Control chart limits as percent of actual mean

[#1]

Dear community,

I'm working in pharma industry and I would like to build a control chart according to pharmacopoeia guideline EP 2.9.5.

The test is as follow:

- weight 20 tablets

- mot more than 2 should deviate more than 7.5% from the observed mean

- none should deviate more than 15% from the observed mean

I there a way to set the limit in the control chart to 7.5% of the mean and 15% of the mean instead as based on sigma?

I know that as a surrogate I can normalized the data to 100% and add fixed ref line in graph builder, but I rather like to keep the original data not normalized to visualized the deviation from 100% (target) as well. 

Thank for your support,

Clément

[#2]

You can also build this type of "grouped" lines in Graph Builder using for example Col Mean and Col Std Dev to calculate those statistics over groups

[#3]

To set spec limits at +/-15% from the mean, use the following script as an example. This will allow you to easily check for and report any points beyond 15%. 

// Based on txnelson's post from Nov 9, 2023. 

// The usual frontmatter: 
Open( "$SAMPLE_DATA/Quality Control/Diameter.jmp" );
Names Default To Here( 1 );
dt = Current Data Table();

// Change column property: DIAMETER
theMean = Col Mean(:DIAMETER);
Eval(
	Substitute(
			Expr(
				dt:DIAMETER << set property(
					"Spec Limits",
					{LSL( _LSL_ ), 
					//Target( _Target_ ), 
					USL( _USL_ ), 
					Show Limits( 1 )}
				)
			),
		Expr( _LSL_ ), 0.85*theMean,
		//Expr( _Target_ ), theMean,
		Expr( _USL_ ), 1.15*theMean
	)
);

To simultaneously check for both points beyond 7.5% and points beyond 15%, that's a bit trickier. One way would be to set 7.5% as the known "historical sigma" of the process. Then you could use the built in Warnings functions in Control Chart Builder to check for points beyond 1 and 2 sigma, respectively. 

Set 7.5% of the mean as the "historical" Sigma using the Red Triangle -> Set Sigma option. Then, you could right click the graph and use Warnings -> Customize Tests and change Test 1 to check for points beyond 1 sigma (or script these steps as shown below).

Then, set KSigma to 2, and now Test Beyond Limits will also check for points beyond 15%.

This isn't usually how control charts are used, but it would get the job done.

To do so, append this to the script above: 

// Control chart builder with manually set historical sigma
Eval(
	Substitute(
			Expr(
				Control Chart Builder(
					Variables( Y( :DIAMETER ) ),
					Set Sigma( _sigma_ ),
					K Sigma( 2 ),
					Customize Tests( Test 1( 1, "1" ) ),
					Chart( Position( 1 ), Limits( Spec Limits( 1 ) ) )
				);
			),
		Expr( _sigma_ ), 0.075*theMean,
	)
);

[#4]

Just to be clear, what you are attempting to do is not a control chart.  Control chart limits have nothing to do with specifications which are independently derived from the actual process variation.  Reacting to specification as if it is assignable/special cause will likely increase variability in the long run (See Deming and Shewhart).

This doesn't mean you can't plot data against specification, but this is not a control chart and you will need to be careful in your reaction to these limits.

[#5]

I tried to do it in graph builder and went that far (I did not succeed in control chart platform).

I created 5 new columns:

- Mean by category

- T2 neg = :mean by category*0.85

- T2 pos = :mean by category*1.15

- T1 neg = :mean by category*0.925

- T1 pos = :mean by category*1.075

Then I used the following script

Graph Builder(
	Spacing Borders( 1 ),
	Variables(
		Y( :Weight in % of target ),
		Y( :T2 neg, Position( 1 ) ),
		Y( :T2 pos, Position( 1 ) ), 
//Y( :T1 neg, Position( 1 ) ),
//Y( :T1 pos, Position( 1 ) ),
		Group X( :"Concatenate[Batch,Tray]"n )
	),
	Elements(
		Points( Y( 1 ) ),
		Line( Y( 2 ) ),
		Line( Y( 3 ) ), 
//Line(Y( 4 )),
//Line(Y( 5 ))
	)
);

*Note: JSL moved into JSL Box by txnelson

With only two lines activated, it work well:

but when I activate the four lines (removing the // in the script), i got weird graph:

Any idea ?

[#6 · Accepted solution]

Maybe the Y-axis is getting grouped together as JMP might do that when you have multiple columns in Y-axis

Graph Builder(
	Size(788, 927),
	Variables(
		Y(:NPN1, Combine("Merged")),
		Y(:neg1, Position(1), Combine("Merged")),
		Y(:pos1, Position(1), Combine("Merged")),
		Y(:neg2, Position(1), Combine("Merged")),
		Y(:pos2, Position(1), Combine("Merged")),
		Group X(:wafer)
	),
	Elements(Points(Y(1), Legend(40)), Line(Y(2), Y(3), Y(4), Y(5), Legend(41))),
	SendToReport(
		Dispatch({"Points"}, "", OutlineBox, {Close(0)}),
		Dispatch({"Line"}, "", OutlineBox, {Close(0)})
	)
);

[#7]

Perfect, Thank you all for the answers.

It works great.

Have a nice day.

Clément