EFC and SPC (SPM)An EFC Example (Paper Making)Appendix: Some Details on the PID Controller for the Paper MachineIE 361 Module 12EFC and SPM: One Thing Control Charting is NotReading: Section 3.6 of Statistical Quality Assurance Methods forEngineersProf. Steve Vardeman and Prof. Max MorrisIow a State UniversityVardeman and Morris (I owa State University) IE 361 Module 12 1 / 11EFC and SPCIn this short module, we try to make explicit the di¤erence between"engineering control" (as understood, for example, by EE’s and ME’s) and"SPC." Recall from Module 10 the basic insight that Shewhart "controlcharting" is about process watching for purposes of change detection asillustrated in the …gure below repeated from that module.Figure: Statistical Process MonitoringVardeman and Morris (I owa State University) IE 361 Module 12 2 / 11EFC and SPMControl Charts are NOT Process-Tweak ing/Process-Guidance ToolsEngineering Feedback Control is process guidance/on-line adjustment asrepresented in the …gure below, where repeatedly an output Y is comparedto a target value T and accordingly a change is ordered in some processvariable X .Figure: Schematic of an Engineering Control SchemeVardeman and Morris (I owa State University) IE 361 Module 12 3 / 11EFC and SPMControl Charts are NOT Process-Tweak ing/Process-Guidance ToolsThe …gures on panels 2 and 3 and the methodologies they represent areNOT the same. Automatic online process adjustment is not the samething as process watching for purposes of change detection.SPM and EFC are NOT Competing Technologiesboth have their placesboth can b e badly doneboth can contribute to variation reduction in an industrial processneither is a "weak version" of the otherIn many industrial applications, EFC creates the physical stability thatSPM monitors.Vardeman and Morris (I owa State University) IE 361 Module 12 4 / 11EFC and SPMControl Charts are NOT Process-Tweak ing/Process-Guidance ToolsHere are some contrasts between EFC and SPMEFC SPMis "automatic" (digital or mechanical) is often manualis compensation-oriented is detection-orientedexpects process "drift" expects "stability"is on-going "tweaking" triggers "rare" interventionsis typically computer-controlled typically alerts a human agentmaintains optimal adjustment warns of "special cause" changesis tactical is strategiccan exploit dynamic models warns of departure from stabilityThe technologies of EFC and SPM are quite di¤erent. SPM deals incontrol charts. EFC deals in feedback algorithms that prescribe exactlyhow adjustment variables are to be manipulated on the basis of processdata. "PID" control algorithms are a common variety of these (seeSection 3.6 of SQAME for a few details on PID control).Vardeman and Morris (I owa State University) IE 361 Module 12 5 / 11An EFC Example (Paper Making)From Section 3.6 of SQAMEProf. Jobe worked with the Miami U. Paper Science Department on thecontrol of a paper-making machine. A schematic of that machine isbelow. Fundamentally, a pump feeds pulp onto a moving conveyor wherethe pulp dries to make paper.Figure: Schematic of a Paper-Making ProcessVardeman and Morris (I owa State University) IE 361 Module 12 6 / 11An EFC Example (Paper Making)From Section 3.6 of SQAMEIssues in developing an appropriate control algorithm included:pulp mix thickness WILL vary, but pump speed can be used tocompensate,this is NOT an SPC problem! (it is an automated compensationproblem),target paper density is 70 g/ m2,1 "tick" on pump dial changes density about .3 g/ m2, andtime delay and potential for over-compensation/oscillation are seriousissues.To remove the time delay issue, a 5-minute sampling/adjustment intervalwas adopted. Through a series of experiments, an appropriate PIDcontrol algorithm was developed (see SQAME exposition and problemsand the appendix to this module for details).Vardeman and Morris (I owa State University) IE 361 Module 12 7 / 11An EFC Example (Paper Making)From Section 3.6 of SQAMEThe following shows "uncontrolled"/baseline density data for 12 periodsand data from 6 periods after the …nal algorithm was implemented andhad been allowed to take e¤ect.Figure: "Before" and "After" Paper DensityTo this point, we have an EFC success story. SPM now could have a rolein monitoring for unexpected changes from this behavior.Vardeman and Morris (I owa State University) IE 361 Module 12 8 / 11Appendix: Some Details on the PID Controller for thePaper MachineA PID (proportional/integral/derivative) control algorithm for the papermaking example is∆X(t)= κ1∆E(t)+ κ2E(t)+ κ3∆2E(t)forY(t)= measured paper density at time t∆X(t)= the knob position change (in "ticks") after observing Y(t)E(t)= the "error" at time t= T(t) Y(t)∆E(t)= E(t) E(t  1)and∆2E(t)= ∆(∆E(t))= ∆E(t) ∆E(t  1)Vardeman and Morris (I owa State University) IE 361 Module 12 9 / 11Appendix: Some PID Control DetailsThe"Integral" part of the algorithm, κ2E(t), reacts to deviation fromtarget/o¤set,"Proportional" part of the algorithm, κ1∆E(t), reacts to changes inerror (/level), and"Derivative" part of the algorithm, κ3∆2E(t), reacts to curvature onplots of error.Jobe’s …nal control algorithm was∆X(t)= .83∆E(t)+ 1.66E(t)+ .83∆2E(t)Vardeman and Morris (I owa State University) IE 361 Module 12 10 / 11Appendix: Some PID Control DetailsThe following table shows some hypothetical values for Y(t)andcomputation of corresponding values of ∆ X(t)for Jobe’s controlalgorithm.t T(t)Y(t)E(t)∆E(t)∆2E(t)∆X(t)1 70.0 65.0 5.02 70.0 67.0 3.0 2.03 70.0 68.6 1.4 1.6 .4 1.3284 70.0 68.0 2.0 .6 2.2 5.6445 70.0 67.8 2.2 .2 .4 3.4866 70.0 69.2 .8 1.4 1.6 1.162Vardeman and Morris (I owa State University) IE 361 Module 12 11 /