1

Six Sigma is a problem solving tool kit that seeks to improve the quality of process outputs by identifying and removing the causes of defects (errors) and minimizing variability in manufacturing and business processes. Six Sigma Green Belts are the tactical leads on improving functions within a job function that are able to apply the Lean Sigma Concepts to their daily work. The methods are universally applicable to anything where a customer is being serviced.

2

This is a unique pedagogical approach and from philosophically is quite “meta”. The objective 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 only occurs when the student is able to apply the material. Johann Wolfgang von Goethe was correct when he said “Knowing is not enough; we must apply.” Given the diversity of the composition of the students in terms of education, life experience, income and industry finding a common task in which to apply the LSS would have been impossible. The only true commonality between the group was that they were all humans and wanted to earn their greenbelt. We were able to leverage this fact in developing the instructional roadmap for course. Also the utilization of Shewhart Control Charts which are used to differentiate between common cause and special cause variation, is fairly novel in academic settings.

3

The instructor for the course, Brandon Theiss, is a Senior Member of ASQ and a Graduate student at Rutgers University. Currently there is not a course offered in the undergraduate Industrial and Systems Engineering Program at Rutgers. This course provided an opportunity for students to not only be exposed to the material but also to earn a nationally recognized certification in the tools techniques and methods of Six Sigma. It represented a first of its kind partnership between the student chapter of the IIE and ASQ Princeton section. Part of the proceeds for the course were used to fund the IIE trip to their national conference in Orlando.

4

The cost of the course for students included the textbook and ASQ student membership The professional rate only included the text. The ASQ Certified Six Sigma Green Belt Requires 3 or more years of work experience in one of more areas of the Body of Knowledge. There was a very long and at times heated exchange with the ASQ certification committee about what constitutes work experience. A compromise was ultimately reached however there were still a large number of qualified students that were denied the right to sit for the exam

5

The course met once per week over an 11 week period from 6:30 to 9:30PM. There were two sessions per week and students were free to attend either the Monday or Tuesday class based upon which ever was more convenient for their schedule

6

Students were notified via email prior to the first night of the course that an exam would be administered on the first night. This provided both a baseline for the future improvement as well as showing students directly the level of mastery they would need to obtain to become certified.

7

Feedback in any system is critically important. With a course that only meets once per week, having students wait a week would be to long. By providing students immediate feedback they were able to best utilize their time to study as well as not mis-learn material thinking that they had been correct on a question when in fact they were not.

8

9

A simple histogram of the exam results from the Monday section with a normal distribution fit. It does appear to be normal but has a very large standard deviation 11.8%

10

The probability plot indicates that there is insufficient data to reject the null hypothesis that the data is normally distributed. This is indicated by the P value which indicates the probability that the difference between the measured data and the model occurred by pure chance. The null hypothesis of normality would have been rejected if the value had been less than alpha (5%) representing a 95% confidence level.

11

It is technically debatable if the test scores are continuous or discrete variable and if a I chart is appropriate. However the point is to introduce students to control charts and 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 the range of the limits is between 17% and 95%. This was caused by the large standard deviation observed. This was used as an opportunity to discuss the difference between statistical significance and actual significance. This reinforces the concept that the math does not know where the numbers came from and can at best direct teams to derive the true underlying meaning.

12

Again there is a technical point if the test scores are discrete or continuous. The above Process Capability study requires that the data be considered continuous. Process capability is essentially the probability of producing a product that will meet your customers specification. In this case the passing score (78%) sets that limit. As you can see in the above chart for every 1,000,000 students from the Monday population that took the pre-test exam ~970,000 students will fail.

13

Everyone has taken a test where the test taker believes there was a question that either 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 above the UCL or too easy below the LCL

14

There were several students who handed in their exams very quickly. We wanted to see if the amount of time a student spent on the exam effected their scores. And for the Monday data set it appears it did.

15

16

A histogram of the Tuesday data set

17

Again the data is normal as indicated by a P value greater than 5%. It is however notable in the above plot that there is a clear outlier.

18

Again we can see that there is clearly an outlier in the data set.

19

The Tuesday process is very similar in its inability to produce a unit meeting customers expectations and again will generate ~970,000 failures for every million students from the population that take the exam

20

In the above graph it does appear that there were questions that a statistically significant number of students got wrong.

21

Interestingly, the order in which a student turned in their exam did not have an effect on the Tuesday data set.

