Description Spectral Tools is a collaborative effort of @JeremyAshJMP and @Bill_Worley . It provides some convenience functions for analyzing spectral data, or related data (chromatograms, etc.). Most of the functionality can already be performed in JMP, but the intent was to streamline the process. Hopefully this will help lower the barrier to entry for new users, and make routine tasks faster for experienced users. See part 1 and part 2 of our blog describing the spectral analysis workflow.   Usage Example Data: An example spectral data set from Martens et al. Anal Chem. 2003 Feb1;75(3):394-404. Import Spectra: When importing spectra, Spectral Tools assumes that each spectra is in a separate file in a single directory.  Import Spectra > Import Delimited Text Files: Spectra can be in delimited text files (.csv or .tsv, for example).  Spectral Tools assumes  the X variable is on the first column, and the Y variable is on the second.  Import Spectra > Import JCAMP-DX Files: The simplest variation of JCAMP-DX files is also supported.  This means JCAMP-DX  files without compression and with a XYDATA=(X++(Y..Y)) variable list.  I have not tested this out on different variations of the file format.  I plan to add to this post some data that I did test with, once I get permission from the owners. Preprocessing > Standard Normal Variate: Makes a new column with the standard normal variate applied to the spectra.  Assumes your data is in the stacked format.  Preprocessing > Savtizky-Golay Smoothing: Launches Graph Builder with a Savitzky-Golay smoother applied to each spectra. Select your smoothing parameter (local width) and then use the button at the top left of the report to make a new column for the smoother.  Assumes your data is in the stacked format.  Only available in JMP 16 and higher. Launch Graph Builder: Launches a spectra line plot for one spectra column or two spectra columns for comparison (e.g., before and after pre-processing). Some of the features you might want to use are set up for you. Assumes your data is in the stacked format.    See this blog post for a Savtizky-Golay derivative filter addin and demonstrated usage.   Disclaimer There is a disclaimer that appears in each launch dialog. Basically it says that this is only a prototype.  This has not been rigorously tested, and does not do much in terms of error handling.  We do not intend to provide regular maintenance or support, and this is only a first step towards making analyzing spectra more convenient in JMP.   That being said, it would be great if you could try it out and give us feedback in the comments, or by message to @Bill_Worley.  We probably won’t have time to implement new features in the add-in, but it would be helpful for development to hear about features you would like to see in the future.  The JMP Wish List is also a great place to make requests.                  ... View more

Level: Intermediate   Jeremy Ash, JMP Analytics Software Tester, SAS   The Model Driven Multivariate Control Chart (MDMCC) platform enables users to build control charts based on PCA or PLS models. These can be used for fault detection and diagnosis of high dimensional data sets. We demonstrate MDMCC monitoring of a PLS model using the simulation of a real-world industrial chemical process: the Tennessee Eastman Process. During the simulation, quality and process variables are measured as a chemical reactor produces liquid products from gaseous reactants. We demonstrate how MDMCC can perform online monitoring by connecting JMP to an external database. Measuring product quality variables often involves a time delay before measurements are available which can delay fault detection substantially. When MDMCC monitors a PLS model, the variation of product quality variables is monitored as a function of process variables. Since process variables are often more readily available, this can aid in the early detection of faults. We also demonstrate fault diagnosis in an offline setting. This often involves switching between multivariate control charts, univariate control charts and diagnostic plots. MDMCC provides a user-friendly interface to move between these plots.     Auto-generated transcript...   Speaker Transcript   Hello, I'm Jeremy Ash. I'm a   statistician in JMP R&D. My job   primarily consists of testing   the multivariate statistics   platforms in JMP, but I also   help research and evaluate   methodology. Today I'm going to   be analyzing the Tennessee   Eastman process using some   statistical process control   methods in JMP. I'm going to   be paying particular attention   to the model driven multivariate   control chart platform, which is   a new addition to JMP 15.   These data provide an   opportunity to showcase the   number of the platform's   features. And just as a quick   disclaimer, this is similar to   my Discovery Americas talk. We   realized that Europe hadn't seen a   model driven multivariate   control chart talk due to all the   craziness around COVID, so I   decided to focus on the basics.   But there is some new material   at the end of the talk. I'll   briefly cover a few additional   example analyses, then I put on   the Community page for the talk.   First, I'll assume some knowledge   of statistical process control   in this talk. The main thing it   would be helpful to know about   is control charts. If you're   not familiar with these, these   are charts used to monitor   complex industrial systems to   determine when they deviate   from normal operating   conditions.   I'm not gonna have much time to   go into the methodology of model   driven multivariate control   chart, so I'll refer to these other   great talks that are freely   available on the JMP Community   if you want more details. I   should also say that Jianfeng   Ding was the primary   developer of the model driven   multivariate control control   chart in collaboration with   Chris Gotwalt and that Tonya   Mauldin and I were testers. The   focus of this talk will be using   multivariate control charts to   monitor a real world   typical process; another novel   aspect will be using control   charts for online process   monitoring. This means we'll be   monitoring data continuously as   it's added to a database and   detecting faults in real time.   So I'm going to start off with   the obligatory slide on the   advantages of multivariate   control charts. So why not use   univariate control charts? There   are a number of excellent   options in JMP. Univariate   control charts are excellent   tools for analyzing a few   variables at a time. However,   quality control data are often   high dimensional and the number   of control charts you need to   look at can quickly become   overwhelming. Multivariate   control charts can summarize a   high dimensional process in   just a couple of control charts,   so that's a key advantage.   But that's not to say that   univeriate control charts aren't   useful in this setting. You'll   see throughout the talk that   fault diagnosis often involves   switching between multivariate   and univariate charts.   Multivariate control charts give   you a sense of the overall   health of the process, while   univariate charts allow you to   monitor specific aspects of the   process. So the information is   complementary. One of the goals   of monitoring multivariate   control chart is to provide some   useful tools for switching   between these two types of   charts. One disadvantage of   univariate charts is that   observations can appear to be in   control when they're actually   out of control in the multivariate   sense and these plots show what I   mean by this. The univariate   control chart for oil and   density show the two   observations in red as in   control. However, oil and density   are highly correlated and both   observations are out of control.   