SAMPLE STANDARD DEVIATION(s) CHART UNDER THE ASSUMPTION OF MODERATENESS AND ITS PERFORMANCE ANALYSIS
DOI:
https://doi.org/10.29121/granthaalayah.v5.i6.2017.2045Keywords:
Mean Deviation, Standard Deviation, Control Charts, Normal Distribution, Moderate Distribution, Statistic, OC Function, ARL CurveAbstract [English]
Moderate distribution proposed by Naik V.D and Desai J.M., is a sound alternative of normal distribution, which has mean and mean deviation as pivotal parameters and which has properties similar to normal distribution. Mean deviation (δ) is a very good alternative of standard deviation (σ) as mean deviation is considered to be the most intuitively and rationally defined measure of dispersion. This fact can be very useful in the field of quality control to construct the control limits of the control charts. On the basis of this fact Naik V.D. and Tailor K.S. have proposed 3δ control limits. In 3δ control limits, the upper and lower control limits are set at 3δ distance from the central line where δ is the mean deviation of sampling distribution of the statistic being used for constructing the control chart. In this paper assuming that the underlying distribution of the variable of interest follows moderate distribution proposed by Naik V.D and Desai J.M, 3δ control limits of sample standard deviation(s) chart are derived. Also the performance analysis of the control chart is carried out with the help of OC curve analysis and ARL curve analysis.
Downloads
References
D.C. Montgomery (2001): Introduction to statistical Quality Control (3rd Edition), John Wiley & Sons, Inc., New York,
E .L. Grant and R. S. Leavenworth (1988): Statistical Quality Control, Tata McGraw-Hill Publishing Company Limited, New Delhi
K.S.Tailor(2016): Moving Average And Moving Range Charts Under The Assumption Of Moderateness And Its 3δ Control Limits, Sankhya Vignan, December-2016,No.2, 18-31
K.S.Tailor(2017):Exponential Weighted Moving Average (EWMA)Charts Under The Assumption Of Moderateness And Its 3δ Control Limits, Mathematical Journal of Interdisciplinary Sciences, paper accepted for March 2017 issue DOI: https://doi.org/10.15415/mjis.2017.52009
Naik V.D and Desai J.M. (2015): Moderate Distribution: A modified normal distribution which has Mean as location parameter and Mean Deviation as scale parameter, VNSGU Journal of Science and Technology, Vol.4, No. 1256-270
Naik V.D and Tailor K.S. (2015): On performance of X ̅ and R-charts under the assumption of moderateness rather than normality and with 3δ control limits rather than 3σ control limits, VNSGU Journal of Science and Technology, Vol.4, No. 1, 243-255
V.D. Naik. and J.M. Desai.(2009): A Review of Debate on Mean Deviation Versus Standard Deviation and a Comparative Study of Four Estimators (Including Two Proposed Unbiased Estimators) of Mean Deviation of Normal Population, VNSGU Journal of Science &Technology, Vol. I, Issue-II, 220-229.
V.D. Naik. and J.M. Desai.(2010): Some more reasons for preferring Mean Deviation over Standard Deviation for drawing inference about first degree dispersion in numerical data, VNSGU Journal of Science &Technology, VNSGU Journal of Science &Technology, Vol. 2, December-2010
V.D. Naik and J.M. Desai (2015): Moderate Distribution: A modified normal distribution which has Mean as location parameter and Mean Deviation as scale parameter, VNSGU Journal of Science and Technology, Vol.4, No. 1, 256-270
Downloads
Published
How to Cite
Issue
Section
License
With the licence CC-BY, authors retain the copyright, allowing anyone to download, reuse, re-print, modify, distribute, and/or copy their contribution. The work must be properly attributed to its author.
It is not necessary to ask for further permission from the author or journal board.
This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge.
