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Six Sigma is a problem solving tool kit that seeks to improve the quality of processoutputs by identifying and removing the causes of defects (errors) and minimizingvariability in manufacturing and business processes.Six Sigma Green Belts are the tactical leads on improving functions within a jobfunction that are able to apply the Lean Sigma Concepts to their daily work.The methods are universally applicable to anything where a customer is beingserviced. 2
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This is a unique pedagogical approach and from philosophically is quite “meta”. Theobjective under examination is in fact the actor performing the examination.The most brilliant of teacher can write the most profound equation on a chalkboard,and the most diligent of students can take pristine notes. However learning onlyoccurs when the student is able to apply the material. Johann Wolfgang von Goethewas correct when he said “Knowing is not enough; we must apply.”Given the diversity of the composition of the students in terms of education, lifeexperience, income and industry finding a common task in which to apply the LSSwould have been impossible. The only true commonality between the group was thatthey were all humans and wanted to earn their greenbelt. We were able to leveragethis fact in developing the instructional roadmap for course.Also the utilization of Shewhart Control Charts which are used to differentiatebetween common cause and special cause variation, is fairly novel in academicsettings. 3
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The instructor for the course, Brandon Theiss, is a Senior Member of ASQ and aGraduate student at Rutgers University. Currently there is not a course offered in theundergraduate Industrial and Systems Engineering Program at Rutgers. This courseprovided an opportunity for students to not only be exposed to the material but alsoto earn a nationally recognized certification in the tools techniques and methods ofSix Sigma. It represented a first of its kind partnership between the student chapter ofthe IIE and ASQ Princeton section.Part of the proceeds for the course were used to fund the IIE trip to their nationalconference in Orlando. 4
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The cost of the course for students included the textbook and ASQ studentmembershipThe professional rate only included the text.The ASQ Certified Six Sigma Green Belt Requires 3 or more years of work experiencein one of more areas of the Body of Knowledge. There was a very long and at timesheated exchange with the ASQ certification committee about what constitutes workexperience. A compromise was ultimately reached however there were still a largenumber of qualified students that were denied the right to sit for the exam 5
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The course met once per week over an 11 week period from 6:30 to 9:30PM. Therewere two sessions per week and students were free to attend either the Monday orTuesday class based upon which ever was more convenient for their schedule 6
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Students were notified via email prior to the first night of the course that an examwould be administered on the first night.This provided both a baseline for the future improvement as well as showing studentsdirectly the level of mastery they would need to obtain to become certified. 7
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Feedback in any system is critically important. With a course that only meets once perweek, having students wait a week would be to long. By providing studentsimmediate feedback they were able to best utilize their time to study as well as notmis-learn material thinking that they had been correct on a question when in factthey were not. 8
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A simple histogram of the exam results from the Monday section with a normaldistribution fit. It does appear to be normal but has a very large standard deviation11.8% 10
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The probability plot indicates that there is insufficient data to reject the nullhypothesis that the data is normally distributed. This is indicated by the P value whichindicates the probability that the difference between the measured data and themodel occurred by pure chance. The null hypothesis of normality would have beenrejected if the value had been less than alpha (5%) representing a 95% confidencelevel. 11
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It is technically debatable if the test scores are continuous or discrete variable and if aI chart is appropriate. However the point is to introduce students to control chartsand an Individuals chart.Since no point lies about the Upper or Lower Control Limit, the process is in a state of“statistical control”. However common sense shows that this is nonsensical as therange of the limits is between 17% and 95%. This was caused by the large standarddeviation observed.This was used as an opportunity to discuss the difference between statisticalsignificance and actual significance. This reinforces the concept that the math doesnot know where the numbers came from and can at best direct teams to derive thetrue underlying meaning. 12
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Again there is a technical point if the test scores are discrete or continuous. Theabove Process Capability study requires that the data be considered continuous.Process capability is essentially the probability of producing a product that will meetyour customers specification. In this case the passing score (78%) sets that limit. Asyou can see in the above chart for every 1,000,000 students from the Mondaypopulation that took the pre-test exam ~970,000 students will fail. 13
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Everyone has taken a test where the test taker believes there was a question thateither had the wrong answer or was too difficult. By using a NP (or P) control chart,one can easily distinguish if a question was statistically significantly too difficult abovethe UCL or too easy below the LCL 14
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There were several students who handed in their exams very quickly. We wanted tosee if the amount of time a student spent on the exam effected their scores. And forthe Monday data set it appears it did. 15
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Again the data is normal as indicated by a P value greater than 5%. It is howevernotable in the above plot that there is a clear outlier. 18
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Again we can see that there is clearly an outlier in the data set. 19
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The Tuesday process is very similar in its inability to produce a unit meetingcustomers expectations and again will generate ~970,000 failures for every millionstudents from the population that take the exam 20
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In the above graph it does appear that there were questions that a statisticallysignificant number of students got wrong. 21
