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Philip Morris

Section 4 Control Charts and the Tools of Statistical Process Control

Date: Aug 1991 (est.)
Length: 64 pages
2053867913-2053867976
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2053867777/2053868265/Rcb Plus Q1 Training Rcb Process Total Quality & Productivity Improvement Principles Tools Techniques Rcb Plus R1060 Act 01mfp770 Singletary, Laura 6772
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Deming, W.E.
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C+I Teams
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Systems Improvement Team
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05 Jun 1998
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INTRODUCTION &OBJECTIVES ~ In this section we will look at the value of developing not just a collection of charts but rather a comprehensive Total Statistical Process (SPC) System which incorporates all of the principles of RCBPIus. We will discuss both the off-line and on-line methods and tools since the participants of 01 need to master and have a firm understanding of both. Section 4 will concentrate on the philosophy, mechanics, application and interpretation of these tools while Section 5 will detail the RCB Process SPC System -the what, who, when, how and the why. Objectives: • 1. Understand what is meant by Off-line versus On-line SPC. Know and understand how to use the tools of each and your responsibilities in each part. 2. Know what is meant by Statistical Process Control, to be in control, an economic state of control, difference between control limits and specifications. 3. Know how appropriate type of control chart is selected, how to calculate control limits, how to plot and interpret a control chart, how to calculate and interpret process capability. 4. Understand the difference between performance and capability. (In-control vs. capable). 5.Know how to use SPC tools (control charts, Cpk) to detect improvement to a process. © 4-1 ~ r~
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WHAT IS SPC? SPC Defined SPC (Statistical Process Control) is a method to manage, control and reduce the variability of product, processes and services. When supple- mental with job and process knowledge and experience, it allows us to achieve the highest level of product, quality, highest levels of productivity and significant reduction in the cost of producing. Statistical Process Control The use of statistically based techniques such as control charts to analyze and run a process so appropriate actions are taken to achieve and maintain a state of control and to improve process capability through problem-solving sources of variation. On-line Versus Off-line SPC In order forthe BL Plant to reap the large benefits possible from implem- entation of a comprehensive TQI SPC System it is necessary that every- one routinely and actively participate - through "on-line" activities and `bff-(ine" activities. Making an SPC System work so it can deliver significant business results and improve everyone's quality of worklife is not a spectator sport! Throughout the rest of this training manual you will see techniques, methods and system components which encompass the on-line as well as off-line aspects of SPC. 4-2 © Techniques and actions used by attendants while the product is being made, to routinely monitor, react to and control the output of that step of the RCB process. The use of statistical problem-solving tools and SPC System data to improve control of the process, reduce variation and change the operating level. The use of tools by supervision to prioritize and manage their work in the improvement of process quality, productivity and cost. a • •
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Examples of On-Line SPC Activities: ~ • Run process stage or standard. Checking standards and documenting off-standard occurrences. • For each parameter- measure, plot, interpret and make necessary control moves to bring back in control. • Checking of equipment standards and documentation of off-standard performance. • • Sampling, testing, reporting of results by QA technicians. • Documentation of process "events" on SPC System Report - attendants, supervisors, maintenance / production / QA), Shift Coordinators. Examples of Off-Line SPC Activities: • Real-time problem solving, led by supervisors, to determine root cause of off-standard or out of control. • C&I Plan problem-solving efforts to reduce variation or change the level of performance. • Improvement of parameters, standards, control moves using the Process for Change. • Quality Council / SIT review of system data and prioritization of BL Plant work. • Quality Council monitoring of adherence to the system, corrective action on employees not performing job responsibilities. • Use of Off-Line measures by Supervisors, Shift Coordinators, Superintendents to prioritize work, monitor progress and measure effectiveness of efforts. • Monitoring of Job Responsibilities by Superintendents, Shift Coordinators, Supervisors. IL? C C!I ~ 64..; - GG!) © 4-3 ~ N s~
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The Foundations of On-line SPC The Foundations of SPC SPC is not just charts-it is a way of viewing, monitoring, running and working on processes. In order to achieve significant and lasting benefits there are three major components which must be pursued equally. SPC should not be viewed as something to do in addition to one's job, but how everyone does their job. Standardized Control Moves Standardization Control Chart of Process System and Actions The success of these three components depends primarily upon one factor-the willingness and commitment of all people within the plant to work at using this approach to run the process. 4-4 © • • •
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Key Points about SPC • "A state of statistical control is not a natural state for a process. It is indeed an achievement, arrived at by elimination, one by one, by determined effort, of special causes of excessive variation." - W. Edwards Deming • • State of Statistical Control-the condition describing a process from which all special causes of variation have been eliminated and only common causes remain. • Economical State of Control-a perfect state of control is rarely attain- able in a production process. A controlled process is considered to be one where only a small percentage (less than 5%) of the points go out of control n~d where out of control points are followed by proper action. • Control Limits-derived from process performance, they define proc- ess variation by showing natural level of variation to be expected. • Specifications those requirements or needs of the process that are imposed upon it. • To be in a state of statistical control and to meet specification are two separate (but related) issues. • For long-term survival and for economic reasons, being in a state of statistical control is far more important than merely meeting specifica- tion. • Control charts can be utilized in many different applications as long as the output you are interested in is quantifiable. • Use of a control chart system to monitor and take action on a process at the time of production, is far more beneficial than measuring the product after the fact to determine its acceptability. • Control charts are not a remedy in themselves, it is the action and decisions that result from them that make the difference. Ry
