One of the assumptions for process behavior requires that each measurement is independent with no relationship between successive measurements. Not all processes generate independent measurements. "In many industrial applications data are obtained periodically, and for many of these sequences of values there will be some relationship between successive values", Advanced Topics in Statistical Process Control, Donald J. Wheeler.
When there is autocorrelation in process data, control limits in standard process behavior charts are too narrow and may generate false alarms. This add-in will compute lag1 autocorrelation coefficient, read control limits from an IMR control chart, compute new control limits that are widened by 1/sqrt(1-r^2) and update the chart with the new limits. Donald Wheeler Proposes this method in Chapter 12, Advanced Topics in Statistical Process Control. This is one of several methods for creating process behavior charts for autocorrelated process data. It may not always be the best. It is up to the user to determine whether this or another method is appropriate to use with their data. Other methods include
*EWMA residuals chart -part of JMP's EWMA report
*IMR charts of residuals from a time series model of the process -involves using JMP's Time Series platform.
Thanks goes to the JMP education team for the inspiration. This script replicates the procedure used in their free online SPC Course:
@ JMP Statistical Process Control Course
I recommend taking the course to understand control charts for autocorrelated data and SPC in general. The explanations are succinct, easy to follow and have exercises for practice.
Add-in procedure:
1. Open data table with autocorrelated process data or choose from a table that is already open.
2. Select the column containing the process data.
Interpretation:
I have left the _Lag1 column and the Fit Y by X report used to obtain the lag1 correlation coefficient open for diagnostic purposes. I recommend using the report to understand the degree of autocorrelation in the data. It is also instructive to generate a standard IMR chart for comparison purposes. Generating a standard IMR chart is not performed by the add-in.
