1、,QSM 754SIX SIGMA APPLICATIONS AGENDA,Day 1 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

2、and Their Uses Correlation Analysis,Day 2 Agenda,Team Report Outs on Day 1 Material Central Limit Theorem Process Capability Multi-Vari Analysis Sample Size Considerations,Day 3 Agenda,Team Report Outs on Day 2 Material Confidence Intervals Control Charts Hypothesis Testing ANOVA (Analysis of Variat

3、ion) Contingency Tables,Day 4 Agenda,Team Report Outs on Practicum Application Design of Experiments Wrap Up - Positives and Deltas,Class Guidelines,Q the mean, the median and the mode.,WHAT IS THE MEAN?,WHAT IS THE MEDIAN?,WHAT IS THE MODE?,MEASURES OF CENTRAL TENDENCY, SUMMARY,SO WHATS THE REAL DI

4、FFERENCE?,SO WHATS THE BOTTOM LINE?,COIN TOSS POPULATION DISPERSION,WHAT IS THE RANGE?,WHAT IS THE VARIANCE/STANDARD DEVIATION?,MEASURES OF DISPERSION,SAMPLE MEAN AND VARIANCE EXAMPLE,SO WHATS THE REAL DIFFERENCE?,SO WHATS THE BOTTOM LINE?,SO WHAT IS THIS SHIFT DF=(r-1)x(c-1). In our case, we have 3

5、 columns (c) and 2 rows (r) so our DF = (2-1)x(3-1)=1x2=2. The second piece of data is the risk. Since we are looking for .95 (95%) confidence (and a risk = 1 - confidence) we know the a risk will be .05. In the c2 table , we find that the critical value for a = .05 and 2 DF to be 5.99. Therefore, o

6、ur c2CRIT = 5.99 Our calculated c2 value is the sum of the individual cell c2 values. For our example this is .04+.18+.27+.25+.81+1.20=2.75. Therefore, our c2CALC = 2.75. We now have all the pieces to perform our test. Our Ho: is c2CALC c2CRIT . Is this true? Our data shows 2.755.99, therefore we fa

7、il to reject the null hypothesis that there is no significant difference between the vendor performance in this area.,Contingency Table Exercise,We have a part which is experiencing high scrap. Your team thinks that since it is manufactured over 3 shifts and on 3 different machines, that the scrap c

8、ould be caused (Y=f(x) by an off shift workmanship issue or machine capability. Verify with 95% confidence whether either of these hypothesis is supported by the data.,Construct a contingency table of the data and interpret the results for each data set.,Learning Objectives,Understand how to use a c

9、ontingency table to support an improvement project. Understand the enabling conditions that determine when to use a contingency table. Understand how to construct a contingency table. Understand how to interpret a contingency table.,DESIGN OF EXPERIMENTS (DOE) FUNDAMENTALS,Learning Objectives,Have a

10、 broad understanding of the role that design of experiments (DOE) plays in the successful completion of an improvement 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.,

11、Why do we Care?,Design of Experiments is particularly useful to: evaluate interactions between 2 or more KPIVs and their impact on one or more KPOVs. optimize values for KPIVs to determine the optimum output from a process.,IMPROVEMENT ROADMAPUses of Design of Experiments,KEYS TO SUCCESS,So What Is

12、a Design of Experiment?,where a mathematical reasoning can be had, its as great a folly to make use of any other, as to grope for a thing in the dark, when you have a candle standing by you. Arbuthnot,A design of experiment introduces purposeful changes in KPIVs, so that we can methodically observe

13、the corresponding response in the associated KPOVs.,Design of Experiments, Full Factorial,Variables Input, Controllable (KPIV) Input, Uncontrollable (Noise) Output, Controllable (KPOV),How do you know how much a suspected KPIV actually influences a KPOV? You test it!,Design of Experiments, Terminolo

14、gy,Mathematical objects are sometimes as peculiar as the most exotic beast or bird, and the time spent in examining them may be well employed. H. Steinhaus,Main Effects - Factors (KPIV) which directly impact output Interactions - Multiple factors which together have more impact on process output tha