in the multivariate sense,   specially observation 51, which   fairly violates the correlation   structure of the two variables,   so multivariate control charts   can pick up on these types of   outliers, while univariate   control charts can't.   Model driven multivariate   control chart uses projection   methods to construct the charts.   I'm going to start by explaining PCA   because it's easy to build up   from there. PCA reduces the   dimensionality of the process by   projecting data onto a low   dimensional surface. Um,   this is shown in the picture   on the right. We have P   process variables and N   observations, and   the loading vectors in the P   matrix give the coefficients for   linear combinations of our X   variables that result in   square variables with   dimension A, where the dimension   A is much less than P. And then   this is shown in equations on   the left here. The X can be   predicted as a function of the   score and loadings, where E is   the prediction error.   These scores are selected to   minimize the prediction error,   and another way to think about   this is that you're maximizing   the amount of variance explained   in the X matrix.   Then PLS is a more suitable   projection method. When you have   a set of process variables and a   set of quality variables, you   really want to ensure that the   quality variables are kept in   control but these variables   are often expensive or time   consuming to collect. The plant   could be making product without   a control quality for a long   time before a fault is detected.   So PLS models allow you to   monitor your quality variables   as a function of your process   variables and you can see that   the PLS models find the score   variables that maximize the   amount of variation explained of   the quality variables.   These process variables are   often cheaper or more readily   available, so PLS can enable you   to detect faults in quality   early and make your process   monitoring cheaper. And from here   on out I'm going to focus on PLS   models because it's more   appropriate for the example.   So PLS model partitions your   data into two components. The   first component is the model   component. This gives the   predicted values of your process   variables. Another way to think   about it is that your data has   been projected into the model   plane defined by your score   variables and T squared monitors   the variation of your data   within this model plane.   And the second component is the   error component. This is the   distance between your original   data and the predicted data and   squared prediction error (SPE)   charts monitor this variation.   Another alternative metric we   provide is the distance to model   X plane or DModX. This is just   a normalized alternative to SPE   that some people prefer.   The last concept that's   important to understand for the   demo is the distinction between   historical and current data.   Historical data are typically   collected when the process was   known to be in control. These   data are used to build the PLS   model and define the normal   process variation so that a   control limit can be obtained.   And current data are assigned   scores based on the model but   are independent of the model.   Another way to think about this   is that we have training and   test sets. The T squared control   limit is lower for the training   data because we expect less   variability for the various...   observations used to train the   model whereas there's greater   variability in P squared when   the model generalizes to E test   set. Fortunately, the theory   for the variance of T squared is   been worked out so we can get   these control limits based on   some distributional assumptions.   In the demo will be monitoring   the Tennessee Eastman process.   I'm going to present a short   introduction to these data. This   is a simulation of a chemical   process developed by Downs and   Vogel, two chemists at Eastman   Chemical. It was originally   written in Fortran, but there   are wrappers for Matlab and   Python now. I just wanted to note   that while this data set was   generated in the '90s, it's still   one of the primary data sets   used to benchmark multivariate   control methods in the   literature. It covers the   main tasks of multivariate   control well and there is   an impressive amount of   realism in the simulation.   And the simulation is based on   an industrial process that's   still relevant today.   So the data were manipulated   to protect proprietary   information. The simulated   process is the production of   two liquid products from   gaseous reactants within a   chemical plant. And F here is   a byproduct   that will need to be siphoned   off from the desired product.   Um and...   That's about all I'll say about that.   So the process diagram looks   complicated, but it really isn't   that bad, so I'll walk you   through it. Gaseous   reactants A, D, and E flow into   the reactor here.   The reaction occurs and the   product leaves as a gas. It's   then cooled and condensed into   liquid in the condenser.   Then a vapor liquid separator   recycles any remaining vapor and   sends it back to the reactor   through a compressor, and the   byproduct and inert chemical B   are purged in the purge stream,   and that's to prevent any   accumulation. The liquid product   is pumped through a stripper,   where the remaining reactants   are stripped off.   And then sent back to the reactor.   And then finally, the   purified liquid product   exits the process.   The first set of variables being   monitored are the manipulated   variables. These look like bow   ties in the diagram. I think   they're actually meant to be   valves and the manipulated   process...or the manipulated   variables mostly control the   flow rate through different   streams of the process.   And these variables can be set   to any values within limits and   have some Gaussian noise.   The manipulated variables are able   to be sampled in the rate,   but we use the default 3   minutes sample now.   Some examples of the manipulated   variables are the valves that   control the flow of reactants   into the reactor.   Another example is a valve   that controls the flow of   steam into the stripper.   And another is a valve that   controls the flow of coolant   into the reactor.   The next set of variables are   measurement variables. These are   shown as circles in the diagram.   They were also sampled at three   minute intervals. The   difference between manipulated   variables and measurement   variables is that the   measurement variables can't be   manipulated in the simulation.   Our quality variables will be   the percent composition of   two liquid products and you   can see the analyzer   measuring the products here.   These variables are sampled with   a considerable time delay, so   we're looking at the purge   stream instead of the exit   stream, because these data are   available earlier. And will use   a PLS model to monitor process   variables as a proxy for these   variables because the process   variables have less delay and   affect faster sampling rate.   So that should be enough   background on the data. In   total there are 33 process   variables and two quality   variables. The process of   collecting the variables is   simulated with a set of   differential equations. And this   is just a simulation, but as you   can see a considerable amount of   care went into modeling this   after a real world process. Here   is an overview of the demo I'm   about to show you. We will collect   data on our process and store   these data in a database.   