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Simulation of a Process: Quincunx Demonstration To best illustrate the use of a control chart system to control a process and the benefits over traditional methods, we will simulate a process through the use of "Quincunx." Although we are dealing with beads and the Quincunx, as we go through this exercise try to visualize the applica- tion to any BL process-whether we are trying to control blend ratios, OV after Burley Dryer, Gas Consumption, QB-IA differences, PG level at weighbelt, Daymix Solids, Forming Line OV, or Sheet Weights, Downtime or any other processes or product quality parameters. We will use these results to look at the application of control chart concepts and then look at some specific examples. Problem We are a major buyer of red beads looking for a good supplier. We have found one which we wish to investigate - ABC Bead Corporation. We have weight requirements for the type of bead we desire: target of 13 oz. You would like all beads to be 13 oz. But might be willing (reluctantly) to accept beads with weights as low as~9-oz_ and as high as f7 oz. ABC has quoted a price of $22 per bead. We will stress to ABC Beadthat we really would like all beads at 13 oz. We will now watch their process, record some of the results we see and draw some conclusions. Questions to Think About 1. Does the process seem to be producing product that meets our expectations? 2. Does the process exhibit a state of control? Are there special causes present? 3. Is ABC Bead a good supplier? Why or why not? 4. What can be done to improve the bead weight performance of ABC Bead? Procedure As the process is producing beads, we will take a sample, perform a weight measurement and record the data on the following sheet. Record any other significant "events" that occur next to that hour. • •
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Simulation Results • TIME BEAD WEIGHT NOTES 2330 f~ 0030 J 0130 ~~ 0230 l~ t l 1~ U 0330 0430 , 0530 f 0630 . 0730 ir e f t ~ ~~°V 0830 0930 1030 F P6F J 5` ~~~5~ ~i71 1130 ` 17, 1230 60 9 .`(~~ 1330 f lo` lv /0 1430 1530 1630 1730 1830 1930 2030 2130 2230 N a G't W Go ~ ft'l CD Z4-7 ~~ O
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Control Chart DATA Now let's see what the results look like using the too[ of control charts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~~ . . . . . . . . . . . . . . . . . . . ~ . . . ~.~ . . . . . . . . . . . . . . R . ~ . •~) . . ~ . ~. . . . . . . . 4 . 1. . . ~, . . . ~~~ . . . . . . . . . : . ,~ . . ~?' . . . ` . . i` . . . . . . . . . . . . . . . . . . . ! . .~~ . . . . . . . . . . . . . . . . . . . . . . ~~ ~ . . . . . . . . . . . . .. .. . . . . . . . (~ . . . . . . . . . . . . . . . .. . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ZSn = Ow ® = O0 Q tBB Qm Bm = = tlm tm ti~f KM tiz 1® TTA IM fo ~ aD 2m ~ ~ 13 A ~~ !' ~~ Is the process in a state of control? 0 Is there more variation in the process than needs to be given the same equipment, materials and "operator"? • What is typical variation for this process? • Is it capable of meeting our specifications? 4-8 © \ ~ ~. ~ l3,C) _~-- ~~ - • •
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Procedure to Derive Control Limits: X Control Charts 0 1. Gather data over representative time period. Plot on run chart. 2. Remove suspicious data. 3. Check to see if data is normal. 4. Calculate average (X ) and standard deviation(s) of the data. 5. Derive UCL (Upper control limit), LCL (Lower control limit). UCL = X +3 • s LCL = X-3•s 6. Check data for control. Delete any data outside the control limits. If any data is eliminated, repeat steps 4-6 until the data settles down (all data within the control limits). 7. Determine if X compatible with target. 8. Set up control chart for use on the process. • Worksheet For Simulation Our objective is to: 1. Derive process control limits for average and range. 2. Determine process capability. I. Deriving Control Limits (we will follow the 8-step procedure) N O G't C.1 ~ El 4-9 C~D~ N
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Final Control Limits for Optimizing Current Process Average UCL = 16, ~ X LCL = ~F 1 s = a.3 II. Process Capability Now that we have data from a stable process, take the in ivi I values left after Step 8 and calculate: Step 1 Mean (7): 13.0 Standard deviation (s): j. ? Step 2 Calculate CPKfrom expectations/specifications uSL = 17 Conclusions: ~ ,2M EN ~ -~CtSt- Cog- _ ~.- 0Y ~ y 1,03 4-10 © L 5 L- :;- 9 q5L -~ 1`? -13 w • .
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OVERCONTROL VS UNDERCONTROL ! As you have seen from the simulation, without the use of an accurately established control chart scheme, it is very easy to commit two types of errors when interpreting data to act on a process... Undercontrol-not reacting or taking action when you should be-there is something special taking place in the process that you should be react- ing to, but you dismiss it as normal variation. Overcontrol-reacting or taking action when there is no need to-there are no special causes present in the system and the value you have just obtained, although it appears high or low, is to be expected because of the system causes of variation. Should not overreact. Both types of errors cause more variation to occur than need be in the process. The table below summarizes what could happen when trying to control a process. True Process Condition • Stable (Process centered at target) Special Cause Present (Process not centered at target) Make a Overcontrol Correct Move (Type I Error) Acti o n A ti c on Leave Co rrect Undercontrol Alone Action (Type II Error) Establishing sound control limits and following control rules through stan- dardized control moves will absolutely minimize the Type I and Type ff errors that are made on the RCB processes. Note: Whenever tracking data, a data point must either go up or go down compared to the last one. The purpose of SPC is to interpret the data N to see if the process truly shifted or are we being tricked by the data O which reflects random fluctuation. ~ P4-11 -15 ~ ~
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CONTROL RULES: TESTS FOR STATE OF STATISTICAL CONTROL In a continuous process like the RCB process it is often not economical to wait for a signal that a single point has gone beyond the control limits. At the same time we do not want to second guess the logic and probabilities of the control chart. The following tests for control will allow us to detect process trends and shifts earlier without altering our chances of taking the wrong action. These are the control rules adopted for all X control charts. For simplification, the letters A, B and C have been used to separate the chart into zones corresponding to 1, 2 and 3 standard deviations. First Test One single point falls beyond Zone C (outside of 3s) F E D X ~ I _ 1i-[ ~ _1iu I_ L u_ i_i A a Q E F Second Test Two out of three points fall on the same side of A and beyond Zone B (outside of 2s) F E D C r - ; B I A A D E F 4-12 IPF • •
