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Statistical control for a chart like this one

FR60

Hi some suggestion on how to control a signal with the behavior showed in the attached picture ?

Thanks Felice

Accepted answers

Mark_Bailey

If the trend is expected, then you might control it. See this Wikipedia article for an approach.

Mark_Bailey

Another approach that is available with JMP Pro is functional data analysis. You could treat each separate trend (after maintenance) as a function.

Collect a set of trends when the process was deemed to be in control and special causes were absent.
I recommend that the data for all the functions be stored in one column (stacked) and use an adjacent column to indicate to which function the data (row) is a member.
Select Analysis > Specialized Modeling > Functional Data Explorer.
1. Enter the data column with the functions in the Y role and the data column with the membership in the ID role.
2. Click OK.
Use a linear B-spline or P-spline model.
Save the functional principle components.
Use control chart builder to analyze the FPCs for stability.

An entire compendium is devoted to using functional data or profiles in a control application. See Noorossana, R., A. Saghaei, and A. Amiri (2011) "Statistical Analysis of Profile Monitoring," John Wiley & Sons, NY. Chapter 2 is devoted to controlling simple linear trends.

All comments

Mark_Bailey

Does this example exhibit the natural variation in the output or does it include intervention events? For example, does the signal rise to some level and then the process is adjusted so that the signal returns to a lower level, only to rise again over time in a new cycle?

FR60

Hi, the signal start to increase after maintenance.

Felice

Mark_Bailey

I invite others to offer help and suggestions.

Your output is not under control in the statistical sense. It is highly positively correlated. What are you looking for or hope to achieve? I want to help but I don't know where you want to go with this request.

Mark_Bailey

If the trend is expected, then you might control it. See this Wikipedia article for an approach.

Mark_Bailey

Another approach that is available with JMP Pro is functional data analysis. You could treat each separate trend (after maintenance) as a function.

Collect a set of trends when the process was deemed to be in control and special causes were absent.
I recommend that the data for all the functions be stored in one column (stacked) and use an adjacent column to indicate to which function the data (row) is a member.
Select Analysis > Specialized Modeling > Functional Data Explorer.
1. Enter the data column with the functions in the Y role and the data column with the membership in the ID role.
2. Click OK.
Use a linear B-spline or P-spline model.
Save the functional principle components.
Use control chart builder to analyze the FPCs for stability.