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Applications of the EWMA

is scaled according to the percentage increase in variability (variance) relative to the open-loop variance with no signal added to the disturbance (ct^, = 1). The horizontal axis represents the percent increase in unadjusted variation, 100(ct^. -1), while the vertical axis represents the percent increase in closed-

loop (adjusted) variation, 100(crJ -1). For areas above and to the left of the

dashed linę the controller is “transmitting” or adding variation, while for areas below and to the right the controller is “absorbing” or reducing variation. Even with L - 2.73 , the EWMA controller maintains a lower control error variance (a \) than the Modified Shewhart algorithm, regardless of the amount of signal added to the process disturbance.

Implementation of Algorithmic SPC at Monsanto

Case #1: Manuał Charts This first example concems a recent implementation of an EWMA/Shewhart chart for the control of an important variable conceming spun carpet staple fiber at Pensacola, Florida. The ąuality parameter, which we will cali Kj (compact notation for Y\_t, where the subscript 1 now distinguishes between variables rather than points in time) is measured with a single sample every eight hours, and adjustments are madę to the RPM of supply pumps. The control charts are maintained by a smali group of employees (one per shift) called line-control operators, although there are plans to place morę responsibility for charting with all of the machinę operators. Modified Shewhart charts had been in use for several years, but there were concems about over-adjustment because Tj is known to affect finished carpet ąuality. Also, there had been few instances where a mle violation led to process troubleshooting and the elimination of special causes, so these charts were not leading to the desired program of continuous improvement

The manuał implementation of Algorithmic SPC is shown on Figurę 9. The EWMA calculations on the top are based on X = .25 and cr_fl = .04,

which were determined from analysis of prior data and knowledge that the sigma of sampling and analytical error (.03) was large in relation to the ratę of process drift away from the target. a_z was determined to be .015, so that the EWMA limits of ±.02 on the lower chart in Figurę 9 are based on L = 1.3. The formula for calculating the process adjustments uses a process gain determined from designed experimentation, and then the adjustments are rounded to the nearest .25 RPM. For the sake of simplicity, the Shewhart chart on the upper portion of Figurę 9 uses the actual Kj data (control errors) rather than the forecast errors as recommended above. This does not seriously increase alpha