The Effect of Instabilities on Estimates of Sigma

Article

Harding, Arved J., Jr.; Lee, Kwan R.; Mullins, Jennifer I.   (1992, ASQC)   Eastman Chemical Company, Kingsport, TN 37662

Annual Quality Congress, Nashville TN    Vol. 46    No. 0
QICID: 9778    May 1992    pp. 1037-1043
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Article Abstract

This abstract is an edited version of the author's original.

In this paper, processes with trends, oscillations, and sudden upsets are simulated, and the estimates of sigma are compared, using five case studies: (1) a stable process, (2) a process with a linear trend, (3) a process with a random shock, (4) a process with a periodic trend, and (5) a process with autocorrelation.

In each of these processes, the mean square errors (MSE) or Sr and Ss are calculated and compared. The author presents the results from these simulations of processes with special causes present, which allow Sr to be a better a better estimate of the actual process standard deviation than Ss.

In the stable case and in the autocorrelated case, the MSE for Ss is smaller than that for Sr, supporting Cryer and Ryan's [1990] position that Ss should be used for future process monitoring of normally distributed data and stable correlated data. When a random shock, a linear trend, or a periodic trend are present, Sr should be used for process monitoring.

These simulations highlight the importance of understanding the underlying behavior of the process before applying an estimate of ´┐Żo the individual control chart.

Keywords

Chemical and process industries,Control charts,Mean square errors (MSE),Oscillations,Standard deviation,Simulations,Statistics,Trends


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