Instructors Manual for Setting Up Simulations
Contents
1. LSL Average y LCL 10 378 1 Subgroup 20 C1 0 70477 u Mal INPUT SETTINGS A Poller Speed RS 100 feet sec Standard 4 Die Temp DT 275 deg F Deviation ty FF t y Viscosity V 2 7 coeff Soy Head Speed HS 90 rpm T E 4 0 0 1 Subgroup 20 Tutorials 9 The equation used to generate Sheeting Thickness 1s Thickness 64 93479 0 10766 RS 0 001058 RS 2 0 48434 DT 0 001058 DT 2 0 001084 RS DT 5 0 V 0 0075 HS Err Besides the 4 main effects there are quadratic effects for RS and DT along with an interaction between them The model includes only a single source of variation Err Other Error Unit to unit standard deviation of 0 3 pounds This simulation cannot be used to illustrate robust design Changing targets does not affect the variation The goal is to adjust the variables to get the average on target There are numerous combinations of the four inputs that will center the process Tutorials 10 1 3 Sonic Sealer This simulation involves optimizing a sonic sealing process The model involved includes a three way interaction making it difficult to model It takes the right combination of the different inputs to get the process above the lower spec limit A good final exam It cannot be used to illustrate robust design The output of interest is tensile strength A small plastic disk is being sealed inside a hollow plastic tube Tensile strength i2. 200 108 56 1 2 0 17 Temperature N Hot Bar 175 1 4 OF 14 17 2 0 150 i 0 5 0 75 1 0 Dwell Time sec Tutorials 6 This leads to the following strategy Adjust HB and DT to minimize variation Adjust P and MT to get on target Set targets of other 4 inputs to minimize cost Ex turn cooling air off Adjusting material temperature requires constructing a pre heating chamber for the material It will be fixed at 75 F since pressure can be used to adjust the average The optimal tagets for the other inputs are HB Hot Bar 200 F DT Dwell Time 0 55 sec P Pressure 52 4 lbs The improved performance is shown below The process is now averaging around 0 05 defective with a Cpk value of 1 874 Seal Strength Ibs Average 26 09 Standard Deviation 1 0673 27 809 UCL Cp 1 874 Cpk 1 846 LSL USL Average LCL 24 372 1 Subgroup 20 2 4526 we INPUT SETTINGS Hot Bar HB 200 deg F Standard Cold Bar CB 100 deg F Deviation Dwell Time DT 0 55 sec x a Pressure P 52 4 Ibs Room Temp RT 75 deg F Cooling Air CA 30 lbs ool4 Thickness TH 14 5 mils 1 Subgroup 20 Matl Temp MT 75 deg F Out of Spec Seals Percent Defective 0 05 aie INPUT SETTINGS Hot Ba HB 200 deg F Cold Ba CB 100 deg F Percent Dwell Tim DT 0 55 sec Defective Pressur P 52 4 lbs Room Tem
3. Lead Gap LG 72 mils Standard Trail Gap TG 52 mils Deviation VY Wall Thick W 85 mils Feed Rate F 22 in min Offset O 85 mils Mandrel Dia MD 62 mils 0 04 Roll Radius R 350 mils ar Subgroup 20 Operato Op Second Shift There is one output the outside diameter of the finished mandrel The equation is Outside Diameter 2 5 466 3 5 19 LG 1 05 TG 4 15 W 0 051424 LG W Err 1000 Only three of the inputs are in this equation LG TG and W There is a single 2 way interaction between LG and W There are no quadratic effects The model includes multiple sources of variation LG Lead Gap Trial to trial standard deviation of 1 0 mils TG Trail Gap Trial to trial standard deviation of 1 0 mils W Wall Thickness Unit to unit standard deviation of 2 0 mils plus Trial to trial standard deviation of 4 5 mils Err Other Error Unit to unit standard deviation of 1 0 mils The setup parameters like trail and lead gaps only vary from trial to trial so may be the cause on instability Changing targets affects the variation so robust design can be explored The goal is to reduce the variation both unstable and short term Running a screening experiment on this example will generally result in identifying the 3 key inputs and one interaction group The inclusion of center points will identify no curvature The correct interaction in the group can generally be identified based
4. O 0 O 0 100 1 1 RT Room Temp deg F 5 75 Fo 80 0 0 O 0 O 0 O 0 100 1 1 CA Cooling Air lbs 5 30 won 30 0 0 0 0 0 0 O 0 100 1 1 TH Thickness mils 5 14 5 14 15 MOGE M O 0 M O 0 O 0 100 1 1 MT Matl Temp deg F 5 75 Fo 110 0 0 O 0 0 0 O 0 100 1 1 Err Other Error lbs 5 o o o 0 8 0 0 0 2 0 8 100 0 0 It starts with the number of input variables Then there are 14 items which must be entered for each input variable Name Type Description Symbol Text String Symbol used to represent variable in equation for output Must be unique consist of only letter digits and underscores and cannot begin with a digit Name Text String More descriptive name for the variable for use on the Control Panel and windows displaying the results of the simulation Units Text String Units of measure used for specifying current minimum and maximum targets Precision Number Number used to specify precision for displaying numbers A positive integer and zero indicates the number of digits after the decimal number to report A negative integer represents the number of significant digits to report Generally a value of 5 works well Initial Target Text String The initial value to target the input at It is Containing frequently the current recommended setting used for Constant process or the midpoint between the minimu