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Interestingly, the order in which a student turned in their exam did not have an effecton the Tuesday data set. 22
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The above shows a box plot comparing the two classes. The median appears to behigher in the Tuesday class. However is the difference significant? 26
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An ANOVA analysis was performed which results in a very high p value which meansthat there is not a statistically significant difference between the two populationmeans. 27
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Nominal Group -> when individuals over power a groupMulti-Voting -> Reduce a large list of items to a workable number quicklyAffinity Diagram -> Group solutionsForce Field Analysis -> Overcome Resistance to ChangeTree Diagram -> Breaks complex into simpleCause- Effect Diagram -> identify root causes 28
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Most Common Model of group Development was proposed by Bruce Tuckman in1965.In order for the team to grow, to face up to challenges, to tackle problems, to findsolutions, to plan work, and to deliver results. They must go through the cycleFormingTeam members getting to know each otherTrying to please each otherMay tend to agree too much on initial discussion topicsNot much work accomplishedMembers orientation on the team goalsGroup is going through “honeymoon period”StormingVoice their ideaUnderstand project scope and responsibilitiesIdeas and understanding cause conflictNot much work gets accomplishedDisagreement slows down the teamNorming 34
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Resolve own conflictsCome to mutually agreed planSome work gets doneStart to trust each otherPerformingLarge amount of work gets doneSynergy realizedCompetent and autonomous decisions are madeAdjourningTeam is disbanded, restructured or project re-scoped.Regression to Forming stage 34
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There does not appear to be a large change between the Pre Test and the Mid Term 42
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A T-Test indicates that there is significant improvement, as indicated by the one tail Pvalue. 43
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ANOVA on the other hand indicates that there is not a difference between the twomeans. 44
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Displays a histogram of the changes in scores, about 40% of the students went downand 60% increased their score. 45
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This is a somewhat novel adaptation of a C chart that allows for negative values.However there appear to be students that did much better and much worse than theother students. 46
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Looking at a Paired-T test there was absolutely a statistically significant improvement. 47
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Why did the test scores not improve more dramatically? Well the exams cover all ofthe material in the CSSGB BoK the course was only half complete. When we looked atthe material covered up to the midterm on both the pre-test and the mid term theabove pie charts show the percentage of the covered material on each exam. 48
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Not surprisingly students performed better on the material that was covered ascompared to the material that was not covered. 49
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However the students also scored better on that same material on the pre test. 50
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The change in the means indicates a ~8% improvement. However is that statisticallysignificant? 52
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ANOVA does indicates that there is a difference in the means. The students did in factlearn the material that was covered. 53
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There does not appear to be a difference in the scores in the material that was notcovered yet in the course. 54
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There was a small increase in the means ~2% is that significant? 55
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No. There is not a statistically significant difference between the pre-test and mid-term scores on the material that was not covered. As a result it would indicate thatthe exams were roughly the same difficulty. 56
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The process is still incapable of generating a passing score on the test. 57
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Minitab is the de facto industry standard for statistical process control. Unfortunatelythe undergraduate program at Rutgers does not include any training in the softwaresuite. It is fairly intuitive however students needed additional instruction. 58
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Unfortunately, as this courses primary purpose was to act preparation for theGreenbelt Exam a larger focus could not placed on this material. However in anindustrial setting most projects fail in the control phase. Regression to the mean isthe natural trend. Anyone that has ever tried to lose weight or quit smoking knowsthat the trouble is always in sustaining the improvement. 61
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The distribution is in fact bimodal. Unfortunately due to ASQ’s interpretation of themeaning of work, a large number of qualified application were unable to sit for theactual Greenbelt exam and became disenchanted with the course and represent thelower distribution. This assumption was supported by a post hoc online survey. 65
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However the test scores did appear to approve (even with the lower distribution) 66
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And the improvement was very significant as indicated P value of 4.91 x 10^-13 67
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On average the students improved 19.4% only a few students scores decreased, 68
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The Paired T Test Results also confirm that the students test scores improved! 69
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A P Chart was again used to detect difficult questions. 70
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A Pareto Chart above shows the topics that generated that special cause variation inthe prior P chart. 71
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The initial process capability was quite poor, producing defects ~970,000 failures per1,000,0000 72
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The final process capability though still not best in class, is much better, producing475,000 failures per million (the observed is used since the data was already provento be non normal as it is bimodal) 73
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*Actual data has not yet been released for the national average yetAs Confucius says “I hear and I forget. I see and I remember. I do and I understand.” 76
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