Abstract
In this paper we discussed the robustness of the mean chart to non-normality and measurement error with known cv. It is seen that many areas of statistical application can easily lead to quite non-normal distribution as well as erroneous observation. The joint effect of non-normality and measurement error on the OC and type-I error has been investigated. The non-normal distribution has been represented by the first four terms of an Edgeworth series visual comparison shows that the effect of non-normality and measurement error is serious on the OC function and type-I error.
Key-Words / Index Term
Mean Chart, OC function, type-I error, non-normality, Measurement error
References
[1]. Borrow , C.M., Montgomer, D.C. , and Myers, R.H. (2002). “Evaluation of Statistical Designs for Experiments Involving Noise Variables”, Journal of Quality Technology 34, pp. 54-70
[2]. Cornell, J.A. (1995). “Fitting Models of Data from Mixture Experiments Containing Other Factors”, Journal of Quality Technology 27, pp.13-33.
[3]. Gayen, A. K. (1949). "Mathematical Investigation in to effect of Non-normality on standard test", Ph.D. Thesis, Combrig University, USA.
[4]. Goldfard, H., Borror, C.M. , Montgomerry, D.C. , and Anderson – Cook, C.M. (2005). “Using Genetic Algorithms to Generate Mixture Process Experimental Designs Involving Control and Noise Variables”, Journal of Quality Technology 37, pp. 60-74.
[5]. Goldfard, H., Borror, C.M. , Montgomerry, D.C. , and Anderson – Cook, C.M. (2004). “Evaluating Mixture Process Designs with Control and Noise Variables”, Journal of Quality Technology 36, pp. 245-262.
[6]. Linna, K. W. and Woodall, W. H. (2001). Effect of measurement error on Shewhart control. Journal of Quality Technology, 33, pp. 213-222.
[7]. Lucas, J.M. (1994). “How to Achieve a Robust Process Using Response Surface Methodology”, Journal of Quality Technology 26, p. 248-260.
[8]. Rao, K. A. and Bhatta, A. (1989). A note on test for coefficient of variation, University of Agricultural Science, Dharwad.
[9]. 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.
[10]. Taguchi, G. (1986). “Introduction to Quality Engineering Quality Resources”, White Plains. NJ.
[11]. Taguchi, G. (1987). “System of Experimental Design : Engineering Methods to Optimize Quality and Minimize Cost. White Plains”, NJ; Quality Resources.
Citation
Singh J.R. and Singh D.P., "Robustness of the Mean Chart to Non-Normality and Measurement Error," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.1, Issue.5, pp.1-12, 2014