Monitoring and Diagnosing Large-Scale Complex Processes

[#1]

See how to compare and contrast situational usefulness of two methods for looking at lots of process variables at the same time: Model Driven Multivariate Control Charts (MDMCC) and Process Screening.

Note: Q&A is included at ~ Times 16:28, 22:00, 23:56, 27:36, 40:24, 43:00 and 45:38.

 

Resources

• 2020 JMP Discovery Summit Presentation, Fault Detection and Diagnosis of the Tennessee Eastman Process using Multivariate Control Charts, by J. Ash, JMP
• 2020 JMP Discovery Summit Presentation, Recent Developments in JMP(R) Quality and SPC, by L. Lancaster, J. Ding and A. Zangi, JMP
• 2020 JMP Discovery Summit Tutorial, Large-Scale Process Monitoring Using JMP, by J. Zing
• Using Partial Least Squares video
• Using JMP Pro Functional Data Explorer for PCA

[gail_massari]

@Byron_JMP  @Ben_Sagalovsky  A thought from August 20 live webinar: I am curious about the role of autocorrelation for Principal Components calculations, etc. And associated with this, the issue of subsampling process data and deciding on what is the most appropriate interval to sample, and how to determine it. 

[PatrickGiuliano]

@gail_massari  that's an interesting question to be sure.  there are a litany of ways to sample from a process but how to avoid autocorrelation?  best way looking back is simply to plot the residuals either by row (no limits, connecting line)or use the studentized residuals plot that JMP produces in the Fit Model Platform.  I prefer saving the residuals and making a run chart in Graph Builder or using the Control Chart Builder (I-MR with Limits or Turn Off limits entirely for I chart and ignore MR chart).

Another more "statistical approach" is to use the Durbin Watson Test:

Among the many sampling approaches include: Systematic, Stratified, Cluster, and Multi-stage.  

I've tried generating Column Formulas in JMP using JSL to mimic each of these sampling strategies:

Consider a random sample of 1000 test data with a sample of size 250 for each of 4 Lots.

Systematic Sample:

If(Sequence(1, 5) == 5, 1, 0)

Stratified Sample:  

If( Col Shuffle( :Lot ) <= 50,
	1,
	0
);

Cluster Sample Select Lots 1 or Lot 3:

If( :Lot == 1 | :Lot == 3,
	1,
	0
)

Random Sample Cluster Lots 1 or Lot 3:

If(
	:Cluster Select Lot 1 or Lot 3 == 1 & If( Col Shuffle( :Lot ) <= 50,
		1,
		0
	),
	1,
	0
)

Multi-stage Sample n of 50 from Lot 1 only:

If( If( :Lot == 1, 1, 0 ) == 1 & If( Col Shuffle( :Lot ) <= 50, 1, 0 ),
	1,
	0
)

Multi-stage Sample of n = 41 + n = 8 for a total sample size of 49 from Lot 1 only: 

Col 1  = 

If( :"Multistage Sample 1 n=50"n == 1,
	0,
	If( If( :Lot == 1, 1, 0 ) == 1 & If( Col Shuffle( :Lot ) <= 50, 1, 0 ),
		1,
		0
	)
)

Col 2 = 

If( :"Multistage Sample 2 n=50 '"n == 1,
	0,
	If(
		If( :Lot == 1, 1, 0 ) == 1 & If(
			Col Shuffle( :Lot ) <= 50 - Col Sum( :"Multistage Sample 2 n=50 '"n ),
			1,
			0
		),
		1,
		0
	)
)