【正文】 importance to the potential variables (X’ s) identified in step A2 ? Purpose ? General a list of important factors (vital few) from the potential variables. Y = f [(x1,x2,x3) (x4,x5,… .,xn)] Vital Few Trivial Many ? Pareto Analysis Rot tenBr ui sedUnder si zedOt her s2 3 5 1 0 0 8 7 1 95 3 . 3 2 2 . 7 1 9 . 7 4 . 3 5 3 . 3 7 6 . 0 9 5 . 7 1 0 0 . 005 01 0 01 5 02 0 02 5 03 0 03 5 04 0 04 5 002 04 06 08 01 0 0D e f e c tC o u n tP e r c e n tC u m %PercentCountP a r e t o C h a r t f o r C A T E G O R I E S? Correlation Analysis ? A statistical analysis to investigate / measurement of association between two variables (X, Y) is called analysis. ? Correlation tells you the trend of Y when X value increase/decrease. ? Correlation Analysis using Scatter Diagram Analysis. ? Correlation coefficient indicates closeness of a relationship between X and Y. ? Regression Analysis (1) Y = f (x1, x2, x3,… ) Status and characteristics of a process Modeling Mathematical equation X Y ? Regression Analysis (2) ? Types of Regression Model ? Simple linear regression ? Multiple linear regression ? Nonlinear regression Y = f(X) Y: dependent variable X: independent variable ? Types of Hypothesis Test Types of Data Discrete Data Continuous Data Mean Test ◎ t –Test ◎ ANOVA Variance Test ◎ F –Test ◎ Chi Square . DMAIC Methodology 5 Stages DMAIC Methodology and Statistical Tools ? Phase: Improve ? Steps。 ? Benchmarking, Entitlement, KANO ? A2 Identify Potential Causes。 (5)Tail asymptotic to Xaxis； (6) Bell shaped； (7) Mean = Median = Mode (8) Total area under curve = 1 (1) The normal distribution has the following properties. ◎ % of the data fall within ?1? ◎ % of the data fall within ?2? ◎ % of the data fall within ?3? (2) In order to assess the quality of the process, we must pare the process characteristics (via the location, spread and shape) to the specification limits and targeted value. ? Continuous Data(3) ? Standardization of Normal Distribution ? The Sigma of a Process is the number of standard deviation between the mean and the Specification Limits. 1 ? Z = (X?)/? No. of standard deviation USL Sigma of the process Z = ? Measurement System and Measurement Error(1) ? Measurement system is viewing as a process. ? Sources of variation: 5M1E ? Validate possible sources of variation in the measurement process P e r s o n n e lM a c h i n e sM a t e r i a l sM e t h o d sM e a s u r e m e n t sE n v i r o n m e n tC a u s e a n d E f f e c t D i a g r a mVariation in measurement System ? Measurement System and Measurement Error(2) Average m (Total) = m (Product) + m(Measurement) Variability s2 (Total) = s2 (Product) + s2(Measurement) Deflection of measurement system (To be decided by calibration) Variation of measurement system (To be decided by RR assessment) ? Process Variance Observed Process Variation Actual Process Variation Measurement Variation Long term process variation Short term process variation Variation within a sample Variation due to operators Variation due to gage Reproducibility Linearity Stability Repeatability Accuracy ? Gage RR Analysis ? Types of Gage RR Analysis Methodology ◎ X bar R Method ◎ ANOVA Types of Variation estimation by the Gage RR ◎ Equipment Variation: EV ◎ Appraiser (Operator): AV ? GRR Decision and Improvement Direction ? Gage RR Decision Criteria ? %GRR ? 10% (Good measurement system) ? 10% ? %GRR ? 30% (May be used) ? %GRR ? 30% (Can not used) ? Gage improvement direction For repeatability error ? reproducibility error ? (Need to taken an action to operator) For reproducibility error ? repeatability error ? (Need to taken an action to gage) ? M3 Identify Sigma Level ? M3 step covers the followings: ? Data stratification ? Graphical cause elimination ? Understand product capability and product performance ? Calculate current sigma level ? Graphical Analysis ◎ Run Chart ◎ Scatter Diagram ◎ Box Plot ◎ Histogram ? Changes to the process may be more easily recognized graphically than tabularly. ? Understanding Variation ? What is Variation? ◎ Different oute of a process or result of a product or service ? Measurement index scattered from center value ? Variation will be appeared in every process and the target of improvement is to reduce it’ s variations ? Why a variation might be occurred? ◎ By a mon cause ◎ By a special cause ◎ 5M1E ? What impacts will be happened if a variation bee big? ? Can not predict/ forecas