5. Speed S 48 2 rpm Back Flow B 0 05 ml All four inputs are in the equation The equation consists of two interaction B S and the more complicated R L B This second interaction dominates leading to R L S R R S R L and S L all testing significant The model includes multiple sources of variation R L S B Radius Unit to Unit Standard deviation of 0 00005 inches plus Trial to trial standard deviation of 0 000075 inches Stoke Length Unit to Unit Standard deviation of 0 00167 inches plus Trial to trial standard deviation of 0 0025 inches Motor Speed Unit to unit standard deviation of 0 167 rpm Trial to trial standard deviation of 0 25 rpm Back Flow Unit to unit standard deviation of 0 005 ml stroke plus Trial to trial standard deviation of 0 0075 ml stroke Analyzing the log of the standard deviation identifies R L S and R all affect the variation Plots of the R L and S effect on the average and standard deviation can be used to identify the optimal settings The optimization routines some DOE packages can also be used Another alternative is to bring the design in VarTran for optimization The optimal settings are R L S Piston Radius 0 17 inches Stroke Length 0 4 inches Motor Speed 18rpm 19 Flow Rate ml min Average 9 7822 Standard Deviation 0 14169 10 161 t UCL 4 Average y yt LCL 9 4103 4 1 Subgroup 2
6. as 2 A Log B C Functions Of form function paraml param2 The following functions are supported Log Logl0 Exponential SquareRoot Sine Cosine Tangent ArcSine ArcCosine ArcTangent HyperbolicSine HyperbolicCosine HyperbolicTangent Gamma LogGamma Beta LogBeta AbsoluteValue Minimum Maximum NormalDistribution InverseNormalDistribution pi and e Most functions require one parameter Exceptions are Beta LogBeta Minimum and Maximum which require 2 and pi and e which require zero Squared brackets must be used with functions Symbol Can enter the symbol of any input variable or output variable For output variables circular or recursive references are not allowed Category Input Variables Of form Symbol Symbol Examples are SS Average Y Standard Deviation and O2 Cpk Properties are used to specify characteristics of output variable and categories of category input variables Rounded Parentheses and are used to control the order that operations are performed Without parentheses the operations are performed in the order determined by the operator precedence and association rules If in doubt about the order the operations will be performed use parenthesis A constant expression is an expression which does not reference any symbols or variables Warning Be sure to use rounded parenthesis for order of operation square brackets for function calls and curved brackets for category i
7. of the interaction plots will suggest 1 or 2 combinations of the inputs producing the optimal performance If two try them both Tutorials 12 Running a response surface study will correctly pick up the 3 key inputs and sort out interactions but will still not include the three way interaction unless the students identified the highly interactive nature of the inputs and included it using a d optimal design Because there are no quadratic effects the optimal must be a corner point The setting that works is G H A Gap 12 mils HD Horn Downtime 150 msec ST Solution Temp 60 F Tensile Strength lbs Average 21 167 Standard Deviation 0 53688 22 032 UCL N t Average Fk OR t M LCL 20 303 1 Subgroup 20 1 2337 7 UCL Standard Deviation 4 0 0 1 Subgroup 20 Tutorials Cp Cpk 0 7249 LS i lll 20 INPUT SETTINGS H A Gap Q 12 mils Guage Force GF 7 lbs Peak Force PF 120 lbs H Downtime HD 150 msec Bag Temp BT 65 deg F Solut Temp ST 60 deg F 13 1 4 Flo Former This simulation involves optimizing a flo former process The model involves 8 candidate input variables which reduce to three key inputs There are multiple sources of variation and interactions allowing for robust design The full set of tools including screening and response surface studies robust design and
8. selectively tightening tolerances all apply to this simulation This example is borrowed from Tom Barker s course on robust design The flo former process is used to crush an extruded metal tube called a mandrel to the right size The output of interest is the finished outside diameter The target is 2 5 inches 0 005 The mandrel is originally extruded slightly larger than needed and then crushed The inputs along with their current settings are shown below LG Lead Gap 72 mils TG Trail Gap 52 mils W Wall Thickness 85 mils F Feed Rate 22 in min O Offset 85 mils MD Mandrel Diameter 62 mils R Roll Radius 350 mils Op Operator Second Shift Mandrel diameter and wall thickness are material properties The remaining parameters are mostly machine settings Many are setup related The exception is the shift operator The mandrel is spun between several rollers that reduce the diameter A diagram of the machine is given below Roll Radius Wall Thickness Trail Gap Lead Gap Mandrel Diameter Offset Tutorials 14 A capability study of the current at the current settings is shown below The process is unstable with excessive short term variation Outside Diameter in Average 2 501 Standard Deviation 0 0014401 290617 Cp 1 157 y Cpk 0 9363 t UCL y Average _ 2 4965 14 1 Subgroup 20 IE 0 0033092 2 505 ie INPUT SETTINGS
