QSM 754 SIX SIGMA APPLICATIONS AGENDA ©The National Graduate School of Quality Management v7 • Day Agenda • Welcome and Introductions • Course Structure  Meeting Guidelines/Course Agenda/Report Out Criteria • Group Expectations • Introduction to Six Sigma Applications • Red Bead Experiment • Introduction to Probability Distributions • Common Probability Distributions and Their Uses • Correlation Analysis ©The National Graduate School of Quality Management v7 • Day Agenda • Team Report Outs on Day Material • Central Limit Theorem • Process Capability • Multi-Vari Analysis ã Sample Size Considerations âThe National Graduate School of Quality Management v7 • Day Agenda • Team Report Outs on Day Material • Confidence Intervals • Control Charts • Hypothesis Testing • ANOVA (Analysis of Variation) • Contingency Tables ©The National Graduate School of Quality Management v7 • Day Agenda • Team Report Outs on Practicum Application • Design of Experiments • Wrap Up - Positives and Deltas ©The National Graduate School of Quality Management v7 • Class Guidelines • Q&A as we go • Breaks Hourly • Homework Readings  As assigned in Syllabus • Grading    Class Preparation 30% Team Classroom Exercises 30% Team Presentations 40%  10 Minute Daily Presentation (Day and 3) on Application of previous days work  20 minute final Practicum application (Last day)  Copy on Floppy as well as hard copy  Powerpoint preferred  Rotate Presenters  Q&A from the class ©The National Graduate School of Quality Management v7 • INTRODUCTION TO SIX SIGMA APPLICATIONS ©The National Graduate School of Quality Management v7 • Learning Objectives • Have a broad understanding of statistical concepts and tools • Understand how statistical concepts can be used to improve business processes • Understand the relationship between the curriculum and the four step six sigma problem solving process (Measure, Analyze, Improve and Control) ©The National Graduate School of Quality Management v7 • What is Six Sigma? Á A Philosophy F F F F Customer Critical To Quality (CTQ) Criteria Breakthrough Improvements Fact-driven, Measurement-based, Statistically Analyzed Prioritization Controlling the Input & Process Variations Yields a Predictable Product Á A Quality Level F 6σ = 3.4 Defects per Million Opportunities Á A Structured Problem-Solving Approach F Phased Project: Measure, Analyze, Improve, Control Á A Program F F F Dedicated, Trained BlackBelts Prioritized Projects Teams - Process Participants & Owners ©The National Graduate School of Quality Management v7 • POSITIONING SIX SIGMA THE FRUIT OF SIX SIGMA Sweet Fruit Design for Manufacturability Process Entitlement Bulk of Fruit Process Characterization and Optimization Low Hanging Fruit Seven Basic Tools Ground Fruit Logic and Intuition ©The National Graduate School of Quality Management v7 • 10 Analysis of a DOE • Calculate the average output for each treatment • Place the average for each treatment after the sign (+ or -) in each cell Treatment A B C AB AC BC ABC AVG +18 +12 +6 +9 -3 -3 -4 -8 + + + + - + + + + - + + + + + + + + + + + + + + + + - 18 18 12 12 6 9 3 3 4 8 RUN1 RUN2 RUN3 ©The National Graduate School of Quality Management v7 • 249 Analysis of a DOE • Add up the values in each column and put the result under the appropriate column This is the total estimated effect of the factor or combination of factors • Divide the total estimated effect of each column by 1/2 the total number of treatments This is the average estimated effect Treatment A B C AB AC BC ABC AVG +18 +12 +6 +9 -3 -3 -4 -8 +18 +12 -6 -9 +3 +3 -4 -8 +18 -12 +6 -9 +3 -3 +4 -8 +18 +12 -6 -9 -3 -3 +4 +8 +18 -12 +6 -9 -3 +3 -4 +8 +18 -12 -6 +9 +3 -3 -4 +8 +18 -12 -6 +9 -3 +3 +4 -8 18 27 6.75 2.25 -1 -0.25 21 5.25 1.75 13 3.25 1.25 SUM AVG 12 3 63 ©The National Graduate School of Quality Management v7 • 250 Analysis of a DOE • These averages represent the average difference between the factor levels represented by the column So, in the case of factor “A”, the average difference in the result output between the + level and the - level is 6.75 • We can now determine the factors (or combination of factors) which have the greatest impact on the output by looking for the magnitude of the respective averages (i.e., ignore the sign) Treatment SUM AVG A B C +18 +18 +18 +12 +12 -12 +6 -6 +6 +9 -9 -9 -3 +3 +3 -3 +3 -3 -4 -4 +4 -8 -8 -8 27 6.75 2.25 -1 -0.25 AB AC BC ABC AVG +18 +12 -6 -9 -3 -3 +4 +8 +18 -12 +6 -9 -3 +3 -4 +8 +18 -12 -6 +9 +3 -3 -4 +8 +18 -12 -6 +9 -3 +3 +4 -8 18 21 5.25 1.75 13 3.25 1.25 63 12 3 This means that the This means that the impact is in the impact is in the following order: following order: A (6.75) A (6.75) AB (5.25) AB (5.25) BC (3.25) BC (3.25) B (2.25) B (2.25) AC (1.75) AC (1.75) ABC (1.25) ABC (1.25) C (-0.25) C (-0.25) âThe National Graduate School of Quality Management v7 ã 251 Analysis of a DOE Ranked Degree of Impact A AB BC B AC ABC C (6.75) (5.25) (3.25) (2.25) (1.75) (1.25) (-0.25) We can see the impact, We can see the impact, but how we know if but how we know if these results are these