- 1. Six Sigma Green Belt Training 6 Methusael Brown Cebrian ITIL v3 LSSBB Certified Lean Six Sigma Black Belt “You cannot Manage, what you cannot measure” – W. Edwards Deming
- 2. What is Six Sigma? - It is a Quantitative, data-driven Define, Measure, Analyze, Improve, Control methodology to Process Improvement based on Statistical and Management tools to increase efficiency in the process. - Simply put, it is a way of using data to solve problems and make businesses more profitable. The term “sigma” is used to designate the distribution or spread around the mean (average) of any process or procedure.
- 3. • Developed by Motorola, used successfully by Texas Instruments, Boeing, Honeywell, Lockheed Martin. • GE, has become the face of Six Sigma due to its wide adoption throughout the organization. • Internal Focus: Improve existing processes – manufacturing, business transaction for service industry. • External Focus: Listens to Voice of the Customer (VoC). • Uses trained teams - Champions: Business Leaders, provide resources and support implementation. - Master Black Belts: Experts and Culture-Changers, train and mentor Black Belts/ Green Belts. - Black Belts: Lead Six Sigma project teams. - Green Belts: Carry out six sigma projects related to their jobs. Driver for Cost Savings and Customer Satisfaction
- 4. Six Sigma is: • An enabler to Business Strategy. • Places customers at the center of the performance improvements. • Fact-based approach for improving business processes and solving problems. • A proven methodology and toolset supported by deep training and mentoring. • Focused on reducing variability of processes • Elimination of Defects/Wastes (Mudas). • A way to develop highly skilled business leaders. • A means for creating capacity in organizations. Quality is Everyone’s Responsibility
- 5. Striving towards Six Sigma Six Sigma Improves Quality by Reducing Defects and Variation
- 6. Quality 99% is never good enough!
- 7. Building on Quality reduces long -term costs Why do we need to pursue Quality Initiatives? • Meet Customer expectations for higher quality. • Provide a competitive differentiator in the Market. • Build greater pride and satisfaction within the company. • Drive other key goals: Productivity and Growth.
- 8. Delighting Customers • Making customers successful • Customer-Centric metrics • Listens to the Voice of the Customer (Voc) • Surveys, Interviews, Net Promoter Score Make customers feel Six Sigma
- 9. The Kano Model • A way to evaluate how customer satisfaction is impacted by an initiative • Three types of improvements • Hygiene factor (green). Customer expect this and is dissatisfied if not fulfilled. Ensuring that these needs are met should have highest priority. • Performance factor (blue). There is a relationship between customer satisfaction and how well the need is met. Important to ensure satisfactory performance. • Delight factor (red). Customers do not expect this and are thus indifferent if the need is not met. A way to create additional satisfaction if all hygiene factors are performing.
- 10. Definitions
- 12. The statistical objective of Six Sigma Reduce Variation and Center Process – Customers feel variation more than the mean.
- 14. What is Variation? • Variation is the extent to which items (things) differ, from one to the next! • There will always be some variation present in all processes. -Nature – shape, size of leaves, height of trees -Human – Handwriting, speed of walk, tone of voice etc. -Mechanical – weight/size/shape of product, content etc. We can tolerate this variation if: - The process is on target (where we want it to be) - The variation is small compared to the customer specifications.
- 15. According to Deming: • 85%-95% of all variation is Common Cause. • 5%-15% of all variation is Special Cause. • Common Cause – variation is random, stable and consistent over time. It is expected variation. • Special Cause – is not random, and changes over time. It is unexpected variation. There is undue influence in the process. Variation is the enemy of Process Improvement efforts.
- 18. 6 Causes of Variation • Man • Machine • Material • Method • Measurement • Mother Nature
- 19. Process Any activity that takes inputs, adds value, and provides an output(s). Variation exists in the process.
- 20. Six Sigma improvement approach Six Sigma is Long Term Commitment to the Philosophy of Quality.
- 21. The heart of Six Sigma Historically the Y – with Six Sigma the X’s Focusing on the X’s relies on a good and steady flow of Data – Metrics!