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• 0 Third Test Four out of five points fall on the same side of Xand beyond Zone A (outside of 1s) F E D ~ r I A F Fourth Test Seven consecutive points on the same side of A F C R ! B 1R ~ \ r- ~ ~ , ~ A l\ t ~ ( A A t 1 D E F C~,ee 4 /xP_ ~ 64~ v~2G eL-'f - c-22 P-a.a. c -e © 4-13 Ca
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Key Points on Plotting & Interpreting Plot all points in the middle of the zone • Draw a vertical line top to bottom, make a control move, and restart the count. • Put an asterisk (') on the top of the chart above all points in the out of control period (eg. if 4 out of 5 rule violated- put * above all 5 points). • Any values that fall on a zone line exactly plot in zone below (if above centerline) or zone above (if below centerline). "Always pull towards center {ine". • Whenever a control rule violation is detected: • Whenever the process goes down, (or restarting the count) do not connect the plotted points. Make a note in the Action Report (covered in Section 5) of why this was done. 4-14 - --- ------- ---- --- ws.1v...wti::Gi\\:i:2Eti:'>. e~.ZMn..wMvn~nssw.vC3n.l..°...-TS.::nM..JnwX:ikd:BCi:n\iivx..~}M6YY © • S
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S Workshop #7 For each of the following parameters: • Interpret for control using all rules. • If out of control put an * above/below the point where you would have made a control move; indicate with an * the entire out of control period. • Indicate correctly where you restart the count OV After Burley Dryer 0 • X 5•0o , . ~ .~ 0 C . . . s . . 'I A . .~ A ~ s . C . . . . . . r ~ . ~ . . 0 . . . . . . •~ • E t , , . m1 . ® . I= ® CM . 10 M t a . v! tm O 1f~ iM fa 0 fQ 1Li UN 1M 1® M a IIi ~ ATA ._ ~ E 0 U C l C • a A A s E Particle Size - After Hammermitt a3 •q e~ Nt t~k V ,~ A at d E • •I c s • •f A ~ . ( A f i ~ C ~ 0 . . . .i t .~ . E . . . . . .~ , . mt . ~ . aM . ® . aa so . aM . a os roa o >v ~ . sa . m~ so n ~m . rr~ ~m xs =s ns • ~ ATA © E s A A a Lc.L C 0 E N ~ W ~ 4-15 ~ N
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QB-IA Difference: Production Dust OV .93 X 3 F a . . I • • p . . .~ . . . . . . . . . . ~ . . C ~ f . ~ . . . . . . . A ; . 'I a r , C ! E . . . . . . • F QL ® Ol~ l0 0 Q Gm sm O tL~ Tm ta ~ SO m D Ri n lO S bi ~7 ATA PG Level in Slurry 5al X 4-`+9 31-7 D ATA F av r E D . . . . . . . . . . . . . . . . . . . . . . . C . . . . . . ' ~ •f ~ A A . . . . . . . . . . . . . . . . . . ~ C . . . . E . . . . . . . . . . . . . . . . . . F . . . . . . . . . 1 . . . . . m1 ® 9tD ® ~ 10) ~ oQl ~ O 1~ tO~ tSA ~ fO ~ T7~ ~ . • • 4-16 11H E D C"`L ® A A ! E E D c v`c-" a A D E
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S Workshop # 8 Use the data and chart below to plot results. Follow the guidelines for plotting, documenting and interpreting results. Indicate any out-of-control periods with an '`. Assume that a control move is made each time an out of control condition occurs. Forming Line 3 OV Time Data . . . . . • . . . . . . . . . . . . . . . . . . • . .. . . • . . .. . .. • . . . . . . . • . . . . . . . . • . . . • . . . nlo Itrto 1 Ibtf t t7~ t~s ta~a tt25 t~p t4~i n l9t5 !~{O ~ tS•t t5•t T~4 ~317 ttg. ri3 t't ft tb. w. tt+~ ta.8 r12 tb~ tto.5 l7.`{ a. t6. t6 ~ Ib .t I t t~ 1628 -Casting Roll Adjustment 74.3 -75.8 ~~~'~ 1757 - Casting Roll Adjustment 75.8 - 75.2 2 E D C 6 A A 6 , D E © . . . . 1- • . • • . . • • . . • . . • • . . . . . . . . . • • • . . . . . . • • . . . . . . . . . . . . • . . . . . . . . . ~ • , , , . . . . . . . . • • . . . . . . . . . . . . • . . . . . • • -1 . . _. . . . > . . s . • ~ . . . . . . . . . • . . ~' • . . . • . . • . • • . . • . . . • . . . . • . . • . • . • • . . . . . . . . . • . . . . . . . . . . . . • . . . . . . . . . . 0 . . . . . . . 0 . . . . . . • . . • . 10 1510 l (b. (S7 4''~ ~ t-,rr 4-17 _k L.0 ~
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SEPARATING PROCESS VARIATION: S YSTEM & SPECIAL CA USES Key Points About Interpreting Process Variation 1. Variation always exists. 2. Any process has both chance (or system) causes and assignable (or special) causes which create variation. 3. The major purpose of SPC is to separate results-system variation from special cause variation-and serve as a basis for action. 4. Eventually, the question for management becomes, how much system variation are we willing to tolerate? B D~ • • • • • • • • B • ~ . • • • • ~~ 0 --------- Is A a special cause? Letting the process "talk B? to us" via control {imits C? allows clear separation D? of causes. You will remember that the 85/15 rule states: 85% of variation is due to System Causes 15% of variation is due to Special Causes Since total measured variation can be viewed as coming from two sources ---this results in two types of problems to be solved-using distinctly different approaches. • • • 4-18 EM •• • • ~
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Type of Problem Definition is Special Cause System (Chronic) Causes Statistical evidence shows that the result is not typical for current process. A unique cause is present and acting on the process. Level of variation is typical, based on the expected variation of all process variables. There is no unique cause currently acting on the process. 85/15: Managing the Improvement Process The SPC System, if actively utilized, can do two things: 1. Give feedback to attendants (and others) so appropriate actions can be taken in a timely manner to maintain the process in a state of control. 2. Give guidance and feedback to system improvement efforts or other changes made to the process, methods or raw materials. It will objec- tively tell you what is working and what is not. Ol The flowchart for improvement is to Stabilize (standardization), Control, Improve. As we attempt to control and improve the process, this se- quence can be accomplished through the steps shown below and on the next page. "Improvement of Quality only comes about by improving the proc- ess. Improvement measures can only be taken after a process is in control." - W. Edwards Deming E4-19 ~ G.~ N
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Current Performance • Improved Control V V D Improvement: Optimize Level 0 lmprovement: Reduced Variability • • 4-20 ©
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Another way to look at this strategy is over a time line with accountabilities for improvements (job positions refer to all departments). S Special Recurring Reduced Optimization (D ® V00 A A a --------------- --------------------- Primary Attendant Supervisors Responsibility Mechanics Shift Coordinators Lab Techs Superintendents Sr.SPC Coordinator C&I Teams Quality Council Systems Improvement Team Project Teams ~ We will look at this in greater detail in the next section under Job Responsibili- ties. There you will see specifically the way in which your job will contribute to this effort. Special System of Level © 4-21 ~ W 0;6
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Sequence of Improvement Process Control Data Product Data Stage 1 System Causes & Special Causes & Control Errors & Measurement error Stage 2 System Causes & Special Causes Stage 3 System Causes I i I • Stage 4 Reduced System Causes Stage 5 Opt€m€ze the Target S ~^ nC"'~~ © 4-22 I I i Qt
