology,30,70-74
[3]. Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multivariate skew normal distribution, J. R. Statist. Soc. B. 61, 579–602.
[4]. Azzalini, A. (1985). A class of distributions which includes the normal ones, Scand. J. Statist. 171–178.
[5]. Azzalini, A. (1986). Futher results on a class of distributions which includes the normal ones, Statistica 46, 199–208.
[6]. Bittanti, S., Lovera, M. and Moiraghi, L. (1998). Application of non-normal process capability indices to semiconductor quality control, IEEE Transactions On Semiconductor Manufacturing 11, 296–303.
[7]. Borror, C. M., Montgomery, D. C., Runger, G. C. (1999). Robustness of the EWMA control chart to non-normality, Journal of quality Technology. 31:309–316.
[8]. Box, G.E.P., Jenkins, G.M. and Reinsel, G.C. (1994). Time Series Analysis: Forecasting and Control, 3rd ed. (Prentice-Hall: Englewood Cliffs, NJ).
[9]. Champ, C.W.,Woodall, W.H. (1987). Exact results for shewhart’s control charts with supplementary runs rules, Journal of quality Technology 19:388–399
[10]. Chan, L. K. and Cui, H. J. (2003). Skewness correction X and R charts for skewed distributions, Naval Research Logistics 50, 1–19.
[11]. Chang, Y. S. and Bai, D. S. (1995). X and R control charts for skewed populations, Journal of Quality Technology 27, 120–131.
[12]. Chang, Y. S. and Bai, D. S. (2001). Control charts for positively-skewed populations with weighted standard deviations, Quality and Reliability Engineering International 17, 397–406.
[13]. Chang, W. (1994). Practical implementation of the process capability indices, Quality Engineering 7, 239–259.
[14]. Chou, C.-Y. , Chen, C.-H and Liu, H.-R. (2005). Acceptance control charts for non-normal data, Journal of Applied Statistics 32 25–36.
[15]. Cowden, D. J. (1957). Statistical Method in Quality Control (Prentice-Hall, Englewood Cliffs, NJ,
[16]. Dodge, Y. and Rousson, V. (1999). The complications of the fourth central moment, The American Statistician 53 267–269.
[17]. Domangue, R., Patch, S.C. (1991). Some omnibus exponentially weighted moving average statistical process monitoring schemes,Technometrics 33:299–313
[18]. Durbin, J. and Watson, G. S. (1950).Testing for serial correlation in least squares regression Biometrika, 37.
[19]. Gayen, A. K. (1949). Mathematical Investigation in to effect of Non-normality on standard test, Ph.D. Thesis, Combrig University, USA.
[20]. Genton, M. G., He, L. and Liu, X. (2001). Moments of skew-normal random vectors and their quadratic forms, Statistics and Probability Letters 51 319–325.
[21]. Gunter, W. H. (1989). The use and abuse of Cpk, Quality Progress 22 108 109.
[22]. Gupta, R. C. and Brown, N. (2001). Reliability studies of the skew-normal distribution and its application to a strength-stress model, Commun. Statist.-Theory Math. 30 2427–2445.
[23]. Lowry, C.A., Champ, C.W., Woodall, W.H. (1995). The Performance of Control Charts for Monitoring Process Variation, Communications in Statistics Simulation and Computation, 24(2), 409–437.
[24]. Lu, C.W. and Reynolds, M.R. Jr. (1999).Control charts for monitoring the mean and variance of autocorrelated processes, Journal of Quality Technology, 31, 259–274.
[25]. Lucas, J.M., Saccucci, M.S. (1990). Exponential weighted moving average control schemes: properties and enhancements,Technometrics 32:1–12
[26]. MacGregor, J. F. and Harris, T. J. (1993). The Exponentially Weighted Moving Variance, Journal of Quality Technology 25: 106–118.
[27]. Maragah, H.O. and Woodall, W.H. (1992).The effects of autocorrelation on the retrospective X-chart, J. Statist. Compu. Simul. 40, 29–42.
[28]. Montgomery, D. C. (1997). Statistical Quality Control, 3rd ed. New York: John Wiley.
[29]. Pyzdek, T. (1995). Why normal distribution aren’t – all that normal, Quality Engineering 7 769–777.
[30]. Rao, K. A. and Bhatta, A. R. S. (1989). A note on test for coefficient of variation, University of Agricultural Science, Dharwad.
[31]. Reynolds, M. R. Jr. (1996b). Variable Sampling Interval Control Charts with Sampling at Fixed Times, IIE Transactions 28: 497–510.
[32]. Reynolds, M.R. Jr. and Stoumbos, Z.G. (2001). Monitoring the process mean and variance using individual observations and variable sampling intervals, Journal of Quality Technology, 33, pp. 181–205.
[33]. Rigdon, S. E., Cruthis, E. N., Champ, C. W. (1994). Design strategies for individuals and moving range control charts, Journal of quality Technology. 26:274–287.
[34]. Ryan, T.P. (2000). Statistical Methods for Quality Improvements. John Wiley & Sons: New York,.
[35]. Srivastava, S. R. and Banarasi (1980). A note on the estimation of mean of asymmetrical population, Jar. Ind. Soc. Agri. Stat. 26(2), 33-36.
[36]. Stoumbos, Z. G. and Reynolds, M. R. Jr. (1997). Control Charts Applying a Sequential Test at Fixed Sampling Intervals, Journal of Quality Technology 29: 21–40.
[37]. Sullivan, J.H., Woodall, W.H. (1996). A control chart for preliminary analysis of individual observations, Journal of quality Technology, 28:265–278
[38]. Zhang, N.F. (1998). A statistical control chart for stationary process data, Technometrics, 40: 24 – 38.

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