15、n any factor individually. Factors - Individual Key Process Input Variables (KPIV) Levels - Multiple conditions which a factor is set at for experimental purposes Aliasing - Degree to which an output cannot be clearly associated with an input condition due to test design. Resolution - Degree of alia

16、sing in an experimental design,DOE Choices, A confusing array.,Full Factorial Taguchi L16 Half Fraction 2 level designs 3 level designs screening designs Response surface designs etc.,For the purposes of this training we will teach only full factorial (2k) designs. This will enable you to get a basi

17、c understanding of application and use the tool. In addition, the vast majority of problems commonly encountered in improvement projects can be addressed with this design. If you have any question on whether the design is adequate, consult a statistical expert.,Mumble, Mumble, blackbelt, Mumble, sta

18、tistics stuff.,The Yates Algorithm Determining the number of Treatments,One aspect which is critical to the design is that they be “balanced”. A balanced design has an equal number of levels represented for each KPIV. We can confirm this in the design on the right by adding up the number of + and -

19、marks in each column. We see that in each case, they equal 4 + and 4- values, therefore the design is balanced.,Yates algorithm is a quick and easy way (honest, trust me) to ensure that we get a balanced design whenever we are building a full factorial DOE. Notice that the number of treatments (uniq

20、ue test mixes of KPIVs) is equal to 23 or 8. Notice that in the “A factor” column, we have 4 + in a row and then 4 - in a row. This is equal to a group of 22 or 4. Also notice that the grouping in the next column is 21 or 2 + values and 2 - values repeated until all 8 treatments are accounted for. R

21、epeat this pattern for the remaining factors.,The Yates Algorithm Setting up the Algorithm for Interactions,Now we can add the columns that reflect the interactions. Remember that the interactions are the main reason we use a DOE over a simple hypothesis test. The DOE is the best tool to study “mix”

22、 types of problems.,You can see from the example above we have added additional columns for each of the ways that we can “mix” the 3 factors which are under study. These are our interactions. The sign that goes into the various treatment boxes for these interactions is the algebraic product of the m

23、ain effects treatments. For example, treatment 7 for interaction AB is (- x - = +), so we put a plus in the box. So, in these calculations, the following apply: minus (-) times minus (-) = plus (+) plus (+) times plus (+) = plus (+) minus (-) times plus (+) = minus (-)plus (+) times minus (-) = minu

24、s (-),Yates Algorithm Exercise,We work for a major “Donut & Coffee” chain. We have been tasked to determine what are the most significant factors in making “the most delicious coffee in the world”. In our work we have identified three factors we consider to be significant. These factors are coffee b

25、rand (maxwell house vs chock full o nuts), water (spring vs tap) and coffee amount (# of scoops).,Use the Yates algorithm to design the experiment.,Select the factors (KPIVs) to be investigated and define the output to be measured (KPOV). Determine the 2 levels for each factor. Ensure that the level

26、s are as widely spread apart as the process and circumstance allow. Draw up the design using the Yates algorithm.,So, How do I Conduct a DOE?,Determine how many replications or repetitions you want to do. A replication is a complete new run of a treatment and a repetition is more than one sample run

27、 as part of a single treatment run. Randomize the order of the treatments and run each. Place the data for each treatment in a column to the right of your matrix.,So, How do I Conduct a DOE?,Calculate the average output for each treatment. Place the average for each treatment after the sign (+ or -)

28、 in each cell.,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 e

29、stimated effect.,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 combina

30、tion of factors) which have the greatest impact on the output by looking for the magnitude of the respective averages (i.e., ignore the sign).,Analysis of a DOE,This means that the impact is in the following order: A (6.75) AB (5.25) BC (3.25) B (2.25) AC (1.75) ABC (1.25) C (-0.25),Analysis of a DO

31、E,Confidence Interval for DOE results,Confidence Interval for DOE results,IMPROVEMENT PHASE Vital Few Variables Establish Operating Tolerances,How about another way of looking at a DOE?,It looks like the lanes are in good condition today, Mark. Tim has brought three different bowling balls with him but I dont think he will need them all today. You know he seems to have improved his game ever since he started bowling with that wristband.,How do I know what works for me. Lane conditions? Ball type? Wristband?,How do I set up the Experiment ?,Facto