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OSSS Black Belt Training Manual Table of Contents Page Define Phase Understanding Six Sigma…………………………………………………..….…….… 1 Six Sigma Fundamentals………………………………..…………………..……..…. 22 Selecting Projects………………………………………………………..……..……… 42 Elements of Waste………………………………………...……………………………64 Wrap Up and Action Items……………………………………………………….……77 Measure Phase Welcome to Measure…………………………………………………….……..….....83 Process Discovery………………………………………………………………………86 Six Sigma Statistics…………………………….………………………………….….135 Measurement System Analysis……………………………………………………....168 Process Capability ………………………………………………………… ……….200 Wrap Up and Action Items ………………………………………………………….221 Analyze Phase Welcome to Analyze…………………………………………………………… .…..227 “X” Sifting………………………………….…………………………….……….….230 Inferential Statistics…………………………………………………..………….…….256 Introduction to Hypothesis Testing…………………………….…………………….271 Hypothesis Testing Normal Data Part 1……………………………..………………285 Hypothesis Testing Normal Data Part 2 ……………………………………….……328 Hypothesis Testing Non-Normal Data Part 1………………………………….……358 Hypothesis Testing Non-Normal Data Part 2……………………………………….384 Wrap Up and Action Items ………………………………………………....……..403 Improve Phase Welcome to Improve…………………………………………………………...…..409 Process Modeling Regression……………………………………………………….412 Advanced Process Modeling……………………………………………………….431 Designing Experiments………………………………………………………………458 Experimental Methods………………………………………………………………473 Full Factorial Experiments………………………………………………………..…488 Fractional Factorial Experiments…………………………………………….……..517 Wrap Up and Action Items…………………………………………………………537 Control Phase Welcome to Control…………………………………………………………………543 Lean Controls…………………………………………………………………………546 Defect Controls…………………………………………………………….…………561 Statistical Process Control…………………………………………………………….573 Six Sigma Control Plans………………………………………………………………613 Wrap Up and Action Items……………………………………………………….…633 Glossary OSSS LSS Black Belt Manual Copyright OpenSourceSixSigma.com 409 Lean Six Sigma Black Belt Training ImproveImprove PhasePhase DesigningDesigning ExperimentsExperiments Now we are going to continue with the Improve Phase “Designing Experiments”. OSSS LSS Black Belt Manual Copyright OpenSourceSixSigma.com 410 Designing Experiments Overview Within this module we WelcomeWelcome toto ImproveImprove will provide an ProcessProcess Modeling:Modeling: RegressionRegression introduction to Design of AdvancedAdvanced ProcessProcess Modeling:Modeling: Experiments, MLRMLR ReasonsReasons forfor ExperimentsExperiments explain what they are, how DesigningDesigning ExperimentsExperiments GraphicalGraphical AnalysisAnalysis they work and when to use DOEDOE MethodologyMethodology them. ExperimentalExperimental MethodsMethods FullFull FactorialFactorial ExperimentsExperiments FractionalFractional FactorialFactorial ExperimentsExperiments WrapWrap UpUp && ActionAction ItemsItems Project Status Review • Understand our problem and it’s impact on the business. (Define) • Established firm objectives/goals for improvement. (Define) • Quantified our output characteristic. (Define) • Validated the measurement system for our output characteristic. (Measure) • Identified the process input variables in our process. (Measure) • Narrowed our input variables to the potential “X’s” through Statistical Analysis. (Analyze) • Selected the vital few X’s to optimize the output response(s). (Improve) • Quantified the relationship of the Y’s to the X’s with Y=f(x). (Improve) OSSS LSS Black Belt Manual Copyright OpenSourceSixSigma.com 411 Designing Experiments Six Sigma Strategy O s u liers Cu ut SIPOC t Supp st p p om In VOC u Co e Project Scope ts nt E rs rac mploy tors ees (X1) (X11) P-Map, XY, FMEA (X2) (X3) (X4) (X8) (X9) Capability (X6) (X7) (X5) (X10) Box Plot, Scatter (X3) (X4) (X1) (X11) Plots, Regression (X8) (X2) (X5) Fractional Factorial Full Factorial (X5) (X3) Center Points (X11) (X4) This is reoccurring awareness. By using tools we filter the variables of defects. When talking of the Improve Phase in the Six Sigma methodology we are confronted by many designed experiments; transactional, manufacturing, research. Reasons for Experiments The Analyze Phase narrowed down the many inputs to a critical few, now it is necessary to determine the proper settings for the vital few inputs because: – The vital few potentially have interactions. – The vital few will have preferred ranges to achieve optimal results. – Confirm cause and effect relationships among factors identified in analyze phase (e.g. regression) Understanding the reason for an experiment can help in selecting the design and focusing the efforts of an experiment. Reasons for experimenting are: – Problem Solving (Improving a process response) – Optimizing (Highest yield or lowest customer complaints) – Robustness (Constant