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S 85/15 Principle Variation in any measured result comes from two sources - system variation and special cause variation due to special or unique causes. In most processes 85% of the variation comes from the system, 15% from special causes. System variation - that routine variation caused by ran- dom fluctuation of system components. If this variation is to be reduced the process/system needs to be changed. [t is management's responsibility to lead this work. Special Cause Variation -that variation of results caused by atypical performance of the process, material, man or method. Those closest to the process are best equipped to react to and address this variation. Typically 15% of the variation in most processes. S Example: Line 1 OV 16.9 15.0 18.8 The amount of variation in Line 1 OV found during data collection was 16.9 +/- .63. This variation (a spread of 3.8) can be traced to the two sources of variation - system and special causes. • What factors contribute to special cause contribution? • What factors contribute to routine system variation? ~ O C1i ~ E4-23 IN'T CD C.7 C'~
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ANALYZING THE RCB PROCESS: CONTROL VS. CAPABLE Introduction When you go out and gather data on: a parameter from the process you should look at the data from two different, but related, perspectives: For this parameter: 1. To what extent does the process currently operate in a state of control? 2. Is the process capable? That is, when operating in a state of control--can it meet our expectations/specifications? When you are finished analyzing representative data from the process you will reach 2 separate conclusions to describe the current state of that parameters. Unfortunately a process does not maintain any one state-it can and wilf fluctuate from one state to another if proper attention and work is not done on that parameter. In all 4 possible states the RCB Process SPC System and tools have a role. Example: Process data was collected on Daymix Solids over a 5-week period of time. The data showed a mean of 18.55 and standard deviation of .31. The control limits derived from this data were: UCL % 19.14 and LCL of 18.00. Conclusions: 1. Plotting the data of these 5 months against the control limits showed the process out of control 29% of the time. 2. Using data from in-controi time periods only showed a mean of 18.57 and standard deviation of .19. Calculating Cpk against the expectations for Daymix Solids of 18.50 f/- .50 showed a Cpk -.75 Therefore, the "current state" for the Daymix solids parameter is: Out of control Non-capable 4-24 © • •
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• • • Out of Control (Greater than 5%) Capable False Security Possible States of Process Parameter State of Control C Capability Not Disaster Capable D In Control Ideal A Conflict B State Description Remedy A B C 0 Ideal-process in control and Use control charts to keep it and capable. that way. Off-line SPC to improve system variation. Stable process but non-capable. Either change expectations Unrealistic expectations. or system. Use control charts Force unnecessary actions. to drive all process actions. Off-line SPC to reduce system variation. Since no product lost, all appears fine-but process riddled with special causes, unexpected/unexplainable losses. Use control charts to identify special causes so they may be identified and removed. C&I efforts to get at root causes. Since process is both out of control an non-capable, actions usually take place. ® Initially need to control the process using SPC System, eliminate sources of special causes, then either change expectations or continue to work on process eliminating major sources of routine variation. ©
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Current State: RCB Process Parameters Based on the Core Team data analysis the following conclusions were arrived at for each of the parameters in the RCB Process SPC System. (As you review these, think of the current "state" that you would place each of these parameters. Parameter Control Performance (% Time Out of Control) % of blend - class 3 43% % of blend - class 5 57% % of blend - CLR 10% % of blend - menthol 71% OV Exiting dust dryer 56% OV After Sweco 56% Production Dust OV -Exiting Dryer 56% Production Dust OV - After Storage 92% Inlet Burley Dryer Temp. 50% Burley Dust OV - After Burley Dryer 61% Burley Dust OV - After Storage 62% Gas consumption - Link Belt Dryer 15% Reject lbs. from Sweco 15% Production Dust OV: QB - IA Difference 25% Burley Dust OV: QB IA Difference 53% Paraben Level - Finished Product Ammonia Level - Finished Product 19°io PG Level - Slurry 12% Glycerine Level - Slurry 5% 4-26 © r ~ ~~) 0-,-' Capability (Cpk) 1.7 1.5 1.0 .9 0 .44 1.00 1.09 1.38 2.26 2.44 2.16 .78 • •
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Parameter Control Performance Capability (% Time Out of Controll (Cpk) • PG Level - Finished Product 47% 2.40 Glycerine Level - Finished Product 73% 1.84 Oil Usage - Line 1 0% - Oil Usage - Line 2 1% - Oil Usage - Line 3 26% - In Line Slurry Pressure 25% - Nitrate Level - Finished Product 8% 5.50 Day mix solids 48% .75 Refined solids 44% .69 Sheet weights - Line 1 0% .46 Sheet weights - Line 2 ~))) 18% .64 Sheet weights - Line 3 {` 4% .64 ~ Forming Line OV - Line 1 44% .72 Forming Line OV - Line 2 59% .60 Forming Line OV - Line 3 54% .72 Forming Line 1 OV: QB-IA Difference 26% .57 Forming Line 2 OV: QB-lA Difference 21% .56 Forming Line 3 OV: QB-IA Difference 15% .53 Packer OV ~ 56 1.3~f Packer OV: QB-IA Difference 17% .54 Tensile Strength - Line 1 - .87 Tensile Strength - Line 2 - .93 Tensile Strength - Line 3 - .87 RCB Waste - Floor 46% - ~ O ~ RCB Waste - Baghouse 74% - W ~ ~ 4-27 _J ~ O
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Discussion Points: I • In terms of added cost to the operation, which is more important to percentages versus high capability numbers of .9 - 1.7? Z • How do you explain the 43% - 71 %. Control performance on Blend look at-control performance or capability? .p- ~'aV & ~ • Burley Dust OV - after storage. What does it mean to have a 62% out of control versus a 1.00 Cpk index? i. y~ 4;0e -(2 Relative to sheet weights, which line has a more stable process? r v Which has a more consistent process? How do you interpret the data on Line 1. What would be the appropriate actions to take to improve this parameter? What benefits (time, $, quality)? x -,~ 0i V_ ~ • In looking at afl of the parameters related to QB-IA differences, what conclusions can you reach regarding the stability of each of the Quadrabeams? Based on this data, which QB would need calibrating most often? ; ~ r ~ Based on this data-which 5 parameters need the most amount of system improvement work? Based on cost savings opportunity, which of these 5 parameters would it make sense to work on first? ,, ~.. Based on this data-which 5 parameters need the most control work (On-line, + off-line)? , -- - 1~ • q • Based on this data - which parameters most easily meet expectations and present opportunities to optimize cost through adjustments to target levels? ( ~) V ( el-0 ) Overall, which 3 parameters are in the "best shape" today? roj,q : ~ ~i-E.2 4-28 © !
