6. Process or Product Monitoring and Control
6.4. Introduction to Time Series Analysis
6.4.2. What are Moving Average or Smoothing Techniques?

## Single Moving Average

Taking a moving average is a smoothing process An alternative way to summarize the past data is to compute the mean of successive smaller sets of numbers of past data as follows.
Recall the set of numbers 9, 8, 9, 12, 9, 12, 11, 7, 13, 9, 11, 10 which were the dollar amount of 12 suppliers selected at random. Let us set $$M$$, the size of the "smaller set" equal to 3. Then the average of the first 3 numbers is:   (9 + 8 + 9) / 3 = 8.667.
This is called "smoothing" (i.e., some form of averaging). This smoothing process is continued by advancing one period and calculating the next average of three numbers, dropping the first number.
Moving average example The next table summarizes the process, which is referred to as Moving Averaging. The general expression for the moving average is $$M_t = \frac{X_t + X_{t-1} + \cdots + X_{t-N+1}}{N} \, .$$

Results of Moving Average

Supplier \$ MA Error Error squared

1 9
2 8
3 9 8.667 0.333 0.111
4 12 9.667 2.333 5.444
5 9 10.000 -1.000 1.000
6 12 11.000 1.000 1.000
7 11 10.667 0.333 0.111
8 7 10.000 -3.000 9.000
9 13 10.333 2.667 7.111
10 9 9.667 -0.667 0.444
11 11 11.000 0 0
12 10 10.000 0 0

The MSE = 2.42 as compared to 3 in the previous case.