- 22. D-M-A-I-C
- 23. Lean Six Sigma Checklist
- 24. The Changing Focus of Six Sigma The GE Experience –> Lean Six Sigma expands the tool set Six Sigma – a dynamic, living initiative
- 31. Identify Project Critical To Quality
- 33. Define Phase Date Version 1.1 The scope of this project will focus on following key aspects: People Process Critical To Quality Machines Workplace Problem / Goal Roles Sponsor BB GB Shift Managers: Allan K, Mark L., John Doe Shift Machine Operators Rey M , Louie G, Rick L. Finance Accountant Julie P. Project Outcome Milestones Define 1-Jun-13 Measure 15-Jun-13 Analyze 15-Jul-13 Improve 15-Oct-13 Control 15-Nov-13 Potential Risks Lack of Buy in from operators Non-Compliance to governance/policy/SOP and difficult to monitor Lack of support from Leadership Signature Sponsor Signature BB / GB We will look at the existing capabilities of the machines to produce the PCB's according to specifications. Including the ways it processes the raw materials being fed to it, as well as its technological limitations to produce a PCB according to specs. We will look at the workplace environment involved in the process of producing PCB's. IF an essential 5S processes are in place. Some aspects that will be looked at, but is not limited to: Machine arrangements, distance, tool placements, lighting, tidiness. The existing process produces a high number of scraps or waste, which affects the pricing model for the product as well as the reliability of delivery schedules, we will pursue key areas of interests such as People, Process, Machines, and Workplace in zeroing down the root causes of the existing issues. In order to meet the Customer requirements for Volumes, we will embark on a project using Lean Six Sigma methodologies to improve the existing process by eliminating 98% from existing Scrap Rates, reduce product cost as well as achieve 100% reliability in delivery schedule. With the elimination of Scraps in the processes, we will be able to provide room for future growth in customer demands. 98% Reduction of Scraps 100% Availablity of Machines to Operate Newly trained Operators Newly published SOP's, Policy, Guideline and Manuals Reduced Product Cost 100% Reliability in Delivery Schedule 35% increase in volume capacity Plant Manager - David Mack Quality Manager - John Loyd Methusael B. Cebrian Core Team Project Charter The Quality and Reliability of our process and products are threatened because of the defects existing in the manufacturing line. Customers are complaining that we can no longer keep up with our committed scheduled deliveries, which also affects their supply chain. The cost of raw materials is also at all time high, and a high rate of scraps is no longer acceptable. The high cost of raw materials and the number of scrap rates, is passed to the customer which coupled with unreliable delivery schedule makes our customers to look for other suppliers. It is therefore imperative to engage the problem and eliminate it using Lean Six Sigma methodology and make our product a reliable and cost competetive one for our customers. Project Name Business Case Project Scope Eliminate Manufacturing Defects Affecting Scrap Rate, Product Cost and Delivery Schedule. 1-Jul-13 We will look at the skill sets, trainings, and capabilities of people involved in the process, to follow the existing instructions, guidelines and SOP's needed to produce the PCB's. We will look at the existing methodologies, instructions, steps if it conforms to the right processes needed to produce the PCB's according to specifications.
- 34. Team Charter
- 35. Five major elements of a Charter
- 37. Problem and Goal Statements Together they provide focus and purpose for the team
- 38. Description of the “pain”
- 42. SMART Problem and Goal Statements
- 44. Milestones
- 57. Simplification is the goal of Lean Six Sigma!
- 60. Example: It is much easier to work on your SIPOC Chart, if you follow POCIS process. SUPPLIERS INPUTS OUTPUTS CUSTOMERS Client Inputs Order order call/email Order Slips Production Planning Control Department Production Planning Control Department Order slips/documents from Clients Internal Production orders Production Material Control Department - Release internal production order Production Material Control Department Production Orders Raw Materials Production Floor - Release Material and other Raw materials to production shop Production Floor Raw Materials for PCB manufacturing Printed Circuit Boards Quality Inspection - PCB Production Process Quality Inspection Output products from production floor. Quality Pass, Defects, Scraps Packaging Facility Packaging Facility Final Product ready for delivery Package PCB's for delivery - Final Product packaged and ready for delivery PROCESS SIPOC DIAGRAM Online OrderSystem Production and Engineering Documentations Packaging - delivery to customers Pre Prod Engineering Check for Specs tolerance, Defects Load Lookup/Look Down Stencil/PWB Alignment Print Wipe Stencil Buttom UnloadSeparate
- 64. Define – make a case for action Measure – define success
- 71. Pareto Chart – 80/20 RULE