9. 0 0 32558 UCL Standard Deviation 4 0 0 H 1 Subgroup 20 Cp 2 353 Cpk 1 84 LSL USL 9 0 11 0 INPUT SETTINGS Radius of Piston R 0 17 in Stroke Length L O 4in Motor Speed S 18 rpm Back Flow B 0 05 ml Further improvements can only be obtained by tightening tolerances Taking the equation into VarTran identifies motor speed as the primary cause of the variation Cutting its tolerance by 50 improves the performance further as shown below Flow Rate ml min Average 9 8804 Standard Deviation 0 10934 10 157 y UCL Average t Bed y 9 6021 1 Subgroup 20 0 25125 UCL Standard Deviation j Pal 0 0 1 Subgroup 20 20 Cp 3 049 Cpk 2 684 LSL USL C_ 9 0 11 0 INPUT SETTINGS Radius of Piston R 0 17 in Stroke Length L 0 4 in Motor Speed S 18 rpm 50 Back Flow B 0 05 mi 2 Structure of Simulation Files The simulations for version 2 0 of the program Simulator are set up using text files that can be easily edited and added or removed When starting Simulator checks the directory the program resides in for text files 1 e having the extension txt It reads each text file to see if it contains a simulation and displays the simulations found on the Startup dialog box Each simulation file contains the n
10. Instructor s Guide Simulator Version 2 0 Dr Wayne A Taylor Copyright 2004 Taylor Enterprises Inc All Rights Reserved Taylor Enterprises Inc 5510 Fairmont Road Suite A Libertyville IL 60048 847 367 1032 Fax 847 367 1037 E mail info variation com Web www variation com Table of Contents Chapter 1 Answers to Exercises 4 1 1 Heat Sealer 4 1 2 Sheeting Extruder 9 1 3 Sonic Sealer 11 1 4 Flo Former 14 1 5 Pump 18 Chapter 2 Structure of Simulation Files 21 2 1 File Structure 21 2 2 Header Section 22 2 3 Input Variables Section 23 2 4 Category Input Variables Section 26 2 5 Output Variables Section 27 2 6 Expressions 29 Answers to Exercises Program Simulator comes with 5 simulations Chapter 1 describes these simulations and how to optimize the performance of each simulation The files associated with these simulations are automatically installed in the same directory as the software These files can be modified and new files added as described in Chapter 2 1 1 Heat Sealer This simulation involves the development of a heat sealing process to form the top seal of a plastic bag This is a good simulation to let the students attempt by trial and error Only 4 of the 8 inputs are significant so it provides a good example for using a screening experiment It also illustrates the importance of robust design It is described in the book Optimization and Variation Reduction in Quality by Wayne A Taylor an
11. RT 75 deg F Cooling Ai CA 30 lbs UCL Thicknes TH 14 5 mils o4 PPT NT TN O SO OO S E EEE HS Matl Tem MT 75 deg F 1 Subgroup 20 The operator should be restricted to using pressure to adjust the machine if it shifts off target Adjusting DT or HB with increase the variation Tutorials Further improvements must be made by tightening tolerances Tightening the tolerance of dwell time by 50 produces the following results Now Six Sigma quality has been achieved Seal Strength lbs Average 26 02 Standard Deviation 0 81798 28 049 Cp 2 445 Cpk 2 437 4 F UCL LSL USL Average _ t LCL 23 921 1 Subgroup 20 1 8796 20 0 32 0 ae INPUT SETTINGS Hot Bar HB 200 deg F Standard lt Cold Bar CB 100 deg F Deviation 4 Dwell Time DT 0 55 sec 50 WW a UP Pressure P 52 4 lbs a t Room Temp RT 75 deg F Cooling Air CA 30 lbs 00 Thickness TH 14 5 mils p Subgroup 20 Matl Temp MT 75 deg F Out of Spec Seals Percent Defective 0 UE INPUT SETTINGS Hot Ba HB 200 deg F Cold Ba CB 100 deg F Percent Dwell Tim DT 0 55 sec 50 Defective Pressur P 52 4 lbs Room Tem RT 75 deg F Cooling Ai CA 30 Ibs Thicknes TH 14 5 mils Matl Tem MT 75 deg F 0 tt tt tt UL 1 Subgroup 20 For the student to determine which tolerance to tighten they need to perform a tolerance anal
12. aking the equation into VarTran identifies LG as the primary cause of the variation Cutting its tolerance by 50 improves the performance further as shown below Tutorials 16 Outside Diameter in Average 2 5003 Standard Deviation 0 00096178 2 5022 m 7 UCL te ty is Average D abe LCL 2 4976 Subgroup 20 0 0022101 UCL Standard Deviation 4 0 0 Subgroup 20 Tutorials Cp 1 738 Cpk 1 636 INPUT SETTINGS Lead Gap LG 80 mils Trail Gap TG 46 mils 50 Wall Thick W 85 mils Feed Rate F 22 in min Offset O 85 mils Mandrel Dia MD 62 mils Roll Radius R 350 mils Operato Op Second Shift 17 This simulation applies to the design of a product rather than a process It only involves 4 inputs so is best handled using a response surface study It provides a great example relative to robust design and tightening tolerances Design offers the first and best opportunity for reducing variation To illustrate the strategies and tools required consider the task of designing a new pump Suppose that the pump must be capable of delivering solution at a constant rate of 10 ml min Customer usage requires that the flow rate remain between 9 and 11 ml min The first step is to develop a design concept Taguchi calls this the system design Suppose we decide to use a piston to push the solution This concept require
