Exponentially Weighted Moving Average Line

This type of moving average can be considered to be a generalization of the simple moving average. Specifically, we could compute each data point for the plot as:

zt = l*x-bart + (1-l)*zt-1

In this formula, each point zt is computed as l (lambda) times the respective mean x-bart, plus one minus l times the previous (computed) point in the plot. The parameter l (lambda) here should assume values greater than 0 and less than 1. You may recognize this formula as the common exponential smoothing formula. Without going into detail (see Montgomery, 1985, p. 239), this method of averaging specifies that the weight for historically "old" sample means decreases geometrically as one continues to draw samples. This type of moving average line also smoothes the pattern of means across samples, and allows the engineer to detect trends more easily.