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S • RCB PROCESS EXAMPLES OF CONTROL VS CAPABLE On the following pages, we will look at several examples of data from the process, interpret it, make conclusions and recommendations on the appropriate remedy to improve the RCB process productivity, quality and worklife. As you review this data there are several key questions to keep in mind. Key questions to Review • How would you describe the current state of control? • How would you describe the current process capability? • What percentage of the time are we operating outside expectations? • What are some of the benefits in cost, time, hours, etc. to reducing system variation? • What would you say are some of the major reasons for out of control occurrences? • What are some of the major causes of system variation? © 4-29
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Parameter: OV After the Sweco Control ~ ~ ~ AV - ---- -- - ~ ~ ~ ; ~ ~ 7 F ? t. r ........... 0 1. 0 20 30 40 SAMPLE NUMBER Capability LSL Nomina2 USL so 60 2.5 3.5 4.5 5.5 6.5 7.5 6.5 9.5 % ov 70 Statistics: x = 6.03 s = .72 if process is in control :~ s = .89 currently Expectations: 5% = +/- 2.0 Conclusions: 4-30 WE K S
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Parameter: Daymix Solids • Control • ~ a- o ( © ~ 0 30 68 90 128 150 180 SAMPLE NUMBER LSL Naminal USL 60 I i se 48 Capability 30 >- 1 c3 ~ z ~ w Z) 20 -~I Q W 0: LL 10 ~ E j [ r 17 17.5 18 18.5 i9 19.5 28 % SOLIDS Statistics: X= 18.57 Expectations: s = .19 if process is in control s = .25 currently 18.75 +l- .5 ~7 4 Conclusions: c 47 0 M ~ 4-31 41 114
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Parameter: Finished Product Ammonia 3.1 Control 2.98 i2.86 7 I ~2. 74 L 2.62 ~ 1 2. 5 l 1 1 1 ~ v ~o ~ e f' c`,~~ ~ ~ 1 ~ 1 -~ VT ~~ r~ a I~ ~p r ~ [ [ l l 0 20 48 60 88 100 - SAMPLE t~fUMBER LSL. Namina2 USL 24 20 2.2 2.4 2.6 2.8 3 % AMMOhlIA Statistics: R= 2.91 S = .08 Expectations: 2.3 - 3.3 Conclusions: 3.2 3.4 4-32 ~ "IAZ ~ • • Ctt
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CALCULAT/NG PROCESS CONTROL LlM1TS ` AND PROCESS CAPABILITY FOR RCB PROCESS PARAMETERS tntroduction In this part we will go through the methods involved in determining proc- ess control limits and true process capabilities. To do this we will look at a number of case studies from the RCB process and the actual data gath- ered by the Core Team. Case Study #1: X chart model: Regular method (Line 2 oil usage) Case Study #2: X chart model: Moving range method (QB-IA difference) Case Study #3: C chart model (RCB-f[oor waste) There are 2 other types of control charts that are frequently used but do not exist currently in the RCB Process System. These are X - R charts ~ and p charts. Information is provided on these two applications for future reference. The general model that should be used in any control chart application is shown below. Each of the case studies will step through this model show- ing the specific outputs and decisions that are made. • © 4-33
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General Model for Control Chart Analysis ,,} ~< Wkj Determine need, benefit to charting/ Determine measurement method fre uenc Collect data during ical" conditions for "t q y, , yp controlling the who shouldcollect long enough period parameter and plot data 1 2 3 ~ ~ ~ ~ `- l l l Run chart. Histogram: Ca cu ate e ementary Check data and Check for normal data statistics (7, standard information for (not in case of c chart deviation) "suspicious" data or p chart) 4 6 -~-. Calculate Preliminary Check data for outliers Recalculate control limits (special causes) and elementary statistics trim them out 7 8 9 Recalculate Check data for outliers. Target vs average: control limits If all data is in control, Does process need to be proceed. Otherwise go recentered? Can it? back to Block 6 10 11 12 Final target, UCL, Define existing Calculate Cpk with final ~ LCL established. ecifications or s data from Block 9 p ~ 3 zones established 13 expectations 14 ~ 5 Y ~ ~ 4-34 © • •
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Case Study #1: (X-chart "regular" method): ~ Line 2 Oil usage Data was gathered daily by the A shift oiler on number of inches of oil used daily. (This could have been converted to gallons and tracked in gallons instead of inches). There were 82 data points collected. First, a run chart was plotted and suspicious data identified. Notes in off-standard logs, area log books or on the data log sheets themselves were used to do this. In this case no suspicious data was identified. Run Chart for Line 2 Oil Usage 1 /6/91 - 3/28/91 • 18 16 } J ¢ 14 O P ~ -_-, r I 0 20 40 60 80 100 SAMPLE hlUMBER N 0 V1 Cj ~ 4-35 ~ ~
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A histogram of the daily values was then constructed. The data appeared normal in shape. (Note: Left side appears to have slight "taiP'. Histograms won't be perfect, especially with only 82 data points.) Line 2 Oil Usage Original Data lA ~, 30 ~ 25 k , 6 8 10 12 14 i6 18 INCHES REMOVED DAILY 4-36 © . •
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• Elementary statistics. Since the data appeared to be normal in shape, statistics were then calculated from the sample data: mean: 13.2876 standard deviation: 2.14863 n = 82 minimum: 6.73 maximum: 18 median : 13.5 Preliminary control limits. Using the statistics (R, sd,) from the previous step, "first pass" or preliminary control limits were derived. UCL=X+(3*sd) LCL=X-(3*sd) UCL = 13.2876 + (3 * 2.14863) = 19.7335 LCL = 13.2876 - (3 * 2.14863) = 6.8417 • Checking data for outliers and trimming. Plotting the data against these control limits showed 1 data point beyond the control limits (9th day) which indicates a special cause occurred on that day. Line 2 Oii Usage - First Pass 21 12 N W S 0 z H 'I 4 4 Ni 1~'J. ~ I.!~k ~, 9 .r. ... i i saiia r -~ 0 20 48 60 88 100 ` SAMPLE NUMBER H
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Trim and recalculate elementary statistics. The 9th data point was removed and the mean and standard deviation were recalculated. 2nd pass X = 13.3683 s=2.0331 Recalculate control limits. Using the 2nd pass statistics, new control limits were then calculated: UCL 13.3683 + (3 *2.0331 ) = 19.4676 LCL 13.3683 - (3 >k 2.0331) = 7.269 Plotting the remaining data against these limits showed a data point below the lower control limit. Line 2 Oil Usage - Second Pass 21 i .--~- ;--. -T-- . 18 ~}zi J} 1 a Q W :> I~f l. I l~~ Ifi( \t i fl it;Yii ~ ~ 12 l1.1 ! ~{ 1 .` t 1 -~. S p L~ ~ Z 0 ~ ,T.269 20 48 68 88 180 SAMPLE NUMBER S 4-38 Eff