13. ame of the simulation a graphic and then a description of the input and output variables The file for the heat sealer simulation is shown below Simulator 2 0 sealer bmp sealer rtf 1 Heat Sealer 9 HB Hot Bar deg F 5 190 WISO T200 0 0 Nas O20 POLO MOO Te CB Cold Bar deg F 5 100 gO A ee TO OT OO TOOT TL00 1 1 DT Dwell Time sec 5 O28 ROLE FLO TOLON TOOT 80 8 NOVO POO DL RE Pressure wibs 8 MIO SO ESOT PEO TO MOTOT FOO LOOT TA RT Room Temp deg BY 5 75 w70 go O20 O20 OVO VOLO 100 I TI CA Cooling Air lbs ao ad wae son 0 0 VO MOROT SOLO TIOTI TH Thickness ind de 5 14 5 14 mo MELON MO OM MELON LOGE SL MT Matl Temp deg EF 5 75 wo WILO 0 0 OO SOON MOON SMO A A Err Other Error lbs Be RON oe wa O8 TOOT KROS ZM n MCE LG OMR CES EG 0 2 SS Seal Strength TEDS 59 403 5 3 6 HB 0 008 HB 2 280 0 DT 80 0 DT 2 0 96 HB DT 0 04 P 0 05 MT Err L TNT T320 SOON 26 0 5 5 OS Out of Spec Seals 5 203 5 346 HB 0 008 HB 2 4 280 0 DT 804 0 DI 2 O 96 HB DT 4 0 04 0 05 MT Err i oO ds 32 0 w20 0 26 0 16 100 The file contains text strings and numbers Text strings start and end with a quotation mark Sometimes the text string will contain an expression as described in the last section Numbers are of the form XX XXe XX The exponent decimal point and si
14. bs 3 403 5 3 6 HB 0 008 HB 2 280 0 DT 80 0 DT 2 0 96 HB DT 0 04 P 0 05 MT Err bh a a T320 MeO eG P26 ES 5 OS Out of Spec Seals 5 403 5 3 6 HB 0 008 HB 2 280 0 DT 80 0 DT 2 0 96 HB DT 0 04 P 0 05 MT Err A Or he NS Or NOUS 26 0 E00 EGG It starts with the number of output variables Then there are 13 items which must be entered for each output variable Name Type Description Symbol Text String Symbol used to represent variable in equation for another output Must be unique consist of only letter digits and underscores and cannot begin with a digit Name Text String More descriptive name for the variable for use on windows displaying the results of the simulation Units Text String Units of measure used for calculated values Precision Number Number used to specify precision for displaying numbers A positive integer and zero indicates the number of digits after the decimal number to report A negative integer represents the number of significant digits to report Generally a value of 5 works well Equation Text String Equation for output in format used by VarTran Can Containing contain numbers symbols of other variables Expression operators and functions The equation can reference any of the input variables and category input variables as well as other output variables A complete description is given below Equation for Value Number T
15. d in the VarTran User manual Forming the top seal closes the bag sealing its contents inside The top seal is a tear seal It must be torn open to remove the contents of the bag Of interest is the seal strength Too weak a seal can result in the bag breaking open during shipping and storage Too strong a seal makes the bag difficult to open Spec limits for seal strength have been set at 20 and 32 pounds The developer would like to 0 Target the process at 26 pounds Reduce the variability of seal strength and Establish a procedure for controlling the process 0 O The plant already has a heat sealer which is believed capable of performing the job The manufacturer of the heat sealer has provided the following recommended cycle Temperature Hot Bar 190 F Temperature Cold Bar 100 F Dwell Time 0 8 seconds Pressure 100 pounds Cooling Air Pressure 30 pounds Material Thickness 145 mils Room Temperature 75 F Material Temperature 75 F The heat sealer works by clamping the material to be sealed between two bars The top bar called the hot bar provides heat to melt the plastic material and cause them to flow together to form the seal The top bar also moves up and down to allow the material to be moved The bottom bar is stationary and has cooling water running through it allowing its Tutorials 4 temperature to be controlled When the top bar comes down to make contact with the material it is lowe