- 83. Failure Modes and Effects Analysis (FMEA) Process or Product Name: Prepared by: Page ____ of ____ Responsible: FMEA Date (Orig) ______________ (Rev) _____________ Process Step Key Process Input Potential Failure Mode Potential Failure Effects S E V Potential Causes O C C Current Controls D E T R P N Actions Recommended Resp. Actions Taken S E V O C C D E T R P N What is the process step What is the Key Process Input? In what ways does the Key Input go wrong? What is the impact on the Key Output Variables (Customer Requirements) or internal requirements? HowSevereisthe effecttothe cusotmer? What causes the Key Input to go wrong? Howoftendoescause orFMoccur? What are the existing controls and procedures (inspection and test) that prevent eith the cause or the Failure Mode? Should include an SOP number. Howwellcanyou detectcauseorFM? What are the actions for reducing the occurrance of the Cause, or improving detection? Should have actions only on high RPN's or easy fixes. Whose Responsible for the recommende d action? What are the completed actions taken with the recalculated RPN? Be sure to include completion month/year 0 0 0 0 0 0 0 0 Process / Product Failure Modes and Effects Analysis (FMEA) • RPN = Severity * Occurrence * Detection
- 84. What is FMEA? • A predictive/ Proactive tool that allows us to identify potential risk failures in the system or process, and prevent it from happening. Opposite of FMEA: Reactive Tool Root Cause Analysis Pareto Chart
- 85. Why do we need FMEA? • Predict possible failure modes in the process. • Reduce Risk of Failure • Prevent Failure from Happening • Identify Potential Effects of Failure • Identify Current Controls in place • Recommended Action.
- 86. When to Use an FMEA ANALYZE PHASE Determine if there is a High Risk of Failure and Determine if the failures are detectable. IMPROVE PHASE Evaluate impact of proposed changes. CONTROL PHASE Determine Which Failure Modes are the Most Critical to Control ->Include in Control Plan
- 98. Who will Do it? Type of Operational Measurement Data Tags Needed Data Collection Person(s) What? Where? When? How Many? Measure Measure Definition or Test Method to Stratify the Data Method Assigned Name of Xor Y Clear definition of Visual Data tags are Manual? State What Location How The number parameter attribute or the measurement inspection defined for the Spreadsheet? who has measure is for often of data or condition discrete defined in such a or automated measure. Such Computer based? the being data the points to be data, way as to achieve test? as: time, date, etc. responsibility? collected collection data collected measured product or repeatable results Test instruments location, tester, is per sample process from multiple are defined. line, customer, collected data observers buyer, operator, Procedures for etc. data collection are defined. Define What to Measure Define How to Measure Sample Plan Data Collection Plan
- 106. Measurement Systems Analysis Where does variation come from?
- 107. Measurement Variation Actual Value Measured Value Variation
- 108. Measuring Process The Process: Variable Data Operators The Tool Part To Be Measured Measurements
- 109. Gage R & R Studies • Measures the Repeatability and Reproducibility of your measurement process and compares it to the variation occurring in your part • Or stated another way, Measures the amount of error introduced in the measurement process
- 110. Total Variation in Measurement: Preferred Actual Variation in Product Operator Environment Gage Process
- 111. Total Variation in Measurement: Unacceptable Actual Variation in Product Operator Environment Gage Process
- 112. Accuracy and Precision Accuracy: How close to the measured. Precision: How repeatable Examples of: • Poor accuracy and precision • Good precision, poor accuracy Actual Value Measured Value Accuracy Repeatability (Precision)
- 113. Target Practice How could the green player improve performance? How could the yellow player improve performance? Which player do you think has a better chance of becoming a champion dart player? Typically, it is easier to shift the average than to reduce variation
- 114. Understanding Accuracy and Precision Target Target Target Target High accuracy & high precision Low accuracy & high precision High accuracy & low precision Low accuracy & low precision
- 115. Gage R&R Example • One gage • Two operators • Measuring the length of a part in meters twice • Blind samples • Spec Limit: +/- 0.1 mm • Gage Tolerance +/-0.0001 mm
- 116. The Data
- 117. Use Minitab Open Minitab, enter data as shown Quality Tools: Gage R&R (Crossed) Follow directions as on following sheets Minitab uses ANOVA to perform analysis • ANOVA was discussed in DOE Class
- 121. The Results
- 122. StatGuide
- 126. Statistical Process Control (SPC) is a technique that enables the quality controller to monitor, analyze, predict, control, and improve a production process through control charts. Control charts were developed as a monitoring tool for SPC by Shewhart. Statistical Process Control
- 127. Understanding Variation The 6 Ms – all variation is from one or more of the 6Ms. • Man (generic) • Machine • Material • Method • Measurement • Mother nature
- 128. USLLSL USLLSL LSL USL Process Variation = Lost $
- 129. Common Cause Variation • Natural, expected variation, Controllable • Characterized by a stable and consistent pattern of variation over time. A process operating with controlled variation has an outcome that is predictable within the bounds of the control limits.