I wanted to have an example that   was easy to share, so I'll be   using a SQLite database, but   the workflow is relevant to most   types of databases since most   support ODBC connections.   Once JMP forms an ODBC   connection with the database,   JMP can periodically check for   new observations and add them to   a data table.   If we have a model driven   multivariate control chart   report open with automatic   recalc turned on, we have a   mechanism for updating the   control charts as new data come   in and the whole process of   adding data to a database would   likely be going on a separate   computer from the computer   that's doing the monitoring. So   I have two sessions of JMP open   to emulate this. Both sessions   have their own journal   in the materials on the   Community, and the session   adding new simulated data to   the database will be called   the Streaming Session and   session updating the reports   as new data come in will be   called the Monitoring Session.   One thing I really liked about   the Downs and Vogel paper was   that they didn't provide a   single metric to evaluate the   control of the process. I have   a quote from the paper here   "We felt that the tradeoffs   among the possible control   strategies and techniques   involved much more than a   mathematical expression."   So here are some of the goals   they listed in their paper,   which are relevant to our   problem. They wanted to maintain   the process variables at   desired values. They wanted to   minimize variability of product   quality during disturbances, and   they wanted to recover quickly   and smoothly from disturbances.   So we'll see how well our   process achieves these goals   with our monitoring methods.   So to start off in the   Monitoring Session journal, I'll   show you our first data set.   The data table contained all of   the variables I introduced   earlier. The first variables are   the measurement variables; the   second are the composition.   And the third are the   manipulated variables.   The script up here will fit   a PLS model. It excludes the   last 100 rows as a test set.   Just as a reminder,   the model is predicting 2   product composition   variables as a function of   the process variables. If   you have JMP Pro, there   have been some speed   improvements to PLS   in JMP 16.   PLS now has a   fast SVD option.   You can switch to the   classic in the red   triangle menu. There's   also been a number of   performance improvements   under the hood.   Mostly relevant for datasets   with a large number of   observations, but that's   common in the multivariate   process monitoring setting.   But PLS is not the focus of the   talk, so I've already fit the   model and output score columns   and you can see them here.   One reason that the monitor   multivariate control chart was   designed the way it is, is that   imagine you're a statistician   and you want to share your model   with an engineer so they can   construct control charts. All   you need to do is provide the   data table with these formula   columns. You don't need to share   all the gory details of how you   fit your model.   Next, I'll provide the score   columns to monitor the   multivariate control chart.   Drag it to the right here.   So on the left here you can see two types of control charts the   T squared and SPE.   Um, there are 860 observations   that were used to estimate the   model and these are labeled as   historical. And then the hundred   that were left out as a test set   are your current data.   And you can see in the limit   summaries, the number of points   that are out of control and the   significance level. Um, if you   want to change the significance   level, you can do it up here in   the red triangle menu.   Because the reactor's in normal   operating conditions, we expect   no observations to be out of   control, but we have a few false   positives here because we   haven't made any adjustments for   multiple comparisons. It's   uncommon to do this, as far as I   can tell, in multivariate   control charts. I suppose you   have higher power to detect out   of control signals without a   correction. In control chart   lingo, this is means you're out   of control. Average run length   is kept low.   So on the right here we   also have contribution   plots and on the Y axis are   the observations; on the X   axis, the variables. A   contribution is expressed   as a portion.   And then at the bottom here,   we have score plots. Right   now I'm plotting the first   score dimension versus the   second score dimension, but   you can look at any   combination of score   dimensions using this   dropdown menus or the arrow   button.   OK, so I think we're oriented   to the report. I'm going to   now switch over to the   scripts I've used to stream   data into the database that   the report is monitoring.   In order to do anything for this   example, you'll need to have a   SQLite ODBC driver installed   for your computer. This is much easier   to do on a Windows computer,   which is what you're often using   when actually connecting to a   database. The process on the Mac   is more involved, but I put some   instructions on the Community   page. And then I don't have time   to talk about this, but I   created the SQLite database   I'll be using in JMP and I   plan to put some instructions   in how to do this on the   Community Web page. And hopefully   that example is helpful to you   if you're trying to do this with   data on your own.   Next I'm going to show   you the files that I put   in the SQLite database.   Here I have the historical data.   This was used to construct   the PLS model. There are 960   observations that are in   control. Then I have the   monitoring data, which at first   just contains the historical   data, but I'll gradually add new   data to this. This is the data   that the multivariate control   chart will be monitoring.   And then I've simulated new   data already and added it to the   data table here. These are   another 960 odd measurements   where a fault is introduced at   some time point. I wanted to   have something that was easy to   share, so I'm not going to run   my simulation script and add to   the database that way. We're   just going to take observations   from this new data table and   move them over to the monitoring   data table using some JSL and   SQL statements. This is just an   example emulating the process   of new data coming into a   database. Somehow you might not   actually do this with JMP, but   this was an opportunity to show   how you can do it with JSL.   Clean up here.   And next I'll show you this   streaming script. This is a   simple script, so I'm going to   walk you through it real quick.   This first set of   commands will open the   new data table and   it's in the SQLite database,   so it opens the table in the   background so I don't have to   deal with the window.   Then I'm going to take pieces   from this data table and add   them to the monitoring data   table. I call the pieces   bites and the bite size is 20.   And then this next command will   connect to the database. This   will allow me to send the   database SQL statements.   And then this next bit   of code is   iteratively sending SQL   statements that insert new   data into the monitoring data.   And I'm going to   initialize K and show you the   first iteration of this.   