16. el 17 131 4 1 Subgroup 20 E io 20 0 su INPUT SETTINGS HA Gap Q 14 mils Standard Guage Force GF 7 lbs Deviation Peak Force PF 120 lbs ry y y H Downtime HD 130 msec Bag Temp BT 65 deg F Solut Temp ST 45 deg F 0 0 1 Subgroup 20 There are two outputs tensile strength and number of below spec seals The same equation is used for both One presents the data in variable format and the other as an attribute The equation is 39 2355 1 10625 G 0 25625 HD 1 1829167 ST 0 015625 G HD 0 07145833 G ST 0 01204166 HD ST 0 0007708 G HD ST Err Tensile Strength Only three of the inputs are in this equation G HD and ST All 3 2 way interactions between these variables exist and there is even a three way interaction There are no quadratic effects The model includes only a single source of variation Err Other Error Unit to unit standard deviation of 0 5 pounds This simulation cannot be used to illustrate robust design Changing targets does not affect the variation The goal is to adjust the variables to get the average above the lower spec limit Running a screening experiment on this example will generally result in identifying 4 key inputs Three are the true key inputs and the other is whatever is confounded with the three way interaction One will also pick up at least three groups of interactions Despite this error in picking up an extra variable careful use
17. entirely ignored The four key inputs are HB Hot Bar DT Dwell Time P Pressure MT Matl Temp The equation used to generate both output variables 1s Seal Strength 403 5 3 6 HB 0 008 HB 2 280 0 DT 80 0 DT 2 0 96 HB DT 0 04 P 0 05 MT Err Besides the 4 main effects there are quadratic effects for HB and DT along with an interaction between them In a screening experiment the group of interactions which includes the HB DT interaction should test significant Also if center points are included you should detect significant curvature The model includes the following sources of variation HB Hot Bar Trial to trial standard deviation of 2 0 F DT Dwell Time Unit to unit standard deviation of 0 08 sec Err Other Error Unit to unit standard deviation of 0 8 pounds Each trial has 1 5 chance of shift with std dev 0 8 pounds The variation within a trial is caused by DT and the error term Further variation from trial to trial is caused by HB and the error term This makes the process slightly unstable However the variation caused by dwell time dominates To make the process robust to dwell time the target of dwell time can be adjusted due to quadratic effect and the target of hot bar can be adjusted due to interaction The targets of the other two key inputs will only affect the average The effect of HB and DT s targets of the variation is shown below CONTOUR PLOT OF SEAL STRENGTH STANDARD DEVIATION
18. gns are all optional Any number of blank characters tabs and line feeds can be inserted between text strings and numbers Therefore the arrangement shown above could be changed to have all the values on one line or to have every value of a separate line The file is broken into 4 main sections Header Information first three lines above Input Variables number followed by list Category Input Variables number followed by list Output Variables number followed by list Simulator is as consistent as possible with the VarTran software package relative to its handling of the 3 types of variables Each section is described separately 21 2 2 Header Section The Header section consists of the following lines Simulator 2 0 sealer bmp sealer rtf 1 Heat Sealer There are six items which must be entered Name Type Description Program Name Text String Must always be set to Simulator File will only be read if it starts with the text string Simulator This prevents the program from accidentally reading other text files Version Number Number Files following the instructions in this document should have a version number of 2 0 This will allow future versions of the program to continue to read the file Graphics File Text String Name of a graphics file containing a picture to be displayed on the Startup dialog box and elsewhere The file must be in the same directory as the program and simula
19. he value of 1 indicates the entered equation is for values of the output The equation is then repeatedly evaluated as the inputs vary to generate data A value of O indicates the equation is for the fraction defective The equation is evaluated once for each trial to obtain the fraction defective and then the binomial distribution is simulated to obtain the data 27 Name Type Description Report Values Number This item 1s only applicable to the case where Equation for Value is set to 1 A value of 1 causes the programs to report the average and standard deviation of the values generated A value of 0 causes the program to only report the percentage of values in spec There are two ways to generate attribute data 1 enter an equation for the fraction defective using the previous variable or 2 enter an equation for values and specify 0 for this variable Display Results For Number A value of 1 causes results to be displayed for this variable for trails and capability studies A value of 0 causes no results to be displayed This allows complex models to be entered were one output variable to be defined in terms of other intermediate output variables without having to display the results for the intermediate outputs Upper Spec Limit Text String Containing Number or Blank Upper spec limit for values Only applicable if the Equation For Values is set to 1 Set to blank string if no u
