After a forecast has been completed, it is important that it not be forgotten. No manager wants to be reminded when his or her forecast is horribly inaccurate, but a firm needs to determine why the actual demand (or whatever variable is being examined) differed significantly from that projected.⁴

One way to monitor forecasts to ensure that they are performing well is to employ a tracking signal. A tracking signal is a measurement of how well the forecast is predicting actual values. As forecasts are updated every week, month, or quarter, the newly available demand data are compared to the forecast values.

The tracking signal is computed as the running sum of the forecast errors (RSFE) divided by the mean absolute deviation:

where

as seen earlier in Equation 5-1.

Positive tracking signals indicate that demand is greater than the forecast. Negative signals mean that demand is less than the forecast. A good tracking signal—that is, one with a low RSFE—has about as much positive error as it has negative error. In other words, small deviations are okay, but the positive and negative deviations should balance so that the tracking signal centers closely around zero.

When tracking signals are calculated, they are compared with predetermined control limits. When a tracking signal exceeds an upper or lower limit, a signal is tripped. This means that there is a problem with the forecasting method, and management may want to reevaluate the way it forecasts demand. Figure 5.7 shows the graph of a tracking signal that is exceeding the range of acceptable variation. If the model being used is exponential smoothing, perhaps the smoothing constant needs to be readjusted.

How do firms decide what the upper and lower tracking limits should be? There is no single answer, but they try to find reasonable values—in other words, limits not so low as to be triggered with every small forecast error and not so high as to allow bad forecasts to be regularly overlooked. George Plossl and Oliver Wight, two inventory control experts, suggested using maximums of $\pm 4$ MADs for high-volume stock items and $\pm 8$ MADs for lower-volume items.⁵

Other forecasters suggest slightly lower ranges. One MAD is equivalent to approximately 0.8 standard deviation, so that $\pm 2 \text{MADs}=1.6$ standard deviations, $\pm 3 \text{MADs}=2.4$ standard deviations, and $\pm 4 \text{MADs}=3.2$ standard deviations. This suggests that for a forecast to be “in control,” 89% of the errors are expected to fall within $\pm 2\text{MADs},98\%$ within $\pm 3$ MADs, or 99.9% within $\pm 4$ MADs whenever the errors are approximately normally distributed.⁶

Here is an example that shows how the tracking signal and RSFE can be computed. Kimball’s Bakery’s quarterly sales of croissants (in thousands), as well as forecast demand and error computations, are in the following table. The objective is to compute the tracking signal and determine whether forecasts are performing adequately.

In period 6, the calculations are

This tracking signal is within acceptable limits. We see that it drifted from $-2.0$ MADs to $+2.5$ MADs.