This is a simple SQL statement,   insert into statement that   inserts the first 20   observations into the data   table. This print statement is   commented out so that the code   runs faster and then I also   have a wait statement to slow   things down slightly so that   we can see their progression   in the control chart.   And this would just go too fast   if I didn't slow it down.   Um, so next I'm going to move   over to the monitoring sessions   to show you the scripts   that will update the report   as new data come in.   This first script is a simple   script. That will check the   database every .2 seconds for   new observations and add them   to the JMP table. Since the   report has automatic recalc   turned on, the report will update   whenever new data are added. And   I should add that   realistically,   you probably wouldn't use a   script that just iterates like   this. You probably use task   scheduler in Windows or   Automator on Mac to better   schedule runs of the script.   And then there's also another   script that will   push the report to JMP Public   whenever the report is updated,   and I was really excited that   this is possible with JMP 15.   It enables any computer with a   web browser to view updates to   the control chart. Then you   can even view the report on   your smartphone, so this makes   it really easy to share   results across organizations.   And you can also use JMP Live   if you wanted the reports to   be on restricted server.   I'm not going to have time   to go into this in this   demo, but you can check out   my Discovery Americas talk.   Then finally down here, there is   a script that recreates the   historical data in the data   table if you want to run the   example multiple times.   Alright, so next...make sure   that we have the historical data...   I'm going to run the   streaming script and see   how the report updates.   So the data is in control at   first and then a fault is   introduced, but there's a   plantwide control system   that's implemented in the   simulation, and you can see   how the control system   eventually brings the process   to a new equilibrium.   Wait for it to finish here.   So if we zoom in,   seems like the process first   went out of control around this   time point, so I'm going to   color it and   label it, but it will   show up in other plots.   And then in the SPE plot,   it looks like this   observation is also out of   control but only slightly.   And then if we zoom in on   the time point in the   contribution plots, you can   see that there are many   variables contributing to   the out of control signal at   first. But then once the   process reaches a new   equilibrium, there's only   two large contributors.   So I'm going to remove the heat   maps now to clean up a bit.   You can hover over   the point at which the process   first went out of control and   get a peek at the top ten   contributing variables. This   is great for giving you a   quick overview which variables   are contributing most to the   out of control signal.   And then if I click on the plot,   this will be appended to the   fault diagnosis section.   And as you can see, there's   several variables with large   contributions and just sorted   on the contribution.   And for variables with   red bars the observation is   out of control in the univariate   control charts. You can see   this by hovering over one of   the bars and these graphlets   are IR charts for an   individual variable with a   three Sigma control limit.   You can see in the stripper   pressure variable that the   observation is out of   control, but eventually the   process is brought back under   control. And this is the case   for the other top   contributors. I'll also show   you one of the variables   where we're in control, the   univariate control chart.   So the process was...   there are many variables out   of control in the process at   the beginning, but   process eventually reaches   a new equilibrium.   Um...   To see the variables that   contribute most to the shift in   the process, we can use mean   contribution proportion plot.   These plots show the average   contribution that the variables   have to T squared for the group   I've selected. Um, here if I   sort on these.   The only two variables with   large contributions measure the   rate of flow of reactant A in   stream one, which is the flow of   this reactant into the reactor.   Both of these variables are   measuring essentially the   same thing, except one   measurement...one is a   measurement variable and the   other is a manipulated   variable.   You can see that there is a   large step change in the flow   rate, which is what I programmed   in the simulation. So these   contribution plots allow you to   quickly identify the root cause.   And then in my previous talk I   showed many other ways to   visualize and diagnose faults   using tools in the score plot.   This includes plotting the   loadings on the score plots and   doing some group comparisons.   You can check out my Discovery   Americas talk on the JMP   Community for that. Instead, I'm   going to spend the rest of this   time introducing a few new   examples, which I put on the   Community page for this talk.   So.   There are 20 programmable faults   in the Tennessee Eastman process   and they can be introduced in any   combination. I provided two other   representative faults here. Fault   1 that I showed previously was   easy to detect because the out   of control signal is so large   and so many variables are   involved. The focus on the   previous demo was to show how to   use the tools and identify.   faults out of a large number of   variables and not to benchmark   the methods necessarily.   Fault 4, on the other hand,   is a more subtle fault,   and I'll show you it here.   The fault i...that's programmed   is a sudden increase in the   temperature in the reactor.   And this is compensated for by   the control system by increasing   the flow rate of coolant.   And you can see that   variable picked up here and   you can see the shift in   contribution plots.   And then you can also see   that most other variables   aren't affected   by the fault. You can see a   spike in the temperature here   is quickly brought back under   control. Because most other   variables aren't affected, this   is hard to detect for some   multivariate control methods.   And it can be more   difficult to diagnose.   The last fault I'll show you   is Fault 11.   Like Fault 4, it also involves   the flow of coolant into the   reactor, except now the fault   introduces large oscillations in   the flow rate, which we can   see in the univariate control   chart. And this results in a   fluctuation of reactor   temperature. The other   variables aren't really   affected again, so this can be   harder to detect for some   methods. Some multivariate   control methods can pick up on   Fault 4, but not Fault 11 or   vice versa. But our method was   able to pick up on both.   And then finally, all the   examples I created using the   Tennessee Eastman process had   faults that were apparent in   both T squared and SPE plots. To   show some newer features in   model driven multivariate   control chart, I wanted to show   an example of a fault that   appears in the SPE chart but not   T squared. And to find a good   example of this, I revisited a   data set which Jianfeng Ding   presented in her former talk, and   I provided a link to her talk   in this journal.   On her Community page,   she provides several   useful examples that are   also worth checking out.   This is a data set from Cordia   McGregor's (?) classic paper on   multivariate control charts. The   data are processed variables   measured in a reactor, producing   polyethylene, and you can find   more background in Jianfeng's   talk. In this example, we   have a process that went out of   control. Let me show you this.   