A Dispersion Control Chart

The study proposes a Shewhart-type control chart, namely Q chart, based on inter-quartile range, for monitoring changes (especially of moderate and large amounts which is major concern of Shewhart-type control charts) in process dispersion assuming normality of quality characteristic to be monitored. The design structure of Q chart is developed and its comparison is made with those of well-known R and S charts and R Q chart proposed by Rocke (1992). The comparisons have revealed superiority of the proposed Q chart as compared to R and S charts in terms of discriminatory power and resistance against non normality and as compared to R Q chart in terms of relaxing the restriction for 25th and 75th ordered positions in the data to be integer values and in terms of detecting special causes in the absence and presence of outliers in the data.

[1]  Lloyd S. Nelson,et al.  Column: Technical Aids: The Shewhart Control Chart--Tests for Special Causes , 1984 .

[2]  Matoteng M. Ncube,et al.  A Comparison of dispersion quality control charts , 1987 .

[3]  Lloyd S. Nelson,et al.  Standardization of Shewhart Control Charts , 1989 .

[4]  Egon S. Pearson,et al.  THE PERCENTAGE LIMITS FOR THE DISTRIBUTION OF RANGE IN SAMPLES FROM A NORMAL POPULATION. (n ≤ 100.) , 1932 .

[5]  A. R. Crathorne,et al.  Economic Control of Quality of Manufactured Product. , 1933 .

[6]  David M. Rocke.  Robust control charts , 1989 .

[7]  Lloyd S. Nelson,et al.  Modern Methods for Quality Control and Improvement , 1989 .

[8]  Frederick S. Hillier,et al.  X-Bar- and R-Chart Control Limits Based on A Small Number of Subgroups , 1969 .

[9]  F. Mosteller.  On Some Useful "Inefficient" Statistics , 1946 .

[10]  Lawrence G. Tatum.  Robust estimation of the process standard deviation for control charts , 1997 .

[11]  William H. Beyer,et al.  Handbook of Tables for Probability and Statistics , 1967 .

[12]  Sheldon M. Ross,et al.  A Course in Simulation , 1990 .

[13]  David M. Rocke.  Xq and Rq charts: Robust control charts , 1992 .

[14]  E. S. Pearson.  Biometrika tables for statisticians , 1967 .

[15]  ©1981 American Mathematical Society 0002-9904/81 /0000-0121 /$04.00 , 2022 .

[16]  Layth C. Alwan.  Statistical Process Analysis , 1999 .

[17]  Stephen A. Freitas,et al.  Modern Industrial Statistics: Design and Control of Quality and Reliability , 1999, Technometrics.

[18]  Nicholas R. Farnum.  Modern Statistical Quality Control and Improvement , 1993 .

[19]  Harrison M. Wadsworth,et al.  Modern methods for quality control and improvement , 1986 .

[20]  H. A. David.  Early sample measures of variability , 1998 .

[21]  W. A. Shewhart,et al.  Statistical method from the viewpoint of quality control , 1939 .