rutgers governor school - six sigma
DESCRIPTION
Presentation for Rutgers Governor School 7/25/2012TRANSCRIPT
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Rutgers Governor School
Introduction
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Goals for Today
Show you to see and (perhaps) solve problems differently
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About Me• Academics
– MS Industrial Engineering Rutgers University – BS Electrical & Computer Engineering Rutgers University – BA Physics Rutgers University
• Professional– Principal Industrial Engineer -Medrtonic– Master Black belt- American Standard Brands– Systems Engineer- Johnson Scale Co
• Awards– ASQ Top 40 Leader in Quality Under 40
• Certifications– ASQ Certified Manager of Quality/ Org Excellence Cert # 13788 – ASQ Certified Quality Auditor Cert # 41232 – ASQ Certified Quality Engineer Cert # 56176 – ASQ Certified Reliability Engineer Cert #7203 – ASQ Certified Six Sigma Green Belt Cert # 3962– ASQ Certified Six Sigma Black Belt Cert # 9641– ASQ Certified Software Quality Engineer Cert # 4941
• Publications– Going with the Flow- The importance of collecting data without holding up your processes- Quality Progress March
2011– "Numbers Are Not Enough: Improved Manufacturing Comes From Using Quality Data the Right Way" (cover story).
Industrial Engineering Magazine- Journal of the Institute of Industrial Engineers September (2011): 28-33. Print
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Agenda9:00 9:30 Introduction9:30 10:00 Define
10:00 10:30 What Makes a Quality Cup of Coffee10:30 11:00 Measuring Coffee11:00 11:30 Analyze11:30 12:00 Making Control Charts12:00 12:30 Lunch12:30 13:00 Lunch13:00 13:30 The Process13:30 14:00 Mapping the Process14:00 14:30 Hypothesis Testing14:30 15:00 Conclusion
Todays slides are available at http://www.slideshare.net/brtheiss/rutgers-governor-school
Also Please Complete the Online Feedback Surveyhttps://www.surveymonkey.com/s/93CJQCV
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So Lets Get Moving
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What is Industrial Engineering?
• is a branch of engineering dealing with the optimization of complex processes or systems.
• “Engineers make things. Industrial engineers make things better.”
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What is a Process?• Formal Definition
– A systematic series of actions directed to some end• Practical Definition
– Any Verb Noun Combination • Eat Sandwich• Read Book• Attend Conference
• Implications of Practical Definition– Same Tools Techniques and Methods of the Lean Six Sigma
Methodologies can be used for virtually anything
Inputs• People• Materials• Methods• Mother Nature• Management• Measurement
System
Process• Sequence of
Value Added Steps
Outputs• Products
• Hardware• Software• Systems• People
• Services
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So How do Make “it” Better
• Statistics• Lean• Six Sigma• Modeling
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Types of Statistics
• Descriptive Statistics– Present data in a way that will facilitate
understanding• Inferential Statistics
– Analyze sample data to infer properties of the population from which the sample is drawn
• Statistical Significance Does not Mean actual significance.– (See US Supreme Court Matrixx Initiatives, Inc. v.
Siracusano
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Population Parameters
p̂x
Size = N
Mean = mStd. Dev. = sProportion = p
Sample StatisticsSample Statistics
Size = n Mean = Std. Dev.= s Prop. =
Key Descriptive Statistical Terms
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Lean Tool Kit
• 5S- – Sort– Straighten– Shine– Standardize– Sustain
• Value Stream Mapping• Kanban• Poka-yoke• Kaizen <- mean continuous improvement
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Six Sigma Tool Kit
• DMAIC– Define– Measure– Analyze– Improve– Control
• SIPOC Diagrams • Statistical Process Control • 5 Whys
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Modeling
• A mathematical model is a description of a system using mathematical concepts and language.
5000004000003000002000001000000
25
20
15
10
5
0
Time
Frequency
Shape 2.007Scale 216106N 94
Histogram of TimeWeibull
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The analogy
The task is to undo a bolt.
Solution 1- Ratchet and Socket
Solution 2- Open Ended /Box Wrench
Solution 3- Vice Grips
Which is Correct?