And it's out of control in...   earlier in the SPE chart than in   the T squared.   And if we look at the mean   contribution   plots for SPE,   you can   see that there is one variable   with large contribution and it   also shows a large shift in the   univariate control chart, but   there are also other variables   with large contributions, but   that are still in control in the   univariate control charts.   And it's difficult to determine from   the bar charts alone why these   variables had a large   contributions. Large SPE values   happen when new data don't   follow the correlation structure   of the historical data, which is   often the case when new data are   collected, and this means that   your PLS model you trained is   no longer applicable.   From the bar charts, it's hard   to know which pair of variables   have their correlation structure   broken. So new in 15.2, you   can launch scatterplot matrices.   And it's clear in the   scatterplot matrix that the   violation of correlations   with Z2 is what's driving   these large contributions.   OK, I'm gonna switch back   to the PowerPoint.   And real quick, I'll summarize   the key features of model driven   multivariate control chart that   were shown in the demo. The   platform is capable of   performing both online fault   detection and offline fault   diagnosis. There are many   methods provided in the platform   for drilling down to the root   cause of faults. I'm showing you   here some plots from a popular   book, Fault Detection and   Diagnosis in Industrial Systems.   Throughout the book, the authors   demonstrate how one needs to   use multivariate and univariate   control charts side by side   to get a sense of what's going   on in a process.   An one particularly useful   feature in model driven multivariate   control chart is how   interactive and user friendly   it is to switch between these   two types of charts.   And that's my talk. Here is   my email if you have any   further questions. And   thanks to everyone that   tuned in to watch this. ... View more

Level: Intermediate   Jeremy Ash, JMP Analytics Software Tester, JMP   The Model Driven Multivariate Control Chart (MDMVCC) platform enables users to build control charts based on PCA or PLS models. These can be used for fault detection and diagnosis of high dimensional data sets. We demonstrate MDMVCC monitoring of a PLS model using the simulation of a real world industrial chemical process — the Tennessee Eastman Process. During the simulation, quality and process variables are measured as a chemical reactor produces liquid products from gaseous reactants. We demonstrate fault diagnosis in an offline setting. This often involves switching between multivariate control charts, univariate control charts, and diagnostic plots. MDMVCC provides a user-friendly way to move between these plots. Next, we demonstrate how MDMVCC can perform online monitoring by connecting JMP to an external database. Measuring product quality variables often involves a time delay before measurements are available, which can delay fault detection substantially. When MDMVCC monitors a PLS model, the variation of product quality variables is monitored as a function of process variables. Since process variables are often more readily available, this can aide in the early detection of faults. Example Files Download and extract streaming_example.zip.  There is a README file with some additional setup instructions that you will need to perform before following along with the example in the video.  There are also additional fault diagnosis examples provided. Message me on the community if you find any issues or have any questions.       Auto-generated transcript...   Speaker Transcript Jeremy Ash Hello, I'm Jeremy ash. I'm a statistician in jump R amp D. My job primarily consists of testing the multivariate statistics platforms and jump but   I also help research and evaluate methodology and today I'm going to be analyzing the Tennessee Eastman process using some statistical process control methods and jump.   I'm going to be paying particular attention to the model driven multivariate control chart platform, which is a new addition to jump and I'm really excited about this platform and these data provided a new opportunity to showcase some of its features.   First, I'm assuming some knowledge of statistical process control in this talk.   The main thing you need to know about is control charts. If you're not familiar with these. These are charts used to monitor complex industrial systems to determine when they deviate from normal operating conditions.   I'm not gonna have much time to go into the methodology and model driven multivariate control chart. So I'll refer to these other great talks that are freely available.   For more details. I should also mention that Jim finding was that primary developer of the model driven multivariate control chart and in collaboration with Chris Got Walt and Tanya Malden I were testers.   So the focus of this talk will be using multivariate control charts to monitor a real world chemical process.   Another novel aspect of this talk will be using control charts for online process monitoring this means we'll be monitoring data continuously as it's added to a database and texting faults in real time.   So I'm going to start with the obligatory slide on the advantages of multivariate control charts. So why not use University control charts there. There are a number of excellent options and jump.   University control charts are excellent tools for analyzing a few variables at a time. However, quality control data sets are often high dimensional   And the number of charts that you need to look at can quickly become overwhelming. So multivariate control charts summarize a high dimensional process. And just a few charts and that's a key advantage.   But that's not to say that university control charts aren't useful in this setting, you'll see throughout the talk that fault diagnosis often involves switching between multivariate in University of control charts.   Multivariate control charts, give you a sense of the overall health of a process well University control charts allow you to   Look at specific aspects. And so the information is complimentary and one of the main goals of model driven multivariate control chart was to provide some tools that make it easy to switch between those two types of charts.   One disadvantage of the university control chart is that observations can appear to be in control when they're actually out of control in the multivariate sense. So I have to   Control our IR charts for oil and density and these two observations in red are in control, but oil and density are highly correlated. And these observations are outliers in the multivariate sense in particular observation 51 severely violates the correlation structure.   So multivariate control charts can pick up on these types of outliers. When University control charts can't   model driven multivariate control chart uses projection methods to construct its control charts. I'm going to start by explaining PCA because it's easy to build up from there.   PCA reduces dimensionality of your process variables by projecting into a low dimensional space.   This is shown in the in the picture to the right we have p process variables and and observations and we want to reduce the dimensionality of the process to a were a as much less than p and   To do this we use this P loading matrix, which provides the coefficients for linear combinations of our X variables which give the score variables. The shown and equations on the left.   tee times P will give you predicted values for your process variables with the low dimensional representation. And there's some prediction air and your score variables are selected.   