- 130. Special Cause Variation • Unnatural, not expected •Perform root cause analysis and eliminate if possible
- 131. Remember! According to Deming: 85% to 95% of all variation is Common Cause. 5% to 15% of all variation is Special Cause.
- 132. “Eighty-five percent of the reasons for failure to meet customer expectations are related to deficiencies in systems and process…rather than the employee. The role of management is to (fundamentally) change the process rather than badgering individuals to do better.” Should We Be Concerned with Common Cause Variation? – W. Edwards Deming
- 133. Types of Data Discrete Data • Is Counted • Can only take certain values • Example: The number of students in class (you cannot have a half student) Continuous Data • Is measured • Can take any value (within a range) • Often involve fractions or decimals. • Example: A person’s height, Time (hour, minutes, seconds), weight, length.
- 134. Control Charts • Control charts are simple but very powerful tools that can help you determine whether a process is in control (meaning it has only random, normal variation) or out of control (meaning it shows unusual variation, probably due to a "special cause"). • Control charts have two general uses in an improvement project. The most common application is as a tool to monitor process stability and control. A less common, although some might argue more powerful, use of control charts is as an analysis tool.
- 135. Choosing Control Chart using Minitab
- 136. Commonly used Control Charts Control Charts for Continuous Data Xbar-R Charts • Xbar charts give the average value each operator obtained per part. • R chart shows the difference between the largest and the smallest measurement for each part. The R chart is used to evaluate the consistency of process variation. • Each subgroup is a snapshot of the process at a given point in time. The chart’s x-axes are time based, so that the chart shows a history of the process. For this reason, it is important that the data is in time-order.
- 137. • The Xbar chart is used to evaluate consistency of process averages by plotting the average of each subgroup. It is efficient at detecting relatively large shifts (typically plus or minus 1.5 σ or larger) in the process average. • The R chart, on the other hand, plot the ranges of each subgroup. The R chart is used to evaluate the consistency of process variation. Look at the R chart first; if the R chart is out of control, then the control limits on the Xbar chart are meaningless.
- 138. Control Charts for Discrete Data C Charts • Assumes a Poisson distribution (counting or integers) • Tracks the # defects and presence of Special Causes • Used when identifying the total count of defects per unit (c) that occurred during the sampling period, the c-chart allows the practitioner to assign each sample more than one defect. This chart is used when the number of samples of each sampling period is essentially the same.
- 139. • This chart is used when the number of samples of each sampling period is essentially the same.
- 140. Control Limits The data determine the control limits with Common Cause variation UCL LCL Ave Measurement Number Value
- 141. Control Limits Differentiate CC and SC Variation LCL Special Cause Variation UCL When a process is stable and in control, it displays common cause variation, variation that is inherent to the process. If the process is unstable, the process displays special cause variation, non-random variation from external factors.