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The Answer
• It depends.– There are certain applications that demand a open
ended wrench– Others require a socket– Finally there are situations that require vice grips
• Most cases all three solutions will work• The same is true for solving Industrial
Engineering problems
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A History Lesson
Six Sigma
Mid-1900s: Shewhart and Deming advocate PDCA methodology 1980’s: Motorola developed MAIC method for reducing defects in it’s
products. Won the Baldrige Quality Award in 1988. GE applies Six Sigma to non manufacturing
1990’s-2000’s: Siemens, Allied Signal and others drive 6 Sigma DMAIC top-down. Companies in many industries practice Six Sigma, some successfully, some not (MDT dabbled in early 1990’s).
Lean
Mid 1800’s: Interchangeable parts 1913: Moving assembly line at Ford Post-WW2: Toyota Develops a Production System (TPS). 1996: James Womack documents general application of TPS and for
any organization and calls it “Lean Thinking”.
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People to Know• William Edwards Deming (October 14, 1900 – December 20, 1993) "There
is no substitute for knowledge.“ – emphasis on total quality management
• Joseph Moses Juran (December 24, 1904 – February 28, 2008) "It is most important that top management be quality-minded. In the absence of sincere manifestation of interest at the top, little will happen below."
- Managing for Quality• Taiichi Ohno (February 29, 1912 – May 28, 1990) -Toyota
– Production System (TPS)- Just in Time (JIT)• Walter Andrew Shewhart ( March 18, 1891 - March 11, 1967) -"Dr.
Shewhart prepared a little memorandum only about a page in length. About a third of that page was given over to a simple diagram which we would all recognize today as a schematic control chart.”– Control Charts
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What is Six Sigma?
• Six Sigma 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.
• It uses a set of quality management methods, including statistical methods, and creates a special infrastructure of people within the organization ("Black Belts", "Green Belts", etc.) who are experts in these methods.
• Each Six Sigma project carried out within an organization follows a defined sequence of steps (DMAIC) and has quantified financial targets (cost reduction and/or profit increase).
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What is Sigma (s)?
4 Definitions:
A letter in the Greek alphabet s
A statistical measure of variation (standard deviation)
A measure of a process defect level
Six Sigma - an improvement methodology (DMAIC)
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Normal Distribution
• Also known as Gaussian, Laplace–Gaussian or standard error curve
• First proposed by de Moivre in 1783• Independently in 1809 by Gauss
All Normal Distributions Defined by two things1. The Average µ2. The Standard Deviation σ
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Area Under the Curve
(c) Probabilities and numbers of standard deviations
Shaded area = 0.683 Shaded area = 0.954 Shaded area = 0.997
68% chance of fallingbetween and
95% chance of fallingbetween and
99.7% chance of fallingbetween and
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Effect of Changing Parameters
160 180 200140 160 180
shifts the curve along the axis
200 140
2 =174
2 = 61 =1 = 6
2 = 12
2 =1701 =
increases the spread and flattens the curve
(a) Changing (b) Increasing
1 = 160
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What is Process Sigma?
A 3s process (3 standard deviations fit between target and spec)
MeanCustomerSpecification
1s
2s
3s
3s
Defects
Before
Mean CustomerSpecification
After2s
6s
6sNo Defects!1s
3s4s
5s
A 6s process
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So what are we going to do?
• We are going to apply DMAIC (Define Measure Analyze Improve Control) to the experience of going to Starbucks
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About Starbucks
• Founded 1971, in Seattle’s Pike Place Market. Original name of company was Starbucks Coffee, Tea and Spices, later changed to Starbucks Coffee Company.
• In United States:– 50 states, plus the District of Columbia– 7,087 Company-operated stores– 4,081 Licensed stores
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?
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Rutgers Governor School
Define
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What is Quality?– Dictionary Definition
1. a distinguishing characteristic, property, or attribute2. the basic character or nature of something3. a trait or feature of personality4. degree or standard of excellence, esp a high standard5. (formerly) high social status or the distinction associated with it6. musical tone colour; timbre7. logic the characteristic of a proposition that is dependent on
whether it is affirmative or negative8. phonetics the distinctive character of a vowel,
– Joseph Juran - > "fitness for intended use" – W. Edwards Deming -> "meeting or exceeding customer
expectations."
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What is Critical To Quality?
• What is important to your customer?• What will delight or excite them?• What are the hygiene factors?
• These are things that have a direct and significant impact on its actual or perceived quality.
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How do move beyond Brainstorming?
• 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
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Nominal Group Technique
• A brainstorming technique that is used when some group members are more vocal then others and encourages equal participation
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Nominal Group Procedure
1. Team Leader Selected2. Individuals Brainstorm for 10-15 minutes
without talking. Ideas are written down3. Round Robin each team member reads idea
and it is recorded by the team leader. There is no discussion of ideas.
