"It is impossible for ideas to compete in the marketplace if no forum for
  their presentation is provided or available."           Thomas Mann, 1896

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PROCESS CONTROL

Technique for visualizing vast amounts of data to characterize the
process stability and capability of meeting customer specifications.

Author: Darryl Dodson-Edgars

Abstract

The mill information network forms the basis of a database that can be viewed in many formats. The typical conversion of a series of data points into a time trend is well known from the days of strip charts and graphic trends on operator DCS displays.  What do we do in order to understand the stability of a process or its capability of producing a product that the customer will accept?  The underlying theory of viewing a histogram from a set of data and noting its relationship to the specification limits expected by the customer is understood.  For that histogram, a capability index, C_pk, may be calculated, yet does that tell us what is happening to that process with time?

This paper describes a method of taking sequential sets of data, arranged into rational subgroups, and converting each subgroup into its corresponding histogram.  The histograms are then transformed from the normal  X-Y bargraph into strips of color based upon the value of the histogram count for each of the incremental bins.  The strips of color for each histogram are then stacked vertically on the page to form a rectangular region on the screen.  Care is given during the procedure to assure each histogram is counted over the same range of values.  The customer specification limits are arranged to the left and right of the rectangle.  The picture now represents the evolution of the process over substantial periods of time.  The patterns formed immediately communicate the nature of the process behavior.  Examples will be shown indicating the expected "normal" well behaved process and the kind of patterns associated with processes that have drifting means, common and special cause deviations from the customer expectations.  The methods useful in comparing subgroups with varying size will be discussed.  The implications of the normalization procedure lead to the interpretation of the pictures as "Sigma-plots", wherein the color bands give the behavior of the standard deviation with time.

Introduction

The process industries make use of measurements to control and understand the nature of their production.  These measurements each have ranges over which their readings are valid.  A level measurement could likely be anywhere over the full range.  A measurement of consistency likewise has a range of operation, but in this case the object is to keep the value of the consistency at some particular setting.  If the control system is designed, installed, tuned and maintained in good condition, the objective can be achieved.  When some aspect of the system changes, adverse effects can limit the ability of the control system to do its job.  The variability in the process directly limits our ability to meet the specifications required.  This discussion will describe a method of organizing processed information from rational subgroups of raw measurement data into images.  These images are able to convey a significant insight about the long-term stability of a process and the capability of maintaining the required specifications.  Pictures of actual data are presented to illustrate various distinct patterns.

Discussion

Variability is a fact with which we all are familiar.  The   process control world is based upon the measurement of   something, in order to decide what to do in the future to   maintain or adjust a process in some particular manner.   The inherent unsteadiness of the measurement world is   based upon both sensor noise and changes in the process   under observation.  The Mathematics’ that describe the   measurement variability assumes that the variation is   normally distributed around some mean value.  This is   shown in figure 1.  The width is parameterized by the standard deviation, s.  The normal distribution is 6s wide.  That is to say, we can expect to find 99.7% of the measurements within plus or minus 3s of the mean value. Distributions of real data form histograms that have the basic shape of the normal distribution for many of the processes in the paper industry.  The most obvious deviation from this case occurs when the process has changes in the mean value.  Human beings induce such changes for deliberate reasons in the course of using the process control systems.

When you set out to observe the ability of your control system to maintain the process at the desired state, the first question raised is “over what range of time to observe the measurement”.  The term “rational subgroup” describes the result of a logical thought process that can follow several paths.  The bottom line is to determine the data to translate into a histogram.  We may only want to do this one time.  On the other hand, it is likely that we want to observe a process on a continuous basis.  In that case, we need to gather data for a fixed period.  This data gets assigned to the time range of the rational subgroup.  The next data is gathered and assigned to the following time range, and so on.  We can now observe the consecutive histograms and begin to understand the longer-term nature of our process.  Does it change from one time interval to the next?  Does the shape of the distribution change?.  Does the mean value drift around?  Are there more than one definite peak values?  Answers to each of these questions would tell us something definite about our process.

The paper industry serves a wide range of markets.  Tissue   customers want a product that is different than Kraft bag   material.  Newsprint is different from photo-copy paper.   Each grade of paper must conform to certain specification   limits.  These limits are referred to as the Lower & Upper   Specification Limits (LSL & USL).  Figure 2 is a diagram   showing a histogram distribution from a normal process   and customer specification limits.  In this case, the   process distribution is contained within the limits for the   specified measurement.  This distribution could, for   instance, represent the variability in the brightness of the pulp, the consistency of the stock, or the basis weight.  Any measurement in the process that must conform to specification limits can be viewed in this manner.