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Trim and recalculate elementary statistics. This outlying data point was removed and for the "3rd pass", the sample statistics were: • S Line 2 Oil Usage - Third and Final Pass , I, : _ , 8 20 40 68 80 SAMPLE NUMBER 3rd pass X= 13.4447 s = 1.9251 Recalculate control limits. Using the 3rd pass statistics, new control limits were then calculated: UCL 13.4447 + (3* 1.9251) = 19.22 LCL 13.4447 - (3 * 1.9251) = 7.67 Plotting the remaining data against these limits showed there were no outliers - all data was within the control limits. .3. .i. -i. -a, W4-39 Ct~ ~
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The proposed control chart can now be set up with the center line at 13.44, UCL at 19.22, LCL at 7.67 and the zones evenly spaced between the limits. 19.22 UCL C 17.28 - - - - - - - - - - B 15.36 - - - - - - - - - - - - - - - A 13.44 x A 11.52 B - - - - - - - - - - - - - - - 9.60 - - - - - - - - - - - - - - - C 7.67 LCL Process capability: The final trimmed data histogram appeared to be normal in shape, therefore we can use the final R(13.44) and standard deviation (1.92) for our Cpk calculations. Line 2 Oil Usage Trimmed 24 r 8 F- 4 I- r ~ J er ~ 8.5 10.5 12.5 14.5 16.5 18.5 INCHES REMOVED DAILY 4-40 WE • • •
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• Suppose the expectation/specification for oil usage was that 13 inches f/- 5 inches would be consumed per day if the process was operating typically. Cpk calculations: X= 13.44 S=1.92 Z usL: 18 - 13.44 1.92 = 2.38 Z LSL: 1 44 - 1.92 = 2.83 Cpk = 2M 3 = .79 Moving Range Method for X charts -When to Use and Procedure S In the first case study we looked at, the pattern of variation we saw in the original run chart was fairly random and that is why the "traditional stan- dard deviation method" was used to derive control limits. S Sometimes you may not see such a random pattern, but rather see a pattern that is known as "batching". That is, the process appears to oper- ate at a given level for a period of time and then jumps to another level and begins to fluctuate around that level. © ~ ~ ~.' ~ ~ 4-41 Gt~ G't
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When we see this pattern, the moving range method to derive control limits needs to be used. The model is very similar to the flow chart de- scribed earlier. The biggest difference is in using the moving range (differ- ence in value between two successive data points) to get a more accurate estimate of standard deviation. If we did not use this technique, we would end up with estimated control limits that would be too wide to fit our process. We will use the procedure to calculate control limits: Procedure for Moving Range Method to Calculate Control Limits for X Chart Step 1. Run chart. Check for suspicious data 2. Histogram. Check for normality 3. Calculate moving ranges for all data points 4. Calculate average moving range (9R) 5. Calculate upper control limit for moving ranges UCL (M ranges) = D4* MR 6. Check list of moving ranges to see if any exceed the UCL (m ranges). If any do, remove the moving range and the corresponding raw data point. 7. Continue steps 3-7 until all moving ranges fall within limits. 8. Calculate Xof remaining data points 9. Calculate control limits for raw data using standard deviation estimated by moving range. UCL = X+ (E2 * MR) LCL = X- (E2 * MR) E2 = 2.66 10. Check raw data to insure it falls within the control limits. If it does not, eliminate the data point and go back through steps 3-9 until all data "settles down" -- falls within control limits. 4-42 EM • •
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• • Case Study #2: (Moving Range Method for X charts) : QB1A OV Difference - Line 3 The difference between Quadrabeam OV reading and the OV reading determined by the Infralyzer (IA) is established as a parameter to deter- mine when the QB needs calibration. The concept is that when this pa- rameter goes out of control it is giving the signal that the QB has drifted and needs calibration. Adoption of this control chart should dictate when the meter needs calibration and the degree of success of the recalibration. Only through this control scheme can we insure that the 13.8 reading that we saw today represents the same RCB product that we saw when we obtained a 13.8 reading four days ago. A 13.8 is a 13.8 is a 13.8! To gather data, we took matched OV readings from the QB and IA three times per shift. For each matched pair we subtracted QB-IA. The differ- ence is the raw data parameter that we are tracking. This data was collected for 4 weeks. Step 1: The run chart was plotted and revealed no suspicious data Run Chart for Line 3 QB - IA Difference 7/9 - 8/6/91 r-T-r-r-I 2.1 F , i m Or -1.9I- -3. 9 t 0 50 100 150 200 250 300 SAMPLE NUMBER ©
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Step 2: The histogram was produced and showed that these differences do form a normal pattern of variation centered roughly around 0. Frequency Histogram Line 3 QB - IA Difference Original Data 1ee ~- s0(- 20 F -3.9 -1.9 0.1 2.1 4.1 QB - IA Step 3 Calculate moving ranges for the 261 data points... • • Data Movi ng Ra nge -.12 -.29 .17 1.82 2.11 _ .53 1.29 1.11 .58 .27 .84 2.03 1.76 -.70 2.73 51 1 21 . . ~ .78 .27 0 CfT 0 4-44 W1
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Step 4 S MR=.997 Step 5 UCLR,,ar,9e=D4*MR = (3.269) (.997) = 3.259 Step 6 Moving Range Chart for Line 3 QB - IA Difference 3 i ! " ~ ~ ~ " ~.. . ~...:~.. .~.... ~. ,.~i F ~ 0 5e 1@8 156 288 258 300 SAMPLE NUMBER 1 point exceeds control limit for moving ranges. Moving range and raw data point (QB-IA difference value) removed. N C? Cd[ C.3 09 ~ 2. .s. m 4-45 LrI on
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Step 7 2nd pass MR=.980 UCL= (3.269) (.98) = 3.20 m v z a ~ ~ z N ~ ~ E Moving Range Chart for Line 3 QB - IA ~ ~ I 'I I 1 ! / ~ ~ I ~: e } S }~ } !. ! ~F It .ii 1 8 58 lee 150 208 SAMPLE NUMBER Afl moving ranges in control Step 8 x (raw data) _ -.178 Step 9 UCL = X+ E2* MR = -.178 + (2.66) (.980) = 2.43 LCL = X- E2* MR = -.178 - (2.66) (.980) = -2.78 4-46 © 250 300 • •
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Step 10 • X Chart for Line 3 QB - IA Difference 25@ -,-r, 3@0 e ~~,-.-r.----,-, 50 100 1.50 2@@ SAMPLE NUMBER Looking through the 260 remaining QB-IA differences shows 5 data points exceeding these limits. Remove these values and recalculate steps 3-10 r P • X=-.165 . MF-t =.943 • UCL nnR = (3.269) (.943) = 3.08 1 moving range exceeds this value. Remove it and recalculate. Moving Range Chart for Line 3 QB - tA Difference ~ 0 z a ~ a z M ~ 0 E 1@@ 15@ Z@@ 25@ 388 0 56 0 SAMPLE NUMBER W ~ 4-47 ~ C7~ 0