4. Once all ideas are recorded discussion begins
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Multi-Voting
• Multi-voting is a group decision-making technique used to reduce a long list of items to a manageable number by means of a structured series of votes
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Multi-Voting Procedure
1. Develop a Large Group Brainstormed list2. Assign a letter to each item3. Each team member votes for their top 1/3 of
ideas.4. Votes are tallied 5. Eliminate all items receiving less than N votes
(rule of thumb 3)6. Repeat voting until there are ~4 items left
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Multi-Voting Example
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Affinity Diagrams
• A tool that gathers large amounts of language data (ideas, opinions, issues) and organizes them into groupings based on their natural relationships
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Affinity Diagram Procedure
1. Record Ideas on Post It Notes2. Randomize Ideas Together3. Sort Ideas into Related Groups4. Create Header Card5. Record Results
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Affinity Diagram Example1. Randomize Ideas Together 2. Group Ideas
3. Create Headers4. Put it Together
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Force Field Analysis
• Is a method for listing, discussing, and assessing the various forces for and against a proposed change. It helps to look at the big picture by analyzing all of the forces impacting on the change and weighing up the pros and cons.
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Force Field Procedure
1. Draw a large letter t2. At the top of the t, write the issue or problem3. At the far right of the top of t write the ideal state you wish
to obtain4. Fill in the chart
– List internal and external factors advancing towards the ideal state– List forces stopping you from obtaining the ideal state
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Force Field Example
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Tree Diagram
• Tree diagrams help link a task’s overall goals and sub-goals, and helps make complex tasks more visually manageable. Accomplished through successive steps digging into deeper detail.
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Tree Diagram Procedure
1. Identify the Goal2. Generate Tree Headings (Sub Goals)
– ~5 slightly more specific topics that are related to the general goal
– Place them horizontally on post it notes horizontally under goal
3. Generate Branches of sub goals as needed4. Record the results
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Tree Diagram Example
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Cause and Effect Diagram(Fishbone or Ishikawa Diagram)
• Is a tool that helps identify, sort, and display possible causes of a specific problem or quality characteristic. It graphically illustrates the relationship between a given outcome and all the factors that influence the outcome.
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Cause and Effect Procedure
1. Identify and Define the Effect2. Draw the Fishbone Diagram
– Place Effect as the Head of the fish
3. Identify categories for the main causes of the effect or use the standard ones (Man, Machine, Methods, Materials, Measurements, Mother Nature)
4. Add causes to the categories5. Add increasing detail to describe the cause
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Cause and Effect ExampleGeneric Format 1. Identify Categories
2. Add Causes 3. Add Details
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Now Apply It!
• Divide yourself into 6 Groups– Group 1- Nominal Group– Group 2- Multi-Voting– Group 3- Affinity Diagrams– Group 4- Force Field Analysis– Group 5- Tree Diagram– Group 6- Cause and Effect Diagram (What Causes a Bad
Cup of Coffee)• Solve the problem “What Makes a Quality Coffee
Experience?”
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Rutgers Governor School
Measure
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Types of Data• Attribute / Discrete Data– Individual unit categorized into a
classification. Examples:• Counts or frequencies of occurrence
(# of errors, # of units)• Categories (good/bad, pass/fail,
low/medium/high)• Characteristics (locations, shift #,
male/female)• Groups (complaint codes, error codes,
problem type)– Finite number of values is possible– Cannot be subdivided meaningfully
Variable / Continuous Data Individual unit can be measured on
a continuum or scale Examples: • Length• Volume• Time• Size• Width• Pressure • Temperature• Thickness
Can have almost any numeric value Can be meaningfully subdivided
into finer increments
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Data Type – Why is this important?
