Table of Contents. Hypothesis Testing Non-Normal Data Part Wrap Up and Action Items Analyze Phase Quiz. 415

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1 Table of Contents Page Define Phase Understanding Six Sigma Six Sigma Fundamentals Selecting Projects Elements of Waste Wrap Up and Action Items Define Phase Quiz.. 83 Measure Phase Welcome to Measure Process Discovery.. 89 Six Sigma Statistics Measurement System Analysis Process Capability Wrap Up and Action Items.224 Measure Phase Quiz Analyze Phase Welcome to Analyze X Sifting Inferential Statistics Introduction to Hypothesis Testing Hypothesis Testing Normal Data Part Hypothesis Testing Normal Data Part Hypothesis Testing Non-Normal Data Part Hypothesis Testing Non-Normal Data Part Wrap Up and Action Items Analyze Phase Quiz. 4 Improve Phase Welcome to Improve Process Modeling Regression.421 Advanced Process Modeling..4 Designing Experiments 467 Experimental Methods. 482 Full Factorial Experiments Fractional Factorial Experiments Wrap Up and Action Items Improve Phase Quiz 552 Control Phase Welcome to Control Lean Controls 559 Defect Controls. 574 Statistical Process Control..586 Six Sigma Control Plans Wrap Up and Action Items Control Phase Quiz Appendix Quiz Answers Glossary

2 3 Understanding Six Sigma What is Six Sigma as a Value? Sigma is a measure of deviation. The mathematical calculation for the Standard Deviation of a population is as shown. Sigma can be used interchangeably with the statistical term Standard Deviation. Standard Deviation is the average distance of data points away from the Mean in a distribution. When measuring the sigma value of a process we want to obtain the distance from the Mean to the closest specification limit in order to determine how many Standard Deviations we are from the mean.our Sigma Level! The Mean being our optimal or desired level of performance. What is Six Sigma as a Measure? By definition, the Standard Deviation is the distance between the mean and the point of inflection on the normal curve. Point of Inflection The probability of creating a defect can be estimated and translated into a Sigma level The higher the sigma level, the better the performance. Six Sigma refers to a process having six Standard Deviations between the average of the process center and the closest specification limit or service level. This pictorial depicts the percentage of data which falls between Standard Deviations within a Normal Distribution. Those data points at the outer edge of the bell curve represent the greatest variation in our process. They are the ones causing customer dissatisfaction and we want to eliminate them.

3 167 Six Sigma Statistics Jitter Example By using the Jitter function we will spread the data apart making it easier to see how many data points there are. This gives us relevance so we don t have points plotted on top of each other. Once your graph is created, click once on any of the data points (that action should select all the data points). Then go to MINITAB menu path: Editor> Edit Individual Symbols Jitter Increase the jitter in the x-direction to.075, click OK, then click anywhere on the graph except on the data points to see the results of the change Individual Value Plot of Weibull, Normal, Bi Modal Data Weibull Normal Bi Bi Modal Time Series Plot Using the MINITAB worksheet Graphing Data.mtw. A Time Series is created by following the MINITAB menu path Graph> Time Series Plot> Simple... Time series plots allow you to examine data over time. Depending on the shape and frequency of patterns in the plot, several X s can be found as critical or eliminated. Graph> Time Series Plot> Simple Time Series Plot of Time 1 Time Series Plots are very useful in most projects. Every project should provide time series data to look for frequency, magnitude and patterns. What X would cause these issues? Time Index

4 274 Inferential Statistics Sample Size and the Mean W hen taking a sample w e have only estimated the true Mean: All we know is that the true Mean lies somewhere within the theoretical distribution of sample Means or the t-distribution which are analyzed using t-tests. T-tests measure the significance of differences between Means. Theoretical distribution of sa mple M ea ns for n = 2 Theoretical distribution of sa mple M ea ns for n = 1 0 Distribution of individuals in the population Standard Error of the Mean The Standard Deviation for the distribution of Means is called the standard error of the Mean and is defined as: ThisformulashowsthattheMeanismorestablethanasingle shows the more stable than a single observation by a factor of the square root of the sample size.