- 142. X bar Control Chart for SPC Sigma 3 Sigma 2 Sigma 1 Sigma 1 Sigma 2 Sigma 3 UCL LCL Centerline = Mean USL LSL
- 143. X bar R Chart - The X bar Part UCL 74.015 CL 74.001 LCL 73.988 73.980 73.985 73.990 73.995 74.000 74.005 74.010 74.015 74.020 S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 S16 S17 S18 S19 S20 S21 S22 S23 S24 S25 Date/Time/Period X bar Observations CL = Center Line; this is the average of the averages (grand average) of each sample average
- 144. Control Limits and Spec Limits CLs are what the process delivers • Typically +/- 3 sigma from mean SLs are what the product needs Hopefully CLs are “tighter” than SLs
- 145. Sigma 3 Sigma 2 Sigma 1 Sigma 1 Sigma 2 Sigma 3 UCL LCL Mean Shewhart Rules Developed by Dr. Walter Shewhart in 1931 Assume Normal Distribution “3 sigma significant” 1891-1967
- 146. Sigma 3 Sigma 2 Sigma 1 Sigma 1 Sigma 2 Sigma 3 UCL LCL Mean Shewhart Rule 1 • One point more than 3 sigma from mean
- 147. Sigma 3 Sigma 2 Sigma 1 Sigma 1 Sigma 2 Sigma 3 UCL LCL Mean Shewhart Rule 2 • Nine points in a row on same side of the mean
- 148. Sigma 3 Sigma 2 Sigma 1 Sigma 1 Sigma 2 Sigma 3 UCL LCL Mean Shewhart Rule 3 • Six points in a row all decreasing or all increasing
- 149. Sigma 3 Sigma 2 Sigma 1 Sigma 1 Sigma 2 Sigma 3 UCL LCL Mean Shewhart Rule 4 • Fourteen points in a row alternating up and down
- 150. Sigma 3 Sigma 2 Sigma 1 Sigma 1 Sigma 2 Sigma 3 UCL LCL Mean Shewhart Rule 5 • Two out of three points more than two sigma from the mean on the same side
- 151. Sigma 3 Sigma 2 Sigma 1 Sigma 1 Sigma 2 Sigma 3 UCL LCL Mean Shewhart Rule 6 • Four out of five points more than one sigma from the mean on the same side
- 152. Sigma 3 Sigma 2 Sigma 1 Sigma 1 Sigma 2 Sigma 3 UCL LCL Mean Shewhart Rule 7 • Fifteen points in a row within one sigma of mean on either side
- 153. Sigma 3 Sigma 2 Sigma 1 Sigma 1 Sigma 2 Sigma 3 UCL LCL Mean Shewhart Rule 8 • Eight points in a row more than one sigma from mean on either side
- 154. Using the Rules Xbar-R charts use 1-8 C Charts 1-4 Often people will select which rules to chose, 7 and 8 are least often used Since 3 sigma is 99.7%, if you analyze large quantities of data you will get rule violations even with CC variation
- 155. The Control Chart Sigma 3 Sigma 2 Sigma 1 Sigma 1 Sigma 2 Sigma 3 UCL LCL Mean x x x + A2R - A2R
- 156. Example Stencil Printing Volume Subgroup size =5 60 subgroups Develop Xbar - Chart
- 157. Xbar-R with Minitab: Enter data (Excel) then…..
- 159. Discussion? Sample SampleMean 554943373125191371 2000 1900 1800 1700 __ X=1870.6 UC L=2007.3 LC L=1733.9 Sample SampleRange 554943373125191371 600 450 300 150 0 _ R=237.0 UC L=501.1 LC L=0 6 1 Xbar-R Chart of Print Volume Data
- 161. Stencil Printing Process The Process: Variable Data Process Parameters: Print Speed Snap Off Downstop Design: PWB Layout Stencil Design Solder Paste Design Materials: PWB Solder Paste Stencil Squeegee The Product: An Acceptable Board For Component Placement Quality Level (Attribute Data)
- 162. C Charts: Control Charts for Attribute Data Measure attribute data Ex: X defects per 1000 parts Can be done manually xxLCL 3 xxUCL 3
- 163. Using Minitab 1. Enter defect data in column C-1 2. Then perform operations as above
- 166. Analysis
- 167. Other Control Charts C and Xbar-R charts are most commonly used in SPC
- 168. Process Capability Analysis Where specs and process capability face off • Use Capability Sixpack (normal) • Assumes Normal Distribution Is your process in spec? How well is it in spec? • Cp • Cpk
- 169. When the Data are Not Normal Control chart theory will be misleading Minitab tests for normality Fortunately, data are often normal, or can be normalized with a transformation X 1 2 3123 Mean
- 170. Capability Analysis: What are Cp and Cpk? Cp – Process Capability ->measures precision only. Cp - is a measurement that considers the spread of the data relative to the specification limits. As shown in the following figure, a high Cp value indicates low process variation. 6 sigma means Cp = 2
- 171. Cpk – Process Capability Index ->measures precision and accuracy. Cpk - is a measurement that considers both the spread of the data and the shift of the data relative to the specification. As shown in the following figure, a process may have good Cp but not meeting specifications (low Cpk). 6 sigma means Cp = 2 and Cpk =1.5
- 172. Remember! It is important to note that capability indices are only useful when the process is stable. In addition, like all other statistical procedures, capability indices are only estimates based on the samples collected. Thus, control charts are often used in conjunction to monitor the process over time rather than relying on a single number.