When a process is able to be maintained within these specification limits, it is thought of as being capable of satisfying the customer.  This has been mathematically defined as parameter C_pk, known as the Capability Index.  This index is the measure of how completely the distribution lies within the limits.  The equation that expresses this value is given by the smaller of:

                              or        

This equation assesses the compliance of the observed   process to the specification.  The C_pk value will be greater   than 1 for processes that are capable of fully meeting the   specification.  Tighter distributions within the specification   range lead to higher calculated values of the capability   index.  Figure 3 shows two different distributions.  The   upper distribution would be from a process that is not fully   capable of meeting the required specifications.  It would   have a value of C_pk less than 1.  The lower distribution is   contained within the limits and therefore would represent a   satisfactory process with a C_pk greater than 1.

The histograms discussed thus far have been from a single sample period for a process.  What happens with time?  The paper mill is run around the clock for most of the year.  How does the process evolve?  The variation of measurements associated with the paper machine in the machine direction (time) can be viewed from the perspective of both their short-term (MDS) and long-term (MDL) behavior. The stability of a process can likewise be considered for the short-term (within the subgroup for a single histogram) and the long-term (among consecutive histograms).  For instance, if the measurement data subgroup was from a reel of paper, what are the relationships of the histograms from different reels?  If the histograms were lined up according to time, would any patterns emerge to aid understanding the process dynamics?

Figure 4. shows the histograms from six consecutive   subgroups.  This image characterizes a process that is   maintaining a stable mean value and has more than full   capability of controlling the process, with the tails of the   histograms inside the specification limits.  The distribution   of measurements are very similar from run to run.  This is   the ideal situation.  A process such as this lends itself to   opportunities for economic optimization.  For instance,   adjusting costly additives to keep the process within   specification but with the mean value shifted appropriately   to your advantage.

Other patterns in the histograms can become evident.    Figure 5 demonstrates another behavior.  The operator of a   process may want to adjust the mean, or set point, of a   process from one value to another.  Normal operations   often require changes in the set point.  The patterns to   expect would show an offset in the mean value from   histogram to histogram.  The change can happen quickly   or slowly.  The eye can easily note the shifting patterns.    This shift will occur until the process has reached the new   operating level.  The image would then return to the steady   state from figure 4 but with the mean now shifted.

Figure 6 is a different situation.  We can see that the tails   of all the distributions are within the control limits.  That   means the process remains capable of meeting the   customers specification.  The problem: the mean value of   this controllable process is drifting around in the   specification range without any noticeable pattern.  The net   effect of this kind of behavior will be that your customer will   perceive your process as having an overall wider variability   than you know to be the case.  The variability from   subgroup to subgroup will give the impression that the   variability is wider.  Is this OK?  The hint to take for the   conscientious operator would be to determine why the drift is occurring and do something about it.  In some cases, this may be perfectly acceptable.  It is more often the case that the customer’s process has a more difficult time coping with your product because the properties change around too much.  The modern machinery in use today continually require narrower specifications.  A situation like figure 6 would be out of tolerance sooner than necessary, unless the mean value would stabilize and be shifted to the center.

Another process could have changes in the distribution    from narrow to wide, centered on a stable mean value.    Figure 7 demonstrates this.  The pattern could indicate a    difficulty with the control system.  Tuning changes would    alter the width of the measurement histogram.  Attention    to details would be warranted to get back to the more    ideal state.

Figure 8 will drive your customer away.  The manufacturing   operation with a wild process like this will find it difficult to   compete.  The mean is shifting, and the width of the   distributions are changing.  This is a picture of Chaos.   Where do our process systems measure up to this form of   scrutiny?  We may have an intuitive idea about what we   have.  Human intuition has proven to be uncannily   accurate.  Despite this, you can not run a business only   upon this intuition. 

The process control systems in use today are bountiful   sources of information.  Many industries have implemented process information systems that gather and archive measurement information from their control systems.  Data by itself is neutral.  We have converted data into information for many years.  One of the common methods of data conversion is with the time trends.  The trends are a two dimensional history of a measurement (y-axis) with time (x-axis).  In the early days it was done with ink on paper.  Now we have high tech CRT’s and computers.  Information about a process can convey more intelligence about a process when presented in more than two dimensions.