22

23

Combined Histogram of the results

24

Both distributions look somewhat similar.

25

The above shows a box plot comparing the two classes. The median appears to be higher in the Tuesday class. However is the difference significant?

26

An ANOVA analysis was performed which results in a very high p value which means that there is not a statistically significant difference between the two population means.

27

Nominal Group -> when individuals over power a group Multi-Voting -> Reduce a large list of items to a workable number quickly Affinity Diagram -> Group solutions Force Field Analysis -> Overcome Resistance to Change Tree Diagram -> Breaks complex into simple Cause- Effect Diagram -> identify root causes

28

29

30

31

32

33

Most Common Model of group Development was proposed by Bruce Tuckman in 1965. In order for the team to grow, to face up to challenges, to tackle problems, to find solutions, to plan work, and to deliver results. They must go through the cycle Forming Team members getting to know each other Trying to please each other May tend to agree too much on initial discussion topics Not much work accomplished Members orientation on the team goals Group is going through “honeymoon period” Storming Voice their idea Understand project scope and responsibilities Ideas and understanding cause conflict Not much work gets accomplished Disagreement slows down the team Norming

34

Resolve own conflicts Come to mutually agreed plan Some work gets done Start to trust each other Performing Large amount of work gets done Synergy realized Competent and autonomous decisions are made Adjourning Team is disbanded, restructured or project re-scoped. Regression to Forming stage

34

35

36

Control Charts are used to differentiate between common cause (normal) and special cause (abnormal) variation.

37

38

39

40

41

There does not appear to be a large change between the Pre Test and the Mid Term

42

A T-Test indicates that there is significant improvement, as indicated by the one tail P value.

43

ANOVA on the other hand indicates that there is not a difference between the two means.

44

Displays a histogram of the changes in scores, about 40% of the students went down and 60% increased their score.

45

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 the other students.

46

Looking at a Paired-T test there was absolutely a statistically significant improvement.

47

Why did the test scores not improve more dramatically? Well the exams cover all of the material in the CSSGB BoK the course was only half complete. When we looked at the material covered up to the midterm on both the pre-test and the mid term the above pie charts show the percentage of the covered material on each exam.

48

Not surprisingly students performed better on the material that was covered as compared to the material that was not covered.

49

However the students also scored better on that same material on the pre test.

50

So was there actual improvement?

51

The change in the means indicates a ~8% improvement. However is that statistically significant?

52

ANOVA does indicates that there is a difference in the means. The students did in fact learn the material that was covered.

53

There does not appear to be a difference in the scores in the material that was not covered yet in the course.

54

There was a small increase in the means ~2% is that significant?

55

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 that the exams were roughly the same difficulty.

56

The process is still incapable of generating a passing score on the test.

57

Minitab is the de facto industry standard for statistical process control. Unfortunately the undergraduate program at Rutgers does not include any training in the software suite. It is fairly intuitive however students needed additional instruction.

58

59

60

Unfortunately, as this courses primary purpose was to act preparation for the Greenbelt Exam a larger focus could not placed on this material. However in an industrial setting most projects fail in the control phase. Regression to the mean is the natural trend. Anyone that has ever tried to lose weight or quit smoking knows that the trouble is always in sustaining the improvement.

61

62

The above histogram does not quite look normal and has a very large standard deviation 14%.

63

A dot plot again shows a strange pattern.

64

The distribution is in fact bimodal. Unfortunately due to ASQ’s interpretation of the meaning of work, a large number of qualified application were unable to sit for the actual Greenbelt exam and became disenchanted with the course and represent the lower distribution. This assumption was supported by a post hoc online survey.

65

However the test scores did appear to approve (even with the lower distribution)

66

And the improvement was very significant as indicated P value of 4.91 x 10^-13

67

On average the students improved 19.4% only a few students scores decreased,

68

The Paired T Test Results also confirm that the students test scores improved!

69

A P Chart was again used to detect difficult questions.

70

A Pareto Chart above shows the topics that generated that special cause variation in the prior P chart.

71

The initial process capability was quite poor, producing defects ~970,000 failures per 1,000,0000

72

The final process capability though still not best in class, is much better, producing 475,000 failures per million (the observed is used since the data was already proven to be non normal as it is bimodal)

73

74

75

*Actual data has not yet been released for the national average yet

As Confucius says “I hear and I forget. I see and I remember. I do and I understand.”

76

77

78