Chitkara University Publications

Exponential Weighted Moving Average (EWMA) Chart Under The Assumption of Moderateness And Its 3∆ Control Limits


Moderate distribution is a very good alternative of normal distribution proposed by Naik V.D and Desai J.M. [4], which has mean deviation as scale parameter rather than the standard deviation. 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. [5] 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 it has been assumed that the underlying distribution of the variable of interest follows moderate distribution proposed by Naik V.D and Desai J.M. [4] and 3δ control limits of exponential weighted moving average chart are derived. Also an empirical study is carried out to illustrate the use these charts.


Kalpesh S. Tailor, Assistant Professor, Department of Statistics, M. K. Bhavnagar University, Bhavnagar-364001



Mean deviation, Moderate distribution, Exponential weighted moving average, 3δ control limits


Hunter J. S. (1986) The Exponentially Weighted Moving Average, Journal of Quality Technology, 18, 203–210.

Lucas J.M. and Crosier R.B. (1982) Fast Initial Response for CUSUM Quality Control Schemes, Technometrics, 24, 199–205

Lucas J.M. and Saccucci M.S. (1990) Exponentially Weighted Moving average Schemes, Properties and Enhancements, Technometrics, 32, 1–29

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. 1 256–270

Naik V.D and Tailor K.S. (2015) On performance of and R-charts under the assumption of moderateness rather than normality and with 3 control limits rather than 3 control limits, VNSGU Journal of Science and Technology, Vol.4, No. 1, 243–255

Kalpesh S. Tailor (2016) Moving average and moving range charts under the assumption of moderateness and its 3 control limits

Roberts S.W. (1959) Control chart Tests Based on Geometric Moving Average Charts. Technometrics, Vol.-1, No.-3, pp .239–250

Tailor K.S. and Naik V.D. (2016) Mean deviation () based control limits of SQC charts for sample standard deviation(s) and sample mean deviation (d) and their performance analysis under 3 control limits against 3 control limits, VNSGU Journal of Science and Technology, (Accepted for Publication).



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