20. l reduced by this quantity Setting to 0 eliminates all variation of the input variable This variable is generally set to 100 initially The percent tolerance is entered as a text string that can contain a constant expression The percent tolerance tightened must be between 0 and 100 A value of 1 causes this variable to be displayed on the control panel allowing its target to be adjusted by the user A value of 0 hides this variable from the user This allows sources of variation like measurement error to be added to the model that the user cannot adjust the target of Able to Tighten Tolerance Number A value of 1 causes this variable to be displayed on the maintenance panel allowing the percent tolerance tightened to be adjusted A value of 0 hides this variable from the user If all are set to zero the tighten tolerance panel will not be displayed 25 2 4 Category Input Variables Section The Category Inputs Variables section for the sealer file consists of the following line 0 This indicates there are no category inputs in this simulation When there are category input variables the section would appear as follows 2 M Material type 2 N New o Old 2 MC Cavity number 5 4 Mir Cavity 1 Lea Cavity 2M 3 Cavity 3 g Cavity 4 1 It starts with the number of category input variables Then there are 8 items which must be entered for each category input variable Na
21. m and Expression maximum targets The value entered must be between the minimum and maximum targets The initial target is entered as a text string that can contain a constant expression Minimum Target Text String The minimum value the user can set the target to Containing The value entered must be less than the maximum Constant target if the variable appears on the control panel Expression The minimum target is entered as a text string that can contain a constant expression 23 Name Type Description Maximum Target Text String The maximum value the user can set the target to Containing The value entered must be less than the maximum Constant target if the variable appears on the control panel Expression The maximum target is entered as a text string that can contain a constant expression Unit Standard Text String The standard deviation from unit to unit in the same Deviation Containing subgroup or trial The unit standard deviation is Expression entered as a text string that can contain an expression containing the symbol Target This allows the unit standard deviation to depend on the target selected For example the expression 0 3 Target causes the standard deviation be always be 3 of the target 1 e sets the CV to 3 The unit standard deviation must always be greater than or equal to zero Setup Standard Text String The standard deviation from subgroup to subgroup Deviation Con
22. me Type Description Symbol Text String Symbol used to represent variable in an equation for an output variable Must be unique consist of only letter digits and underscores and cannot begin with a digit Name Text String More descriptive name for the variable for use on windows displaying the results of the simulation Units Text String Units of measure While this field must be entered for all variables it is ignored for category input variables Precision Number Number used to specify precision for displaying numbers While this field must be entered for all variables it is ignored for category input variables Number of Number Number of category or levels associated with Categories variables Must be at least 1 Category Symbol Text String Symbol used to represent a category in an equation for an output variable Must be unique consist of only letter digits and underscores and cannot begin with a digit The category symbol and name are entered next to each other and then repeated for each category Category Name Text String More descriptive name for the category for use on windows displaying the results of the simulation Selected Category Number The selected category for performing simulations Must be an integer between 1 and the number of categories 26 2 5 Output Variables Section The Output Variables section consists of the following lines 2 SS Seal Strength l
23. nput variables Log A means to take the log of the variable A Log A means to multiply the variables Log and A Log A is the category A of the category input variable Log 29