Variable / Continuous Data• More analysis tools available• Smaller sample size needed• Higher confidence in results• To see variation, you can also
look at the distribution
Attribute / Discrete Data Requires larger sample size Usually readily available To see variation you stratify
0%
20%
40%
60%
80%
100%
FM OD ID Burr
1
0%
1%
2%
3%
4%
Days
% Defective
Data type is a key driver of your Project Strategy
Control Chartfor Individuals
Pareto Chart
Dotplot Histogram
160140120100806040
Median
Mean
1201101009080
Anderson-Darling Normality Test
Variance 1048.78Skewness 0.00716Kurtosis -1.63184N 500
Minimum 41.77
A-Squared
1st Quartile 68.69Median 104.203rd Quartile 130.81Maximum 162.82
95% Confidence Interval for Mean
97.15
27.11
102.85
95% Confidence Interval for Median
82.78 117.66
95% Confidence Interval for StDev
30.49 34.53
P-Value < 0.005
Mean 100.00StDev 32.38
95% Confidence Intervals
Summary for Mystery
Descriptive Statistics
Week
Pro
port
ion
11/510/18/277/236/185/144/93/51/29
0.4
0.3
0.2
0.1
0.0
_P=0.1972
UCL=0.3539
LCL=0.0404
1
P Chart of Resolved
Tests performed with unequal sample sizes
Control Chart
1
0%
1%
2%
3%
4%
Days
% Defective
Individuals Chart
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So how do we translate our CTQs Into Measurements?
Y into Y into x
From the Customer Means Something Internally
You Can Measure it`
• Quality Functional Deployment (House of Quality)
• “Whats into Hows”
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So What are We Going To Measure?
– Taste (what is taste?)• pH• Total Dissolved Solids• Temperature
– Consistency• Weight of the beverage• Taste
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Go Measure!
• Create the Following Control Charts– Group 1: Starbucks Regular– Group 2: Starbucks Decaffeinated– Group 3: Dunkin Donuts Regular– Group 4: Dunkin Donuts Decaffeinated
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So How Do We Display the Data?
• Dot Plot• Run Chart• Box Whisker Plot• CUSUM• EWMA• Scatter Diagrams• Pareto Charts
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Dot Plot
• Is a statistical chart consisting of data points plotted on a simple scale, typically using filled in circles representing the frequency of observation
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Run Chart
• Is a graph that displays observed data in a time sequence. Often, the data displayed represent some aspect of the output or performance of a manufacturing or other business process.
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Box Plot (Box and Whisker Diagram)
• Is a graphic depiction of groups of numerical data through their five-number summaries: the smallest observation (sample minimum), lower quartile (Q1), median (Q2), upper quartile (Q3), and largest observation (sample maximum). A boxplot may also indicate which observations, if any, might be considered outliers.
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CUSUM(Cumulative Sum Chart)
• Is a sequential analysis technique used for monitoring changes
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EWMA(Exponential Weight Moving Average)
• Is a type of control chart used to monitor either variables or attributes-type data using the monitored business or industrial process's entire history of output
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Scatter Diagrams
• Is used to display a relationship or association between two variables
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Pareto Chart
• Named after Vilfredo Pareto, is a type of chart that contains both bars and a line graph, where individual values are represented in descending order by bars, and the cumulative total is represented by the line.
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Control Chart• Time plot of data with Center Line (mean average) & Control Limits
– Control limits are based on actual process variation (Not specs!)• UCL = X-bar (i.e., data mean) + 3s; LCL = X-bar - 3s
10
15
20
25
30
35
40
0 5 10 15 20 25
Center Line (X-bar)
Upper Control Limit (UCL)
Lower Control Limit (LCL)
Voice Of the Process (X-bar, UCL, LCL are based on actual data!): Control Limits and Center Line reflect process variation and stability A process is predictable (stable) when data points vary randomly within control
limits. Referred to as a process “in control.”Page 110
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Before Using Control Charts Check for Normality
Negative
Frequency
1801501209060300
250
200
150
100
50
0
Histogram of Negative
Positive
Frequency
300270240210180150
200
150
100
50
0
Histogram of Positive
Normal
Frequency
24021018015012090
100
80
60
40
20
0
Histogram of Normal
Normal
Perc
ent
25020015010050
99.9
99
95
90
80706050403020
10
5
1
0.1
Mean
0.328
168.0StDev 24.00N 500AD 0.418P-Value
Probability Plot of NormalNormal
Positive
Perc
ent
300250200150100
99.9
99
95
90
80706050403020
10
5
1
0.1
Mean
<0.005
168.0StDev 24.00N 500AD 46.489P-Value
Probability Plot of PositiveNormal
Negative
Perc
ent
250200150100500
99.9
99
95
90
80706050403020
10
5
1
0.1
Mean
<0.005
168.0StDev 24.00N 500AD 44.491P-Value
Probability Plot of NegativeNormal
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Attribute (discrete)Variable (continuous)What Type Of Data?
Data Collected In Groups or Individuals?
Counting Specific Defects or Defective Items?