response time) – Screening (Further screening of the critical few to the vital few X’s) Design where you’re going - be sure you get there! Designs of Experiments help the Belt to understand the cause and effect between the process output or outputs of interest and the vital few inputs. Some of these causes and effects may include the impact of interactions often referred to synergistic or cancelling effects. OSSS LSS Black Belt Manual Copyright OpenSourceSixSigma.com 412 Designing Experiments Desired Results of Experiments Designed experiments Problem Solving allows us to – Eliminate defective products or services. describe a – Reduce cycle time of handling transactional processes. mathematical Optimizing relationship – Mathematical model is desired to move the process response. between the inputs and outputs. – Opportunity to meet differing customer requirements (specifications or However, often VOC). the mathematical Robust Design equation is not – Provide consistent process or product performance. necessary or used – Desensitize the output response(s) to input variable changes including depending on the NOISE variables. focus of the – Design processes knowing which input variables are difficult to maintain. experiment. Screening – Past process data is limited or statistical conclusions prevented good narrowing of critical factors in Analyze Phase When it rains it PORS! DOE Models vs. Physical Models Here we have models that are the result of designed experiments. Many have difficulty determining DOE models from that of physical models. A physical model includes: biology, chemistry, physics and usually many variables, typically using complexities and calculus to describe. The DOE model doesn’t include any variables or complex calculus: it includes most important variables and shows variation of data collected. DOE will focus on the specific region of interest. What are the differences between DOE modeling and physical models? – A Physical model is known by theory using concepts of physics, chemistry, biology, etc... – Physical models explain outside area of immediate project needs and include more variables than typical DOE models. – DOE describes only a small region of the experimental space. The objective is to minimize the response. The physical model is not important for our business objective. The DOE Model will focus in the region of interest. OSSS LSS Black Belt Manual Copyright OpenSourceSixSigma.com 413 Designing Experiments Definition for Design of Experiments Design of Experiments (DOE) is a scientific method of Design of Experiment shows planning and conducting an experiment that will yield the cause and effect the true cause-and-effect relationship between the X relationship of variables of variables and the Y variables of interest. interest X and Y. By way of input variables, designed DOE allows the experimenter to study the effect of many input variables that may influence the product or process experiments have been simultaneously, as well as possible interaction effects (for noted within the Analyze example synergistic effects). Phase then are executed in the Improve Phase. DOE The end result of many experiments is to describe the tightly controls the input results as a mathematical function. variables and carefully y = f (x) monitors the uncontrollable The goal of DOE is to find a design that will produce the variables. information required at a minimum cost. Properly designed DOE’s are more efficient experiments. One Factor at a Time is NOT a DOE Let’s assume a Belt has found One Factor at a Time (OFAT) is an experimental style but not a in the Analyze Phase that planned experiment or DOE. pressure and temperature The graphic shows yield contours for a process that are impact his process and no unknown to the experimenter. Trial Temp Press Yield one knows what yield is Yield Contours Are 1 125 30 74 achieved for the possible Unknown To Experimenter 75 2 125 31 80 3 125 32 85 temperature and pressure 4 125 33 92 combinations. 80 5 125 34 86 6 130 33 85 7 120 33 90 If a Belt inefficiently did a 135 85 6 130 One Factor at a Time 90 1 2 3 4 5 Optimum identified experiment (referred to as 125 95 with OFAT Pressure (psi) Pressure 120 OFAT), one variable would 7 be selected to change first while the other variable is True Optimum available 30 31 32 33 34 35 with DOE held constant, once the Temperature (C) desired result was observed, the first variable is set at that level and the second variable is changed. Basically, you pick the winner of the combinations tested. The curves shown on the graph above represent a constant process yield if the Belt knew the theoretical relationships of all the variables and the process output of pressure. These contour lines are familiar if you’ve ever done hiking in the mountains
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