24. on which terms tested significant individually From this a model can be fit without with going to a response surface study Tutorials 15 When analyzing the standard deviation as a response variable only lead gap tests significant A plot is shown below The key to reducing the variation is setting lead gap to 80 This takes advantage of the LG WT interaction and makes the process robust to material 0 0024235 OD SD 0 0015931 80 mils 0 00078276 65 mils LG Setting LG to 80 minimizes the variation MT is a material parameter that is more difficult to change so it will be left alone Trail Gap affects only the average and will be used to adjust the average to 10 mils A setting of 46 for TG centers the process The results are shown below Outside Diameter in Average 2 4998 Standard Deviation 0 0010692 2 5035 Cp 1 559 Cpk 1 491 UCL LSL USL Average x LCL 7 2 4969 1 Subgroup 20 i BL 0 0024569 a 2 495 2 505 an INPUT SETTINGS t Lead Gap LG 80 mils Standard Trail Gap TG 46 mils Deviation tyt Wall Thick W 85 mils R Feed Rate F 22in min Offset O 85 mils Mandrel Dia MD 62 mils 0 0 Roll Radius R 350 mils Subgroup 20 Operato Op Second Shift While this represents a big improvement it is still not Six Sigma Further improvements can only be obtained by tightening tolerances T
25. pper spec limit Lower Spec Limit Text String Containing Number or Blank Lower spec limit for values Only applicable if the Equation For Values is set to 1 Set to blank string 1f no lower spec limit Target Number of Samples Per Trial Text String Containing Number or Blank Number Target for values Only applicable if the Equation For Values is set to 1 Set to blank string if no target When there are two spec limits the target is frequently the midpoint Specifies the number of samples to be generated for each trial A value of 5 is common when values are generated and a value of 100 is common for attribute data Number of Samples Per Subgroup Number Specifies the number of samples to be generated for each subgroup of a capability study A capability study always consists of 20 subgroups A value of 5 is common when values are generated and a value of 100 is common for attribute data 28 2 6 Expressions An expression consist of numbers operators functions variables and parenthesis as described below Numbers Examples are 1 1 0 1 1 1 1042 and 1 1 104 2 Operators Unary operators and Binary operators and If parenthesis are omitted the operations are performed in the order determined by the operator precedence and association rules Multiplication operators may be omitted For example the expression 2 A Log B C is interpreted
26. red until it exerts a preset pressure on the material It is then held there for a preset time Before moving the material cooling air is blown on the seal to facilitate hardening There are two outputs seal strength and out of spec seals They are actually the same test but reported on both an attribute and variable basis Seal Strength Ibs Average 26 116 Standard Deviation 2 5139 30 16677 LOL Cp 0 7956 Cpk 0 7801 A LSL USL Average t E L 22 045 1 Subgroup 20 5 7768 as INPUT SETTINGS Hot Bar HB 190 deg F Standard fk Cold Bar CB 100 deg F Deviation kt Dwell Time DT 0 8 sec y4 Pressure P 100 lbs Room Temp RT 75 deg F Cooling Air CA 30 lbs 0 0 Thickness TH 14 5 mils 1 Subgroup 20 Matl Temp MT 75 deg F Out of Spec Seals Percent Defective 3 35 Fe P INPUT SETTINGS Hot Ba HB 190 deg F Cold Ba CB 100 deg F Percent p4 UCL Dwell Tim DT 0 8 sec Defective Pressur P 100 lbs Room Tem RT 75 deg F LCL Cooling Ai CA 30 lbs Thicknes TH 14 5 mils T t TT Matl Tem M 75degF Subgroup 20 The process is averaging around 3 defective primarily due to excessive short term variation The focus should be on reducing the variation Tutorials 5 Of the 8 inputs only four are actually key inputs included in model The targets selected for the other four inputs are
27. s a motor to drive the piston and a valve to control the direction of the flow This is the creative part of design Now the work begins We need to determine all the specifics such as How far should the piston travel and How fast should the motor turn To accomplish this task we need to make a list of all the factors affecting flow rate Three obvious factors are the piston radius R the stroke length L and the motor speed S Another possible factor is the amount of backflow through the valves B It is the output flow rate for which we want to optimize the average and reduce the variation This is accomplished by establishing requirements and controls for the inputs Initial settings for the inputs are shown below R Piston Radius 0 1 inches L Stroke Length 0 5 inches S Motor Speed 48 2 rpm B Back Flow 0 5 ml stoke A capability study of the current at the current settings is shown below The process has excessive short term variation 18 Flow Rate ml min Average 10 112 Standard Deviation 0 23152 10 93 7 t UCL A verage N y LCL 9 3924 Subgroup 20 0 53201 UCL Standard t Deviation 0 0 Subgroup 20 There is one output the flow rate The equation is F 16 388 x R L B S Cp 1 44 Cpk 1 278 LSL USL _ 0 11 0 INPUT SETTINGS Radius of Piston R 0 1 in Stroke Length L 0 5 in Motor