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4th aa$j • R=-.157 • R =.926 UCL MR = (3.269) (.926) = 3.03 Moving Range Chart for Line 3 QB - IA Difference 0 58 i08 15 8 200 SAMPLE NUMBER AII moving ranges in control • Raw values: UCL = -.157 + (2.66) (.926) = 2.31 LCL = -.157 - (2.66) (.926) _ - 2.62 250 308 X Chart for Line 3 QB - IA Difference Fourth and Final Pass 8 50 180 158 200 258 380 SAMPLE NUMBER 4-48 © • •
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All raw data falls within these control limits. That is, the variation that we should expect to see whenever we get Line 3 QB reading and a matching ~ IA OV value and subtract them is a difference from 2.31 to -2.62. We can now set up a chart to monitor this parameter and initiate the appropri- ate control moves (including calibration) when the chart signals an atypical process condition. Line 3(QB - IA) Difference in OV Readings 2.31 1.49 .666 -.156 -.978 -1.80 -2.62 C A - - - - - - - - - - - - - - - A - - - - - - - - - - - - - - - B - - - - - - - - - - - - - - - C UCL X LCL The final histogram showing the variation in difference values that we should expect to see if the Line 3 QB meter is functioning typically. Line 3 QB - tA Difference Trimmed Data 8e 60 20 r r-r, -. . , ~ r r i I -2.6 -1.6 -0.6 0.4 1.4 2.4 DIFFERENCE ~ 4-49 ~ cn 2V
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c Charts: When to Use, Model Introduction Sometimes when you look at a histogram of data it does not form the typical normal pattern but takes on the skewed shape that we looked at in an earlier section. Normal Skewed (right) In applications like these, it is inappropriate to use an x control chart to monitor a parameter. Instead, the c chart must be used. (Doesn't matter if it is skewed left or skewed right). You are likely to see this where there is an artificial barrier that prevents the data from "spreading out" in both directions or where you are dealing with discrete or counting type data or in cases where there is a large opportunity for something to occur but you don't see it occur that much. 4-50 Kff Zti? 0 Ul ~ c7~ CD M CJ • • •
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• • J When To Use c Charts • Histogram shows skewed pattern- to the left or right • Dealing with counting - type data (discrete) and... • Opportunity for "occurrence" is large, but actual occurrences" are low • Examples: Process stage downtime, number of accidents, pounds of waste,number of hogsheads refed/day, number of damaged hogsheads/boxes Procedure For c Charts 1. Gather data based on a constant "window of time". Plot run chart. Remove suspicious data. 2. Histogram. Check to insure it is skewed in shape. 3. Calculate average (Z-) 4. Calculate control limits UCL - c+ 3.=c LCL= c-3.F- 5. Check data for "outliers" - any points beyond the control limits 6. Remove outliers and repeat steps 3-5 until all data falls within control 7. Set up the control chart with the center line at the median and control limits at the final ones from step 6 ~ 4-51 ~ ~ ~
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Case Study #3 (c Chart): RCB Floor Wastes Scrap materials that are swept from the floor in Bay 4 and Packing were weighed up once per shift by the cutter helper. The data was collected over several weeks. The parameter that we are interested in tracking is the total pounds per shift. Step 1 Data (total pounds per shift) was gathered over a 5 week period of time and plotted on a run chart. Run Chart for RCB Floor Wastes , es r . 2• c® 6® 80 s90 SAriPLE NUf18ER Step 2 The histogram for the shift total waste values definitely showed the skewed pattern. In this case, skewed to the right. RCB Floor Waste e® 40 s. ® 6 20 40 60 80 100 LHS OF WQS7E 4-52 ~
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• Step 3 From the data, the calculated average pounds per shift was ~=23.1 Step 4 UCL=c+ 3.j~ = 23.1 +3~23. = 37.5 LCL = c- 3 fe = 23.1 --~(23.1) =8.7 • Step 5 From the graph, you can see 7 points that fall outside the upper control limit. We assume that in each of these cases a special cause was present in the process to produce this result. Since we are attempting to describe system variation only with the control limits, these 7 points need to be removed. C Chart for RCB Floor Waste 1.ee f- se[- 26 ~- ~]~ J 1~ . ~ - Mg 4 ~' ~' A I W\IIWV V Q Y 0 20 4@ Be SAMPLE NUMBER I se n 186 O Ut w ~ 0 11 ~ 4-53 ~ ~
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Step 6 Remove the 7 data points and recalculate c and the control limits Second pass c = 20.4 UCL=20.4+3 20.4=33.9 LCL=20.4-3 20.4=6.8 C Chart for RCB FLoor Waste 20 F eL ~ JI~ ~ i "i4 I ~ ~ e 20 48 6e ee GpMP! F N/ IMRFP There are now 3 points beyond the current limits. These need to be eliminated and a new c calculated. 3rd ass c = 19.8 UCL=19.8+3 19.8=33.1 LCL=19.8-3. 19.8=6.5 C Chart for RCB Floor Waste soe 6e ~ ¢ 60 ~ a ~ ~t 40 m ~ ~..-. ------------------ ~ 1 z® f~V eL e 20 40 60 80 All data points now fall within the control limits. Now a control chart can be set up to track, control, and improve the performance of this parameter. 4-54 K~E • • •
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Step 7 The median of the final data set from step 6 is 19. S 33.1 19 6.5 UCL c LCL Note: With this type of control chart only two of the control rules can be used: single point beyond a control limit, 7 points on the same side of the center [ine.I. ~~---~ ~ ~ ~ 4-55 ~ Gt~
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OTHER TYPES OF CONTROL CHARTS (p, X-R) There are two other types of control charts which are not presently in the RCB SPC System. They are provided here for future reference. Any indi- vidual or team that identifies the opportunity to apply these tools should consult the SPC Analyst for support. P CHART When to use: • Used where you are interested in monitoring and detecting shifts in percentages levels and the base fluctuates. • Example: Month HH Produced P HH Refed Q R 1 3015 241 .079 2 2975 182 .061 3 220 3 196 .060 , ~ - °G7 • Only use the same two control rules as c chart to interpret Procedure: 1. For each data point gather n (sample size) and np (number of observed). In the example n would be hogsheads produced for the month, np would be number of hogsheads refed. 2. Calculate p,-ff + - sum of nR av Iues sum of n values ,~- average number of samples over all of the data 3. Control limits: UCL: ~+ 3 R(1.00 -p~ ,In L(CL: ~5- 3 -- ~ c~~ ~_ , -~ , 4.Trim and recalculate steps 2-3 until data settles down 4-56 © Q~~o O`00 ~ ` 7 ' 0~ r ~ • • I ;~C/j S