- 173. Good Cp and Cpk X 1 2 3123 Mean, 99.74% with +/- 3 sigma LSL USL Tolerance Width of Distribution
- 174. Good Cp, Poor Cpk X 1 2 3123 Median, Mean, Mode LSL USL Width of Distribution 3 standard deviations
- 175. Cp and Cpk • Cp = USL – LSL 6 • Cpu = USL – Xbar 3 • Cpl = Xbar - LSL 3 • Cpk = min (Cpu, Cpl )
- 176. What is the Cp and Cpk of this Distribution? X 1 2 3123 Median, Mean, Mode 99.74% LSL USL Tolerance Width of Distribution Cpl Cpu 3 standard deviations
- 177. Current process has 3 standard deviations between target and USL. USLLSL 1 Standard Deviation Target Process Center 3 Improved process (reduced variation) has 6 standard deviations between target and USL. What 6 Sigma Looks Like USLLSL Target Process Center 1 Standard Deviation 3 +6 3 SQL = 3.0 SQL = 6.0 -6 Spec limits are from the customer Spec limits are from the customer Spec limits are from the customer Spec limits are from the customer
- 178. X X 10 LSL 15 20 USL 10 LSL 20 USL 18 X X USL 10 LSL 16 20 10 LSL 15 20 USL For σ = 1.66 For Cpk = 4 What are Cp, Cpk or σ? For Cp = 2.5 For σ = 1
- 179. Sugar Concentration in Soda A manufacturer wants the sugar concentration in his soft drink to be 10 teaspoons +/- 0.25 at a 3 sigma level in a 12 oz can Analyze the data with the Capability Sixpack Comment on the results
- 183. Introduction to DOEs and Regression
- 184. Objectives DOE = Design of Experiment To be able to set up, solve and analyze simple DOEs Perform simple Regression analysis
- 185. Experiments The experimental method is the foundation of science and engineering • Without it we would live short, savage lives They are a new invention • Only practiced consistently since Galileo Aristotle could have avoided the mistake of thinking that women have fewer teeth than men, by the simple device of asking Mrs. Aristotle to keep her mouth open while he counted. --- Bertrand Russell
- 186. What is DOE? Most processes are affected by multiple factors • Example: Stencil Printing • Factors: Stencil, paste, snap off speed, print speed, wipe frequency With DOE, the effect of all the factors can be determined with a minimum amount of testing • The results are “statistically significant,” not an opinion The old way: one experiment for each factor => not effective • Requires much more data, interactions are a problem
- 187. History 1830 – Gauss • Curve fitting with least squares • The “Normal” or “Gaussian” Curve 1908 – “Student” develops t -Test to analyze beer 1920 - DOE Concepts Developed • First in Agriculture….calculations harder than experiments 1950-80s “Taguchi” Developed 1951 - Central Composite Design 1990’s - D optimal designs • Experiments harder than calculations
- 188. DOE: Step 1 Clarifying the process mechanisms is crucial Hence, have a brainstorming session to identifying independent variables (factors)
- 189. Guidelines for Brainstorming Team Makeup • Experts • “Semi” experts • Implementers • Analysts • Technical Staff who will run the experiment • Operators
- 190. Guidelines for Brainstorming Discussion Rules • Suspend judgement • Strive for quantity • Generate wild ideas • Build on ideas of others
- 191. Guidelines for Brainstorming Leader’s Rules for Brainstorming • Be enthusiastic • Capture all ideas • Make sure you have a good skills mix • Push for quantity • Strictly enforce the rules • Keep intensity high • Get participation from everybody
- 192. Conducting a DOE Steps 1 through 5 1. State the Problem 2. Define the Objective 3. Set the start and end dates 4. Select the Response – e.g., Solder paste volume 5. Select the factors – e.g., Print Speed, Separation Speed, Paste, Stencil, etc.
- 193. 6. Define the team and resources 7. Select design type – e.g., Full factorial, etc. 8. Conduct experiment 9. Analyze data 10. Plan and execute further tests from these results Conducting a DOE Steps 6 through 10
- 194. Score Random Variation = Variance: SDR 2 AverageNumberofRounds Random Variation: Dr. Ron Golf Score
- 195. Tiger Dr. Ron Score Difference in averages Implies that there is a greater difference between Tiger and Dr. Ron than among them 2 >> Sr 2 NumberofRounds STiger 2 Variation from Factors: Tiger and Dr. Ron SDR 2
- 196. For example: Phil Mickelson and Steve Stricker. Then, 2 << Sr 2 MultipleRounds Golf Score Sr 2 When Variation from Factor Change is Small…….