28. s the force required to pull the disk out There is a lower spec limit of 20 pounds This is a new process The goal is to demonstrate the feasibility of this approach The inputs and one of the settings run are G H A Gap 14 mils GF Gauge Force 7 lbs PF Peak Force 120 lbs HD Horn Downtime 130 msec BT Bag Temp 65 F ST Solution Temp 45 F The sonic sealer works by focusing sound energy of the disk to get it to melt to the surrounding tube The horn is the metal tooling inserted into the tube used to focus the sound energy on the disk The tube has just been used to a fill sterile bag The temperatures are the temperature of the bag before filling and the temperature the solution just placed in the bag Dozens of different settings like the one given above have been tried without success The results always look like the capability study on the next page Yes that is the lower spec limit above all the values The project is about to be canceled However since you have been exhorting the benefits of designed experiments you are being given the weekend to run a study true story Nobody expects much but at least it will keep you quite in the future Don t expect to make the process Six Sigma only to demonstrate feasibility Tutorials 11 18 757 Tensile Strength lbs Average 17 944 Standard Deviation 0 50517 UCL Cp as Cpk 1 357 LSL KV y Tr verage 4 T
29. taining or trial to trial The setup standard deviation is Expression entered as a text string that can contain an expression containing the symbols Target and UnitStandardDeviation This allows the setup standard deviation to depend on these two values The setup standard deviation must always be greater than or equal to zero Probability of a Text String The probability that a shift in the average occurs Shift Containing between subgroups or trials The probability of a Constant shift is entered as a text string that can contain a Expression constant expression The probability of a shift must be between zero and one Shift Standard Text String Standard deviation of distance above or below target Deviation Containing following a shift Shifts are not cumulative Each Expression time a shift is determined to have occurred a new distance from target is determined This results in a stationary time series process that remains centered around the target The shift standard deviation is entered as a text string that can contain an expression containing the symbols Target and UnitStandardDeviation This allows the shift standard deviation to depend on these two values The shift standard deviation must always be greater than or equal to zero 24 Name Type Description Percent Tolerance Display on Control Panel Text String Containing Constant Expression Number The standard deviations are al
30. tion text files If no graphic is provided enter the blank text string The file should be in bmp jpg ico emf or wmf formats 30 by 30 pixel files will appear without distortion All other files will be automatically shrunk or expanded to fit the space provided Description File Text String Name of a rich text file containing a description of the simulation that is incorporated into the help system The file must be in the same directory as the program and simulation text files If no description file is provided enter the blank text string The file should be in rtf format It can be created in Word using the Save As menu item Sequence Number Number The sequence number is used to control the order that the simulations appear on the Startup dialog box starting with the smallest numbers Simulations with the same sequence number sorted alphabetically by title Title Text String The name of the simulation as it is to appear on the Startup dialog box Control panel and windows displaying the results of the simulation 22 2 3 Input Variables Section The Input Variables section consists of the following lines 9 HB Hot Bar deg F 5 190 150 200 0 0 2 0 0 0 0 0 100 1 1 CB Cold Bar deg F 5 100 som 120 0 0 0 0 0 0 0 0 100 1 1 DT Dwell Time sec 5 0 8 0 5 1 0 0 08 0 0 O 0 O 0 100 1 1 P Pressure lbs 5 100 50 150 0 0 0 0
31. ysis The VarTran software package can be used to perform this purpose It comes with a file for the heat sealer The model in this file is slightly different than the model described above because it uses an equation obtained using a response surface study rather than the true equation It also used a slightly different error structure None of these differences are evident to the student Tutorials 8 1 2 Sheeting Extruder This simulation involves optimizing a sheeting extrusion process It is a simple example for starting out with It has only four inputs all of which are important making it most suitable for a response surface study It cannot be used to illustrate robust design The output of interest is sheeting thickness The target is 10 0 mils thousands of an inch The spec limits are 9 0 to 11 0 mils The current settings for the inputs are RS Roller Speed 100 feet sec DT Die Temp 275 F V Viscosity 2 7 coeff HS Head Speed 90 rpm The extruder works by forcing molten plastic through a die The material is first heated to the die temperature Increasing head speed increases the pressure the material is forced out with Roller speed is the speed at which the roller receiving the extruder sheeting is turning Viscosity is a material property The current process is off center Sheet Thickness mils Average 10 872 Standard Deviation 0 3067 11 366 UCL Cp 1 087 Cpk 0 1391
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