5 460 Advanced Process Modeling Flight Regression Example Matrix Plot Now we are given a fairly confusing graph of outputs and inputs to interpret. Do not be discouraged, this is just a plethora of sporadically plotted, outputs and inputs, flight speeds vs. altitudes. Seeing at least two input having correlation shows the necessity to continue with a Multiple Linear Regression. The lower half has identical data as the upper half of the outputs just the axis are not reversed. Look for plots that show correlation. Output Response Matrix Plot of of Flight Speed, Altitude, Turbine Angl, Fuel/Air rat, Flight Flight Speed Speed Altitude Altitude Turbine Angle 34.5 Turbine Angle Fuel/Air ratio Fuel/Air ratio ICR ICR Temp Temp Since 2 or more predictors show correlation, run MLR. Predictors Flight Regression Example Best Subsets Best Subsets Regression: Flight Speed versus Altitude, Turbine Angl,... Response is Flight Speed F T u u e r l b / i A A n i l e r t i A r t n a T u g t I e Mallows d l i C m Vars R-Sq R-Sq(adj) C-p S e e o R p X X X X X X X X X X X X X X X X X X X X X X X X X In MINITAB TM using Best Subsets Regression command is efficient and powerful by loading all inputs to a single output; we use the Free predictors: box and place all inputs of interest inside it. This particular command can be helpful in other circumstances, however, now by placing the output column of data in the Response: box it should be on the right of your screen. This is very simple, evaluation is done and results are given to you in rows; 1st column - # of variables, 2nd column - R squared, 3rd column - R squared adjusted, 4th column is mallows Cp, 5th column - Standard Deviation of the model error and finally the 6th column - input variables.

6 614 Statistical Process Control Pre-Control Charts Pre-Control Charts use limits relative to the specification limits. This is the first and ONLY chart you will see specification limits plotted for statistical process control. This is the most basic type of chart and unsophisticated use of process control RED Yellow GREEN Yellow Red LSL Target USL Red Zones. Zone outside the specification limits. Signals the process is out-of-control and should be stopped Yellow Zones. Zone between the PC Lines and the specification limits, indicates caution and the need to watch the process closely Green Zone. Zone lies between the PC Lines, signals the process is in control The Pre-Control Charts are often used for startups with high scrap cost or low production volumes between setups. Pre-Control Charts are like a stoplight are the easiest type of SPC to use by operators or staff. Remember Pre-Control Charts are to be used ONLY for outputs of a process. Another approach to using Pre-Control Charts is to use process capability to set the limits where yellow and red meet. Process Setup and Restart with Pre-Control Qualifying i Process To qualify a process, five consecutive parts must fall within the green zone The process should be qualified after tool changes, adjustments, new operators, material changes, etc Monitoring Ongoing Process Sample two consecutive parts at predetermined frequency If either part is in the red, stop production and find reason for variation W hen one part falls in the yellow zone inspect the other and If the second part falls in the green zone then continue If the second part falls in the yellow zone on the same side, make an adjustment to the process If second part falls in the yellow zone on the opposite side or in the red zone, the process is out of control and should be stopped If any part falls outside the specification limits or in the red zone, the process is out of control and should be stopped

7 Quiz Sample Questions

8 1 Quiz Sample Define Sample What item(s) below best describes variation in a process? (check all that apply) A. Points not centrally located outside the Mean B. A cluster of outcomes located at one Central Point C. How tightly all the various outcomes are clustered around the average D. The overall calculated point cluster to the right of the Mean Measure Sample A Black Belt was entering data into MINITABTM. The data being entered is the name of the countries that his company supplies product to. This is an example of: A. Nominal Scale Data B. Ration Scale Data C. Continuous Data D. Ordinal Scale Data Analyze Sample Contingency Tables are used to test for association (or dependency) between two or more classifications. True False Improve Sample Which statements are true about Experimental Designs? (check all that apply) A. Experimental designs include RSM, full factorials and fractional factorials. B. If an Experimental Design was created with no replicates on the Corner Points and Center Points were added, the number of experimental runs is larger than the same design without Center Points. C. Fractional factorial designs have too few runs to obtain a mathematical expression between the output(s) of interest and the statistically significant inputs. D. A fractional factorial or full factorial 2-level design can give the experimenter a mathematical expression between the output(s) of interest and the statistically significant inputs. E. All fractional factorial designs for experiments with 7 or fewer factors have some aliasing or confounding. F. A resolution III design is an appropriate design for optimizing a process. G. An Experimental Design should not have more than one output because of the difficulty in selecting factor levels. Control Sample SPC is an excellent tool for telling us why a process is exhibiting Special Cause variation. True False Certified Lean Six Sigma Green Belt Book