We can choose to manipulate the data in   our process measurement archive in   order to transform it into the kind of   diagrams discussed above.  Figure 9   shows a flowchart of the main operations.   As this procedure is formulated for a   particular measurement several   considerations must be attended to.  This   may best be understood by tracking an   example measurement.  Let’s convince   ourselves that gathering a data point   every five minutes for the period of 24   hours will give us reasonable subgroup.   This gives us a data set made up of 288   samples.  Next we need to obtain the   specification limits.  We can then easily   compute the histograms for consecutive   24 hour periods.  In the case where the   subgroups contain the same number of   data points we can directly compare one   histogram to the next.  What if we were   looking at a measurement on the paper   machine and the source of data had been   the scanning platform?  This is where the   amount of initial data can become   immense.  It is not uncommon to have   the production reels consist of different   numbers of scans of the sheet.  Each   scan can consist of 100 individual   measurements.  The number of scans can be 150 during the manufacturing of the reel.  That makes each reel contain on the order of 15,000 individual data values.  The reel is a natural subgroup candidate for the paper machine.  In this case, we can normalize the individual data groups by assuring that they all have the same area under the histograms.  This is a simple procedure.  The histogram with the most data samples becomes the benchmark.  A different scaling factor is multiplied with each of the other histograms to make the sample sets equal in size.  This makes their area the same.  Other manners of normalization will be useful in the transformation of the neutral data into the intelligence we seek.

It becomes evident when we want to look at   more than few consecutive histograms that the   pictures shown above will get overcrowded and   difficult to read.  The two dimensional plot of   the histogram can be compressed into a one   dimensional strip of color.  This transformation   is given in figure 10.  The preferred method is   to use color.  The use of gray scales will work   but will lack the vibrancy of color.  The Y-axis   in figure 10 is divided into 10 equally spaced   colors, arranged in whatever manner appeals   to the viewer.  The data for the histogram is   then converted to the color associated with the   its position on the Y-axis.  
 

The normal distribution then maps into the   strip of color (or grays).  This procedure then   allows the vertical stacking of many individual   strips that correspond to the consecutive   histograms.  The mapping can be done in   many different ways to achieve different   interpretations of the images.  When the data   from the individual histograms have been   normalized so that the peak value of each   histogram has the same maximum value, the   nonlinear mapping given in figure 11 then leads   to the interpretation of the images as “Sigma   Plots.”  This mapping has the upper color   corresponding to the 60.7% to 100% range, the next color corresponds to the 13.5% to 60.7% range, the third color corresponds to the 1.1% to 13.5% range and the last corresponds to the 0% to 1.1% range.  These values are the normalized amplitude of the Gaussian (normal) distribution at the 1, 2 and 3 sigma points.  The obvious interpretations of the color bands on the transformed color strip are for the +/- 1 sigma, +/- 1 to 2 sigma and the +/- 2 to 3 sigma bands around the mean.  Notice that they are linear in the transformed strip domain.

Up to this point, the discussion has been theoretical or hypothetical.  We still have not seen how a real process could appear.  The next six images are selected from actual data.  The subgroups were the data from individual paper machine reel measurements.  The data were sorted by grade.  The data represents three months of operation for a specific grade of paper.  Specific patterns were then selected in order to demonstrate the different types of image patterns that could be seen.

Figure 12 represents the transformed   histograms from more than three hundred   individual reels of paper.  Each subgroup   contained more than 100 passes of the   scanner over the sheet of paper during its   manufacturing.  Each pass of the scanner took   over one hundred measurements.  The picture   then represents the interpretation of nearly   3,000,000 measurements.  Specification limits   are shown along the left and right of the figure.   The pattern is typical of the well functioning   process.  The mean value of the distribution is   maintained in the center of the specification   limit range.  The width of the spread of the histograms is well within the limit range.  Reel after reel, grade run after grade run, the process remains where it should.  The event indicated near the upper left in figure 12 indicates a brief shift in the mean.  This shift was rapidly corrected and the process returned to the centerline. 

Figure 13 demonstrates the situation where a   process mean was shifting in an erratic   manner for half of the run.  The cause of the   erratic operation, whether control, machine,   process or human related was stabilized with   the result the eye can immediately perceive.    The upper portion of figure 13 is much the   same as figure 12.  The conclusion one could   reach from figure 13 is that we are in good   shape with this process now.  We have the   ability to keep the average process   measurement in the middle of the specification   range.  Concentration of effort can now be   redirected to those parts of the process where   the picture indicates the need.