- 197. ANOVA ANOVA (Analysis of Variance) • Compares S2 to 2 The F Statistic: Large F => factors have a significant effect on result “Large” varies with sample size, typically > 4 for 95% confidence 2 2 rS F
- 198. The Null Hypothesis H0: The mean response at two different factor levels is the same. Example: The Tiger and Dr. Ron score the same. Typically, we want to see if we can reject H0 at a certain “level of confidence” F ~ 4 can reject H0 with >95% confidence: • P<0.05
- 199. DOE Size The amount of data needed quickly grows with the number of factors and levels F = number of factors, L= number of levels Data Points = LF • a 6 factor, 4 level experiment = 4096 data points
- 200. DOE Size Must work to minimize # of factors and levels “If it’s too big, it won’t get done.” - Joe Belmonte Fractional factorial, Taguchi, Plackett- Burman, and D-Optimal Designs were created to minimize data collection But, always with the loss of something
- 201. DOE Example and Theory Apple growth Two Factors: Water and fertilizer are believed to increase the quantity of apples. It is not known if there are interactions between the two factors Two Levels: For each Factor Response: Crates of Apples We will do a “full factorial” experiment
- 202. The Data Run Water (A) Fertilizer (B) Resp1 (100 crates) Resp2 1 70 100 2.2 2.8 2 70 200 3.2 3.6 3 90 100 5.0 4.6 4 90 200 5.8 5.4
- 203. Parallel lines => No Interaction! Apple Production vs Amount of Irrigation 0 1 2 3 4 5 6 60 65 70 75 80 85 90 95 Units of Water Apples(100Crates/tree) 200 Units Fertilizer 100 Units Fertilizer
- 204. Interaction Water Apples P1 P2 Non Parallel Lines => Factor Interaction
- 205. (2.2-2.5)2 + (2.8-2.5)2 Water Fertilizer
- 206. Number of responses minus 1 Cross Product Term
- 207. If we reject Ho we are wrong only 5% of the time. (4.8+5.6)/2 -(3.4+2.5)/2
- 208. Still can reject strongly H0
- 209. Cross product term not significant
- 210. Strong A and B dependence, weak AxB
- 211. What does ANOVA Do? ANOVA uses the analysis of variance to determine if the “treatment” is more significant than random error
- 212. Factors in a Chemical Reaction Feed rate, Catalyst, Stir rate, Temperature and Concentration are to be evaluated on their effect to increase the percent reacted Two levels for each factor are considered: • Feed rate: 10, 15 (g/min) • Catalyst: 1, 2 • Stir rate: 100,120 (stirs/min) • Temperature: 140, 180 (degrees F) • Concentration: 3, 6 (g/L)
- 218. Now Paste in your Data
- 220. Note: If you only have one replicate, do not select more than a 2nd order fit
- 224. MeanofPercentReacted 1510 75 70 65 60 55 21 120100 180140 75 70 65 60 55 63 Feed rate Catalyst Stir rate Temperature Concentration Main Effects
- 226. Feed rate 21 120100 180140 63 90 75 60 Catalyst 90 75 60 Stir rate 90 75 60 Temperature 90 75 60 Concentration 10 15 rate Feed 1 2 Catalyst 100 120 Stir rate 140 180 Temperature Interaction Plot
- 227. But Always….. Look at the raw data
- 228. DOE Class Problem: using Minitab on your own Three new additives are being pursued to increase stainless steel cutlery hardness. Each additive (A,B,C) is tested at four levels. In addition, two new cold quench temperatures are tried. The data are “Stainless DOE/Regression.” Use DOE techniques (Full Factorial, turn randomizer off, 1 replicate, select 2nd order) to determine which additives have an effect on the hardness and whether quench temperature is important. Using factorial plots, comment on the results. What formulation and treatment would you suggest from these data to maximize hardness? What future experiments might you want to do to learn more about hardness as a function of the factors?
- 229. Don’t jump ahead, answers are on the next slide!
- 230. Analysis of Variance for Rockwell C Hardness, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P A 3 18.141 18.141 6.0471 682.78 0.000 B 3 38.567 38.567 12.8555 1451.5 0.000 C 3 12.227 12.227 4.0755 460.17 0.000 Quench Temp 1 0.0021 0.0021 0.0021 0.24 0.626 A*B 9 0.1127 0.1127 0.0125 1.41 0.196 A*C 9 0.0516 0.0516 0.0057 0.65 0.754 A*Quench Temp 3 0.0220 0.0220 0.0073 0.83 0.483 B*C 9 0.0708 0.0708 0.0079 0.89 0.540 B*Quench Temp 3 0.0052 0.0052 0.0017 0.20 0.899 C*Quench Temp 3 0.0066 0.0066 0.0022 0.25 0.862 Error 81 0.7174 0.7174 0.0089 Total 127 69.9228 S = 0.0941094 R-Sq = 98.97% R-Sq(adj) = 98.39%
- 231. Session Window Conclusions: Additives A, B & C are statistically significant. Need to find optimal level to achieve specified hardness. Quench temperature and interactions not statistically significant.