In a way that minimizes this squared prediction air. Another way to think about it is, you're maximizing the amount of variance explained x   Pls is more suitable when you have a set of process variables and a set of quality variables and you really want to ensure that the quality variables are kept in control, but these variables are often expensive or time consuming to collect   At planet can be making out of control quality for a long time before fault is detected, so   Pls models allow you to monitor your quality variables as a function of your process variables. And you can see here that pls will find score variables that maximize the variance explained in the y variables.   The process variables are often cheaper and more readily available. So pls models can allow you to detect quality faults early and can make process monitoring cheaper.   So from here on out. I'm just going to focus on pls models because that's that's more appropriate for our example.   So pls partitions your data into two components. The first component is your model component. This gives you the predicted values.   Another way to think about this as your data has been projected into a model plane defined by your score variables and t squared charts will monitor variation in this model plane.   The second component is your error component. This is the distance between your original data and that predicted data and squared prediction error charts are sp charts will monitor   Variation in this component   We also provide an alternative distance to model x plane, this is just a normalized version of sp.   The last concept that's important to understand for the demo is the distinction between historical and current data.   historical data typically collected when the process is known to be in control. These data are used to build the PLS model and define   Normal process variation. And this allows a control limit to be obtained current data are assigned scores based on the model, but are independent of the model.   Another way to think about this is that we have a training and a test set, and the t squared control limit is lower for the training data because we expect lower variability for   Observations used to train the model, whereas there's greater variability and t squared. When the model generalized is to a test set. And fortunately, there's some theory that's been worked out for the   Variants of T square that allows us to obtain control limits based on some distributional assumptions.   In the demo will be monitoring the Tennessee Eastman process. I'm going to present a short introduction to these data.   This is a simulation of a chemical process developed by downs and Bogle to chemists at Eastman Chemical and it was originally written in Fortran, but there are rappers for it in MATLAB and Python now.   The simulation was based on a real industrial process, but it was manipulated to protect proprietary information.   The simulation processes. The, the production of to liquids.   By gassing reactants and F is a byproduct that will need to be siphoned off from the desired product.   The two season processes pervasive in the in the literature on benchmarking multivariate process control methods.   So this is the process diagram. It looks complicated, but it's really not that bad. So I'm going to walk you through it.   The gaseous reactants ad and he are flowing into the reactor here, the reaction occurs and product leaves as a gas. It's been cooled and condensed into a liquid and the condenser.   Then we have a vapor liquid separator that will remove any remaining vapor and recycle it back to the reactor through the compressor and there's also a purge stream here that will   Vent byproduct and an art chemical to prevent it from accumulating and then the liquid product will be pumped through a stripper where the remaining reactants are stripped off and the final purified product leaves here in the exit stream.   The first set of variables that are being monitored are the manipulated variables. These look like bow ties and the diagram.   Think they're actually meant to be valves and the manipulative variables, mostly control the flow rate through different streams of the process.   These variables can be set to specific values within limits and have some Gaussian noise and the manipulative variables can be sampled at any rate, we're using a default three minutes sampling in   Some examples of the manipulative variables are the flow rate of the reactants into the reactor   The flow rate of steam into the stripper.   And the flow of coolant into the reactor   The next set of variables are measurement variables. These are shown as circles in the diagram and they're also sampled in three minute intervals and the difference is that the measurement variables can't be manipulated in the simulation.   Our quality variables will be percent composition of to liquid products you can see   The analyzer measuring the composition here.   These variables are collected with a considerable time delay so   We're looking at the product in the stream because   These variables can be measured more readily than the product leaving in the exit stream. And we'll also be building a pls model to monitor   monitor our quality variables by means of our process variables which have substantial substantially less delay in a faster sampling rate.   Okay, so that's an a background on the data. In total there are 33 process variables into quality variables.   The process of collecting the variables is simulated with a series of differential equations. So this is just a simulation. But you can see that a considerable amount of care went into model modeling. This is a real world process.   So here's an overview of the demo, I'm about to show you will collect data on our process and then store these data in a database.   I wanted to have an example that was easy to share. So I'll be using a sequel light database, but this workflow is relevant to most types of databases.   Most databases support odd see connections once jump connects to the database it can periodically check for new observations and update the jump table as they come in.   And then if we have a model driven multivariate control chart report open with automatic re calc turned on. We have a mechanism for updating the control charts as new data come in.   And the whole process of adding data to a database will likely be going on on a separate computer from the computer doing the monitoring.   So I have two sessions of jump open to emulate this both sessions have their own journal in the materials are provided on the Community.   And the first session will add simulated data to the database and it's called the streaming session and the next session will update reports as they come into the database and I'm calling that the monitoring session.   One thing I really liked about the downs and Vogel paper was that they didn't provide a single metric to evaluate the control of the process. I have a quote from the paper here. We felt like   We felt that the trade offs among possible control strategies and techniques involved, much more than a mathematical expression.   So here's some of the goals they listed in their paper which are relevant to our problem maintain the process variables that desired values minimize variability of the product quality during disturbances and recover quickly and smoothly from disturbances.   So we will assess how well our process achieve these goals, using our monitoring methods.   