XmR Control Chart in Excel with Autocorrelation

Use an XmR Chart to Evaluate Stability of Processes using Autocorrelated Data

Autocorrelation (aka serial correlation) describes how the values in a time series are correlated with other values from that same time series - and successive values show how they are correlated with each other.

And if your Moving Range chart indicates points that are vastly different within your data set, it is clear that there has been a signficant change between successive values.

For more information regarding Autocorrelation with a Control Chart, visit the following link to read Donald Wheeler's article: https://www.qualitydigest.com/inside/statistics-column/autocorrelated-data-080717.html


Here is an example of an autocorrelated XmR chart created using QI Macros for Excel.

individual moving range XmR chart


How to Conduct XmR Autocorrelation in Excel using QI Macros

Below is an example of XmR Autocorrelation anlysis in Excel, using QI Macros.

  1. Select one column of data:
  2. Single-Column Autocorrelated Sample Data

    The sample data shown above is found in QI Macros Help > Open QI Macros Sample Data > XmRChart.xlsx > Autocorrelation tab

  3. Next, click on the QI Macros menu and choose Control Charts (SPC) > Variable (XmR, XbarR/S) > XmR Autocorrelated:
  4. XmR Autocorrelated Menu

  5. Evaluate the Autocorrelation results:

Chart Output of an XmR Autocorrelation


XmR chart data

XmR chart data assumes independent samples, but what happens when the next data point depends on the previous point? This example shows a cyclical or season dataset where the next point is related to the next one. If we use a regular XmR chart, this will result in too many points outside of the control limits.

"By determining the highest autocorrelation, we can adjust the control chart constant (normally 2.66) to factor in the autocorrelation." (Wheeler)

The XmR chart can help you evaluate a process when there is only one sample and they are farther apart (e.g., monthly postage expense, time to write a computer program, and so on).

Calculate, plot, and evaluate the range chart first. If it is "out of control," so is the process. If the range chart looks okay, then calculate, plot, and evaluate the X chart.

*Functionality introduced in the July 2022 version of QI Macros*


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