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X-RChart 0 When to use: • Used where you want to track average level and range of variation at a point in time. • Need to gather data in "subgroup" form. • Example: Suppose we wanted to track sheet weights on the forming line by taking 3 samples across the sheet every hour. Sheet Weights Hour Weig hts _ _(SubgroM Front Edge Middle Back Edae X g 7:00 11.8 10.9 11.4 11.7 .9 8:00 12.1 11.7 11.9 11.90 ,4 9:00 11.1 10.4 11.5 11.00 1,1 10:00 12.0 11.0 12.3 11.77 1.3 ! 11:00 11.9 10.0 11.7 11.20 1,9 • You would only use this chart if you were interested in and could take control moves on both the X as well as the R. • You would have 2 charts to monitor an X portion and R portion. UCL X LCL X UCL R X ~ 0 ~ ~ LCL Go ~ ~ 4-57 ~g ~ C
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• Control Rules: X: Use all 4 rules to interpret each data point R: Use only the two rules that are used on the c chart Procedure For Developing X-R Chart Control Limits 1. Gather data, organized by subgroup. Plot on run chart. 2. Calculate average and range for each subgroup. 3.Checkto see if subgroup averages are normal. (Histogram) 4. Calculate average range (R) 5. Derive UCL, LCL for range. Check_data for control. Delete any data outside control limits. RUCL = D4 R, RLCL = D3 R. Repeat steps 3 and 4 if any points were eliminated. Subgroup Size D3 D4 2 - 3.267 3 - 2.574 4 - 2.282 5 - 2.114 6 - 2.004 7 .076 1.924 8 .136 1.864 6. Calculate Grand Mean (X) of data remaining after range trimming. Calculate standard deviation (sX) of subgroup averages. 7. Derive UCL, LCL for X. UCL= X+3sX LCL = 7-3sX 8. Check data for control. Delete any data outside control limits. Repeat steps 5,6, and 7 if necessary. Continue this until data "settles down." (All data within control limits.) 9. Determine if X is compatible with desired target. If not-need to reconcile. 10. Set up control chart for process control. R chart: Solid line at X, solid lines at UCLx, LCLX R chart: Solid line at R, solid lines at UCLR, LCLR 4-58 WE • • •
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Control Charts for Diagnostic Work 40 The most frequent use of control charts will be for on-fine SPC efforts as a part of the RCB SPC System or with the SPC System created in mainte- nance or QA through their Departmental Implementation efforts. How- ever, control charts can also be a very effective tool to be used by indi- viduals or teams in their off-line SPC efforts. In cases where problem- solving work has been done to change/modify equipment, methods or materials and you are trying to find out if the implemented change has truly had a significant effect. It allows us to go beyond opinion or feelings but rather use facts and data to objectively assess process improvement efforts. • 7~1 O C1t C.~ ~ 4-59 ~ ~ r~
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Procedure Procedure to use control chart technique to check for significant change 1.Collect data (using appropriate technique - x, c, p, X-R) before change is made or on one of the two "conditions" you are comparing. 2.Derive control limits using the standard procedure. 3.Collect data for after the change is made or for the other "condition" you are comparing. 4.PIot the data from step 3 on the control chart already derived in step 2. Interpret for control. (using appropriate rules) 5.lnterpret Results. If the second condition plots out of control, then there is a significant difference between the two alternatives. If it falls in a state of statistical control, then there is no difference between the alternatives. yw-. ~- ~J a:uG-f ~-- 4-60 Eff • • •
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CONTROLLING TO TARGET: 40 One of the benefits of a TQI SPC System such as the RCB Process System is that it puts the tools and methods in the hands of attendants, supervisors and others to consistently control a parameter around a target. The target and the way in which it is controlled is the same regardless of shift, regardless of what attendant is operating the process that day or who is supervising that process stage. As we saw with the concept of the Loss Function, the big advantage once everyone is operat- ing within the system is that you can reduce variation and then set the target to optimize cost and quality of the process and product. Example: Forming Line 2 OV Shown below is a histogram of OV readings from Line 2 gathered every 15 minutes over a period of several days. From the histogram, it appears the data contains several populations. (Doesn't appear to be single peaked but several peaks). Frequency Histogram Forming Line 2 OV • 88 68 20 I LJ 14 15 16 17 18 % OV Looking at a run chart of this time period explains why there are several populations. Although during this time period the fine was "running to one ~ target" (there were no instructions from the cutter man to adjust fine O target), without the tools of SPG and everyone using the same system to ~ react to data - the result is many populations of product created. GO ~ 4-61 ~ ~ ~
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Forming Line 2 OV iT F r , t 14r 0 50 1.. 15® 2.0 250 300 35. SAMPLE ltUKBER Using the same scale and amount of variation - look what happens to overall OV variation if the tools of SPC were used to react to OV data. Frequency Histogram Forming Line 2 OV Controlled to Target ~ € 1 , ,~\\ ! I 14 15 16 17 1a i ov With this improved level of variation: • The target can be o ptimized to a g reater extent • True process capa bilities can be d etermined • The cost of low OV results (dryin g costs) can be reduced O • The risk of high OV product failu re s can be reduced • The risk of z-test fa ilures can be re duced C•3 4-62 EM •
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Example 2: Nitrates after washing 40 Looking at the histogram shows wide variation Frequency Histogram Nitrates After Washing 6 /25 - 8/10/90 24 F 4 20 r 16r 8{- 4r e 0.14 8.24 0.34 0.44 0.64 X NITRATES • Run Chart for Nitrates After Washing 6/25 - 8/10/91 0.44C I• jI•I ~~ t ~G~.I1~1Tr111~~ I j ~1 ~ 11.34 [ ~ €( ~j1~ . 11 I(I - ~~ 1 ~ ' ~ kt~if% i 0.24 F , lt ri • • j ~i 1tfi 3 C ~ IF 0.14` 26 e 0 S2 78 SAMPLE NUMHER 104 -I 130 LV c ~ ~ elm " © Looking at the run chart reveals distinctly different operating levels. t av 4-63 ~ ~ ~ O~
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