Okay.   So to start off, I'm in the monitoring session journal and I'll show you our first data sent the data table contains all the variables I introduced earlier, the first set are the measurement variables. The next set our composition variables. And then the last set are the manipulated variables.   And the first script attached here will fit a pls model it excludes the last hundred rose is a test set.   And just as a reminder, this model is predicting our two product composition variables as a function of our process variables but pls model or PLS is not the focus of the talk. So I've already fit the model and output score columns here.   And if we look at the column properties. You can see that there's a MD MCC historical statistics property that contains all the information   On your model that you need to construct the multivariate control charts. One of the reasons why monitoring multivariate control chart was designed this way was   Imagine you're a statistician, and you want to share your model with an engineer, so they can construct control charts. All you need to do is provide the data table with these formula columns. You don't need to share all the gory details of how you fit your model.   So next I will use the score columns to create our control turn   On the left, I have to control charts t squared and SPE there 860 observations that were used to estimate the model. And these are labeled as historical and then I have 100 observations that were held out as a test set.   And you can see in the limit summaries down here that I performed a bond for only correction for multiple testing.   As based on the historical data. I did this up here in the red triangle menu, you can set the alpha level, anything you want and   I did this correction, because the data is known to be a normal operating conditions. So, we expect no observations to be out of control and after this multiplicity adjustment, there are zero false alarms.   On the right or the contribution proportion heat maps. These indicate how much each variable contributes to the outer control signal each observation is on the Y axis and the contributions are expressed as a proportion   And you can see in both of these plots that the contributions are spread pretty evenly across the variables.   And at the bottom. I have a score plant.   Right now we're just plotting the first score dimension versus the second score dimension, but you can look at any combination of the score dimensions using these drop down menus, or this arrow.   Okay, so we're pretty oriented to the report, I'm going to switch over to the monitoring session.   Which will stream data into the database.   In order to do anything for this example, you'll need to have a sequel light odd see driver installed. It's easy to do. You can just follow this link here.   And I don't have time to talk about this but I created the sequel light database. I'll be using and jump I have instructions on how to do this and how to connect jump to the database on my community webpage   This is example might be helpful if you want to try this out on date of your own.   I've already created a connection to this database.   And I've shared the database on the community. So I'm going to take a peek at the data tables in query builder.   I can do that table snapshot   The first data set is the historical data I I've used this to construct a pls model, there are 960 observations that are in control.   The next data table is a monitoring data table this it is just contains the historical data at first, but I'll gradually add new data to this and this is what our multivariate control chart will be monitoring.   And then I've simulated the new data already and added it to this data table here and see it starts at timestamp 961   And there's another 960 observations, but I've introduced a fault at some time point   And I wanted to have something easy to share. So I'm not going to run my simulation script and add the database that way.   I'm just going to take observations from this new data table and move them over to the monitoring data table using some JSON with sequel statements.   And this is just a simple example emulating the process of new data coming into a database, somehow, you might not actually do this with jump. But this is an opportunity to show how you can do it with ASL.   Next, I'll show you the script will use to stream in the data.   This is a simple script. So I'm just going to walk you through it real quick.   The first set of commands will open the new data table from the sequel light database, it opens up in the background. So I have to deal with the window, and then I'm going to take pieces from this new data table and   move them to the monitoring data table I'm calling the pieces bites and the BITE SIZES 20   And then this will create a database connection which will allow me to send the database SQL statements. And then this last bit of code will interactively construct sequel statements that insert new data into the monitoring data. So I'm going to initialize   Okay, and show you the first iteration of this loop.   So this is just a simple   SQL statement insert into statement that inserts the first 20 observations.   Comment that outset runs faster. And there's a wait statement down here. This will just slow down the stream.   So that we have enough time to see the progression of the data and the control charts by didn't have this this streaming example would just be over too quick.   Okay, so I'm going to   Switch back to the monitoring session and show you some scripts that will update the report.   Move this over to the right. So you can see the report and the scripts at the same time.   So,   This read from monitoring data script is a simple script that checks the database every point two seconds and adds new data to the jump table. And since the report has automatic recount turned on.   The report will update whenever new data are added. And I should add that realistically, you probably wouldn't use a script that just integrates like this, you probably use Task Scheduler and windows are automated and Max better schedule schedule the runs   And then the next script here.   will push the report to jump public whenever the report is updated.   I was really excited that this is possible and jump.   It enables any computer with a web browser to view updates to the control chart. You can even view the report on your smartphone. So this makes it easy to share results across organizations. You can also use jump live if you wanted the reports to be on a restricted server.   And then the script will recreate the historical data and the data table in case you want to run the example multiple times.   Okay, so let's run the streaming script.   And look at how the report updates.   You can see the data is in control at first, but then a fault is introduced, there's a large out of control signal, but there's a plant wide control system that's been implemented and the simulation, which brings the system to a new equilibrium   I give this a second to finish.   And now that I've updated the control chart. I'm going to push the results to jump public   On my jump public page I have at first the control chart with the data and control at the beginning.   And this should be updated with the addition of the data.   So if we zoom in on the when the process first went out of control.   Your Jeremy Ash It looks like that was sample 1125 I'm going to color that   And label it.   So that it shows up in other plots and then   In the SP plot it looks like this observation is still in control.   