results are significant or just significant or just random variation? random variation? What tool you What tool you think would be think would be good to use in this good to use in this situation? situation? ©The National Graduate School of Quality Management v7 • 252 Confidence Interval for DOE results Ranked Degree of Impact A AB BC B AC ABC C (6.75) (5.25) (3.25) (2.25) (1.75) (1.25) (-0.25) Confidence Interval Confidence Interval = Effect +/- Error = Effect +/- Error Some of these factors not seem to have much impact We can use them to estimate our error We can be relatively safe using the ABC and the C factors since they offer the greatest chance of being insignificant ©The National Graduate School of Quality Management v7 • 253 Confidence Interval for DOE results Ranked Degree of Impact A AB BC B AC ABC C (6.75) (5.25) (3.25) (2.25) (1.75) (1.25) (-0.25) Confidence = ± tα / , DF (ABC + C ) ∑ DF DF=# of groups used In this case we are using groups (ABC and C) so our DF=2 For α = 05 and DF =2 we find tα/2,df = t.025,2 = 4.303 Confidence Confidence Since only groups meet or exceed Since only groups meet or exceed our 95% confidence interval of +/our 95% confidence interval of +/3.97 We conclude that they are the 3.97 We conclude that they are the only significant treatments only significant treatments Confidence = ± 303 ∑ (1.25 + ( − 25 ) 2 ) Confidence = ±( 4.303)(.9235 ) Confidence = ±3.97 ©The National Graduate School of Quality Management v7 • 254 How about another way of looking at a DOE? What Do I need to to improve my Game? 6σ GUTTER! IMPROVEMENT PHASE Vital Few Variables Establish Operating Tolerances MEASURE - Average = 140.9 ©The National Graduate School of Quality Management v7 • 255 How I know what works for me Lane conditions? Ball type? Wristband? It looks like the lanes are in good condition today, Mark Tim has brought three different bowling balls with him but I don’t think he will need them all today You know he seems to have improved his game ever since he started bowling with that wristband ©The National Graduate School of Quality Management v7 • 256 How I set up the Experiment ? What are all possible Combinations? (Remember Yates Algorithm?) Factor A Factor B Factor C Wristband (+) Wristband (+) Wristband (+) Wristband (+) No Wristband(-) No Wristband(-) No Wristband(-) No Wristband(-) hard ball (+) hard ball (+) soft ball (-) softball (-) hard ball (+) hard ball (+) soft ball (-) softball (-) oily lane (+) dry lane (-) oily lane (+) dry lane (-) oily lane (+) dry lane (-) oily lane (+) dry lane (-) A factor, level full factorial DOE would have 3=8 experimental treatments! Let’s Look at it a different way? ©The National Graduate School of Quality Management v7 • 257 dry lane oily lane hard ball oily lane hard bowling ball wearing a wristband wristband soft ball hard ball no wristband soft ball dry lane hard bowing ball not wearing wrist band This is a Full factorial Let’s look at the data! ©The National Graduate School of Quality Management v7 • 258 What about the Wristband?? Did it help me? dry lane hard ball oily lane 188 183 174 191 158 Average of “with wristband” scores =184 141 wristband soft ball hard ball without wristband 154 159 Higher Scores !! Average of “without wristband” scores =153 soft ball The Wristband appears Better This is called a Main Effect! ©The National Graduate School of Quality Management v7 • 259 What about Ball Type? dry lane hard ball oily lane 188 183 Your best Scores are when: wristband soft ball hard ball no wristband 174 158 191 141 Dry Lane OR Oily Lane 154 Hard Ball Soft Ball 159 soft ball The Ball Type depends on the Lane Condition This is called an Interaction! ©The National Graduate School of Quality Management v7 • 260 Where we go from here? With Wristband and When lane is: use: Dry Hard Ball Oily Soft Ball You’re on your way to the PBA !!! ©The National Graduate School of Quality Management v7 • 261 Where we go from here? Now, evaluate the results using Yates Algorithm What you think? ©The National Graduate School of Quality Management v7 • 262 Learning Objectives • Have a broad understanding of the role that design of experiments (DOE) plays in the successful completion of an improvment project • Understand how to construct a design of experiments • Understand how to analyze a design of experiments • Understand how to interpret the results of a design of experiments ©The National Graduate School of Quality Management v7 • 263 ... Frequency 500 400 30 0 200 σ 100 70 NUMBER OF HEADS SIGMA VALUE (Z) CUM % OF POPULATION 80 90 100 110 120 130 58 65 72 79 86 93 100 107 114 121 128 135 142 -6 -5 -4 -3 -2 -1 0 03 135 2.275 15.87 50.0... 130 ? greater than 130 ? 600 Frequency 500 400 30 0 200 σ 100 70 NUMBER OF HEADS SIGMA VALUE (Z) CUM % OF POPULATION 80 90 100 110 120 130 58 65 72 79 86 93 100 107 114 121 128 135 142 -6 -5 -4 -3 . .. POPULATION 80 90 100 110 120 130 58 65 72 79 86 93 100 107 114 121 128 135 142 -6 -5 -4 -3 -2 -1 0 03 135 2.275 15.87 50.0 84.1 97.7 99.86 99.997 ©The National Graduate School of Quality Management