- 232. Main Effects plot 2.01.51.00.5 60.0 59.5 59.0 58.5 1.000.750.500.25 3.22.41.60.8 60.0 59.5 59.0 58.5 -100-200 A Mean B C Quench Temp Main Effects, Rockwell C Hardness
- 233. Main Effects Conclusions Additive A achieves optimal hardness between 1.0 & 2.0. Further experimentation with greater resolution between these points recommended. • If cost prohibits, can recommend to use level 1.5, as this produces the hardest steel of levels tested
- 234. Additives B & C do not achieve any local or global optimum. Further experimentation at higher dosages recommended • Or if costs prohibit, use the highest levels Quench temp is not statistically significant. • Can choose to use level that is cheaper • This information is just as important because it allows the business to do what is cheaper.
- 235. Interaction Plot 1.000.750.500.25 3.22.41.60.8 -100-200 60 59 58 60 59 58 60 59 58 A B C Quench Temp 0.5 1.0 1.5 2.0 A 0.25 0.50 0.75 1.00 B 0.8 1.6 2.4 3.2 C Interaction Plot - Rockwell C Hardness
- 236. Interactions discussion No interactions statistically significant. • Seen previously in your session window • Seen here as there are no non-parallel lines
- 237. Extra Problem: French Fries McDonalds is concerned that their French fries are losing favor to Burger King. They perform a DOE to optimize taste. Professional testers evaluate the taste of the fries that have been cooked under varying conditions. The average of 10 tasters is the “response.” Ten is the best rating, one is the worst. The experiments are performed twice to get two replicates of data. The factors are: Potato Type: Maine or Idaho, Cooking Oil Type: lard or vegetable, cooking temperature: 320, 330, 340, 350oF and cooking time 10, 11 or 12 minutes. The results are in the spreadsheet in tab “French Fry DOE”. Historically, lard has made better tasting fries, but the vegetable oil is a new version, specifically designed for improved taste. Analyze and discuss.
- 239. IdahoMaine 9.2 9.0 8.8 8.6 8.4 LardVeg 350340330320 9.2 9.0 8.8 8.6 8.4 121110 Potato Type Mean Oil Type Temp Cook time Main Effects Plot for Taste Rating Data Means
- 241. LardVeg 350340330320 121110 9.0 8.5 8.0 9.0 8.5 8.0 9.0 8.5 8.0 Potato Type Oil Type Temp Cook time Maine Idaho Type Potato Veg Lard Oil Type 320 330 340 350 Temp Interaction Plot for Taste Rating Data Means
- 242. Improvement
- 248. Tool Overview *It is not expected that all tools be used – the project focus and questions must drive the tool selection. Define Measure Analyze Improve Control Kaizen RACI Stakeholder Analysis Norms/Ground Rules SIPOC Baseline Measurements Contract Project Plan Review Process Cost Benefit Analysis Integrated Flowchart 8 Types of Waste Pareto Diagram Kano Model Customer /Results Matrix Results/Process Matrix Operational Definitions Sampling Plan Data Collection Form Measurement Analysis Control Chart Process Capability DPMO Histogram Run Charts Cause and Effect Diagram Pareto Diagram Affinity Diagram Interrelationship Diagraph Control Chart Scatter Diagram Pareto Diagram Stratification Hypothesis Testing Regression Analysis Tree Diagram Design of Experiment Cube Plot PDSA Test Plans Brainstorming Lateral Thinking 5S Solution and Effect Diagram Implementation Plan Gantt Chart Flow Chart (To Be) Control Chart Pareto Visual Management Line Balancing Poke-Yoke FMEA Arrow Diagram Gantt Chart Risk Assessment Stakeholder Analysis Communication Plan SOP Control Chart Control Plan Training Plan Force Field Analysis Cost Benefit Analysis Final Project Review Document Success Story for Publication Review Process Communication Plan Key Tools / Techniques Typically Used in Each Phase