Figure 14 tells us something else.  The first   histograms at the bottom of the picture are   wider than most of the other histograms.    Changes were occurring that increased the   inherent capability of the process.  We can   see that an event occurred where the mean   shifted significantly to the right and   immediately corrected.  After the shift, the   mean value of the next several distributions   was shifting to the right.  This offset was then   quickly reversed and the centerline was re-  established.  Obvious other transitions are   noticeable between the consecutive grade   runs.  The distributions are wider than those in   figure 12.  This corresponds to the fact that this process in less capable than the process for figure 12.  Nevertheless, the customer specification was met except for the few special cause events.

Figure 15 is a good example of run-to-run   variability.  Each run consists of several reels.    During each of these short runs, the mean   value is maintained at some point.  This point   does change though.  Is this from different   operators using their own preferred settings?    Is there a shift in the process caused by other   parts of the operation?  Many questions will   arise based upon the particular process under   observation.

Figure 16 indicates the before and after for a   process change.  At the bottom of the figure,   the mean is shifted to the right and the width of   the histograms was around two thirds of the   specification limits.  The process was altered   and afterward, the mean shifted down and the   width of the distributions decreased.   The   variability had decreased as predicted.   This   provides graphic evidence that the process had   been improved.  The audience for  this   perspective expands.  The engineer who   designed and installed the improvement to the   system can be certain of the project success. 

Has figure 17 thrown us a curve?  Is the   movement of the mean along the variable path   due to things beyond our control?  Is the   adjustment to the process done for   predetermined reasons?  This picture should   prompt dialog among the humans involved in   the operation of the process.  We either know   what we are doing or we don’t know. 

Conclusion

We are looking at the process is a way that has not been available in the past.  We are seeing the process from a very different vantage point.  This is the forest.  The measurement from a single scan is the realm of information typically available in the manufacturing environment.  We are now looking at the historical path of our process dynamics.  We can ask many questions and get the inspiration to consider subtle aspects of the total operating system.  This system incorporates the process, the machines, the computers, the people and their practices.  Is the overall operation giving our customers what they want?

Acknowledgment

The author wishes to recognize the contributions of Dr. M. J. Coolbaugh in the discussions about data normalization and Mr. J. Huff for his encouragement to explore.

About the Author:

Mr. Dodson-Edgars founded Dodson-Edgars Associates in April, 2001. He has over 25 years in information technology, including development and implementation of several major technology plans. He is the former Chief Technology Officer for Multivision, Inc, one of two national video clipping services with offices in New York, Los Angeles, Chicago and San Francisco. Mr. Dodson-Edgars was brought on-board to move the fulfillment channel from overnight messengers to video streaming over the Internet.

Prior to joining Multivision, Mr. Dodson-Edgars served as the Chief Technology Officer of Fed2U.com, an Internet company created to devise and implement the strategy in delivering the new federal government information portal E-commerce website. This fast-track site was brought from inception to launch in four months, integrating the content of a dozen Federal web sites with political news feeds. The subscription-based business-to-business target market included lobbyists, law firms, and organizations seeking to automate mining the governmental data sources.

Before his work at Fed2U.com, Mr. Dodson-Edgars spent 15 years at Boise Cascade, the $6 billion forest products company. During his tenure at this company he served in a variety of technology roles, including the top Web and computer technologist for the company. His extensive background in computer programming and process engineering lead to national award-winning software applications.  He pioneered the creation of Intranet and Extranet applications, which lead Boise Cascade into receiving national recognition as the top manufacturing operation poised to reap the harvest of true ERP.

While with Boise Cascade, Mr. Dodson-Edgars also served as the chief technology officer and principal investigator for DynaMetrix Corporation, a high-tech startup company developing the commercialization of his patented technology under a Department of Energy research grant.

After graduation, he spent several years as a physicist at Naval Research Laboratories and with NASA at Cal-Tech’s Jet Propulsion Laboratory. He has bachelor’s degrees from the University of California at Irvine, where he graduate magna-cum-laude in mathematics and physics. Under a fellowship from the Naval Laboratory he pursued Ph.D. studies in engineering at the University of California, Los Angeles.