Cumulative Sum (CUSUM) charts is another kind of control chart; As its name suggests, it plots the cumulative sum (of observation, means, or range), either positive or negative, for looking at the deviation from the target. It helps to detect a slight shift from the target. On the other hand, it’s challenging to maintain, and it’s slower to find significant data changes.


It can be visualized in a typical tabular format (like the other chart of the previous chapter) by plotting the formula in the image1.

Image1 – CUSUM tabular format formula

The CUSUM chart can also be visualized in a V-mask format like image2.

Image2  - Cusum as a VMask
Image2 – CUSUM as a VMask

The VMASK gets the shape from the value of k, d and h calculated with the formula in image3.

image3 - CUSUM V-Maks formula
image3 – CUSUM V-Maks formula

Where:

  • Alfa = probabilityu of a false allarm;
  • Beta = probability of not detecting a shift;
  • Delta = amount of shift that we wish to detect.


The exponentially Weighted Moving Average (EWMA) chart controls the variable working with the entire output history. It helps when you have a continuous variable with the actual data from the start of the process. In addition, it is often used to smooth fluctuation in order to reveal patterns better and cycle over time.

So for calculate the EWMA you can look at the formula in the image4.

image4 - EWMA formula
image4 – EWMA formula

Where you need to remember that:

  • You have all the observations of the series;
  • EWMA is Zi and also is the value that you plot on the graph as representative of the sample;
  • Xi is the sample observation;
  • Lambda weight the impact of the old value on the series. For example you can use 0.2;
  • Zi-1 is the precedent value of the series;
  • mu_0 is the target value for the process.


For instance, we are using the data in image5.

image5 - Data
image5 – Data

We can plot the EWMA Chart of the image6.

image 6 - EWMA Chart
image 6 – EWMA Chart

References:

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