And what chart will catch faults earlier depends on your model. And how many factors, you've chosen   We can also zoom in on   That time point in the contribution plot. And you can see when the process. First goes out of control. There's a large number of variables that are contributing to the out of control signal. But then when the system reaches a new equilibrium, only two variables have large contributions.   So I'm going to remove these heat maps so that I'm more room in the diagnostic section.   And to make everything pretty pretty large so that the text would show up on your screen.   If I hover over the first point that's out of control. You can get a peek at the top 10 contributing variables.   This is great for quickly identifying what variables are contributing the most to the out of control signal. I can also click on that plot and appended to the diagnostic section and   You can see that there's a large number of variables that are contributing to the out of control signal.   zoom in here a little bit.   So if one of the bars is red. This means that variable is out of control.   In a universal control chart. And you can see this by hovering over the bars.   I'm gonna pan, a couple of those   And these graph, let's our IR charts for the individual variables with three sigma control limits.   You'd see for the stripper pressure variable. The observation is out of control in the university control chart, but the variables eventually brought back under control by our control system. And that's true for   Most of the   Large contributing variables and also show you one of the variables where observation is in control.   So once the control system responds many variables are brought back under control and the process reaches   A new equilibrium   But there's obviously a shift in the process. So to identify the variables that are contributing to the shift. And one thing you can look at is a main contribution.   Plot   If I sort this and look at   The variables that are most contributing. It looks like just two variables have large contributions and both of these are measuring the flow rate of react in a in a stream one which is coming into the reactor   And these are measuring essentially the same thing except one is a measurement variable and one's a manipulated variable. And you can see   In the university control chart that there's a large step change in the flow rate.   This one as well. And this is the step change that I programmed in the simulation. So these contributions allow us to quickly identify the root cause.   So I'm going to present a few other alternate methods to identify the same cause of the shift. And the reason is that in real data.   Process shifts are often more subtle and some of the tools may be more useful and identifying them than others and will consistently arrive at the same conclusion with these alternate methods. So it'll show some of the ways that these methods are connected   Down here, I have a score plant which can provide supplementary information about shifts in the t squared plant.   It's more limited in its ability to capture high dimensional shifts, because only two dimensions of the model are visualized at a time, however, we can provide a more intuitive visualization of the process as it visuals visualizes it in a low dimensional representation   And in fact, one of the main reasons why multivariate control charts are split into t squared and SPE in the first place is that it provides enough dimensionality reduction to easily visualize the process and the scatter plot.   So we want to identify the variables that are   Causing the shift. So I'm going to, I'm going to color the points before and after the shift.   So that they show up in the score plot.   Typically, when we look through all combinations of the six factors, but that's a lot of score plots to look through   So something that's very handy is the ability to cycle through all combinations quickly with this arrow down here and we can look through the factor combinations and find one where there's large separation.   And if we wanted to identify where the shift first occurred in the score plots, you can connect the dots and see that the shift occurred around 1125 again.   Another useful tool. If you want to identify   Score dimensions, where an observation shows the largest separation from the historical data and you don't want to look through all the score plots is the normalized score plot. So I'm going to select a point after the shift and look at the normalized score plot.   I'm actually going to choose another one.   Okay. Jeremy Ash Because I want to look at dimensions, five, and six. So the   These plots show the magnitude of the score and each dimension normalized, so that the dimensions are on the same scale. And since the mean of the historical data is is that zero for each score to mention the dimensions with the largest magnitude will show the largest separation.   Between the selected point and the historical data. So it looks like here, the dimensions, five and six show the greatest separation and   I'm going to move to those   So there's large separation here between our   Shifted data and the historical data and square plot visualization is can also be more interpreted well because you can use the variable loadings to assign meaning to the factors.   And   Here I have   We have too many variables to see all the labels for them.   Loading vectors, but you can hover over and see them. And you can see, if I look in the direction of the shift that the two variables that were the cause show up there as well.   We can also explore differences between sub groups in the process with the group comparisons to do that I'll select all the points before the shift in call that the reference group and everything after in call that the group I'm comparing to the reference   These   And this contribution plot will will give me the variables that are contributing the most to the difference between these two groups. And you can see that this also identifies the variables that caused the shift.   The group comparisons tool is particularly useful when there's multiple shifts in a score plot are when you can see more than two distinct subgroups in your data.   In our case, as, as we're comparing a group in our current data to the historical data. We could also just select the data after the shift and look at a main contribution score plot.   And this will give us   The average contributions of each variable to the scores in the orange group. And since large scores indicate large difference from the historical data. These contribution plots can also identify the cause.   These are using the same formula is the contribution formula for t squared. But now we're just using the, the two factors from the score plot.   Okay, I'm gonna find my PowerPoint again.   So real quick, I'm going to summarize the key features of the model driven multi variant control chart that were shown in the demo.   The platform is capable of performing both online fault detection and offline fault diagnosis. There are many methods, providing the platform for drilling down to the root cause of the faults.   I'm showing you. Here's some plots from the popular book fault detection and diagnosis in industrial systems throughout the book authors.   Demonstrate how one needs to use multivariate and universal control charts side by side to get a sense of what's going on in the process.   And one particularly useful feature and model driven multivariate control chart is how interactive and user friendly. It is to switch between these types of charts.   So that's my talk here. Here's my email. If you have any further questions, and thanks to everyone who tuned in to watch this. ... View more