GROUPS(Averages)(n>1)
INDIVIDUALVALUES(n=1)
X-Bar R (Means w/Range)X-Bar S (Means w/St Dev)
Individuals (I Chart)With Moving Range (I-MR)
SpecificTypes Of “Defects”
DefectiveItems
You can count only defects
You can count how many are bad and how many are good
Poisson Distribution Binomial Distribution
Area ofOpportunity Constant In Each SampleSize?
YESNO
c Chart oru Chart
u Chart
Constant Sample Size?
np Chart orp Chart
NO YES
p Chart
Control Chart Decision Tree
NOTE: X-Bar S is appropriate
for subgroup sizes of > 10
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X-Bar R
Used to monitor a variable's data when samples are collected at regular intervals from a business or industrial process for a relatively small sample size.
The , and constants are from Appendix D (Page 369)
𝑈𝐶𝑙=𝐷4 𝑅
𝐿𝐶𝑙=𝐷3 𝑅
𝑈𝐶𝑙=𝑋+ 𝐴2 𝑅
L
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X-Bar S
𝑈𝐶𝑙=𝐵4𝑆
𝐿𝐶𝑙=𝐵3𝑆
𝑈𝐶𝑙=𝑋+ 𝐴3 𝑆
L
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Used to monitor a variable's data when samples are collected at regular intervals from a business or industrial process for a relatively large sample size.
The , and constants are from Appendix D (Page 369)
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P Chart
Used to monitor the proportion of nonconforming units in a sample, where the sample proportion nonconforming is defined as the ratio of the number of nonconforming (defective) units to the sample size, n
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𝑈𝐶𝐿=𝑝+3√ 𝑝 (1−𝑝)𝑛
L𝐶𝐿=𝑝−3 √𝑝 (1−𝑝 )𝑛
𝑛=𝑇𝑜𝑡𝑎𝑙¿𝑜𝑓 𝑂𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛𝑠 ¿𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑆𝑎𝑚𝑝𝑙𝑒𝑠
𝑝=𝑇𝑜𝑡𝑎𝑙¿𝑜𝑓 𝐷𝑒𝑓𝑒𝑐𝑡𝑖𝑣𝑒𝑠 ¿𝑇𝑜𝑡𝑎𝑙¿
𝑜𝑓 𝑂𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛𝑠 ¿
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Np Chart
Used to monitor the number of nonconforming units in a sample. It is an adaptation of the p-chart and used in situations where personnel find it easier to interpret process performance in terms of concrete numbers of units rather than the somewhat more abstract proportion.
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𝑈𝐶𝐿=𝑛𝑝+3√𝑛𝑝 (1−𝑛𝑝𝑛 ) constant
)
L
464136312621161161
40
30
20
10
0
Sample
Sam
ple
Count
__NP=15.44
UCL=24.25
LCL=6.63
1
11
1
11
11
11
NP Chart of Wrong Answers
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I-MR
𝑈𝐶𝑙=𝐷4 𝑀𝑅
𝐿𝐶𝑙=𝐷3 𝑀𝑅
𝑈𝐶𝑙=𝑋+𝐸2 𝑀𝑅
L
Page 317
Used to monitor variables data from a business or industrial process for which it is impractical to use rational subgroups
The , and constants are from Appendix D (Page 369)
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Words Have Meaning
• Defect– any nonconformance of the unit of product with
the specified customer requirements• Defective
– is a unit of product which contains one or more defects that effects the operability of the product as determined by the customer
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C Chart
Used to monitor "count"-type data, typically total number of nonconformities (defects) per unit. It is also occasionally used to monitor the total number of events occurring in a given unit of time.
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𝑈𝐶𝐿=𝑐+3√𝑐
𝐿𝐶𝐿=𝑐−3√𝑐
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U Chart
used to monitor "count"-type data where the sample size is greater than one, typically the average number of nonconformities per unit
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𝑈𝐶𝐿=𝑢+ 3√𝑢√𝑛
𝐿𝐶𝐿=𝑢− 3√𝑢√𝑛
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Interpretation
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Now Apply it
• Create the Following Control Charts– Group 1: I-MR Chart for pH– Group 2: I-MR Chart for Temperature– Group 3: I-MR Chart for TDS– Group 4: I-MR Chart for Weight
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Regular Starbucks
10987654321
130
125
120
115
Observation
Indiv
idual V
alu
e
_X=122.69
UCL=128.95
LCL=116.43
10987654321
8
6
4
2
0
Observation
Movin
g R
ange
__MR=2.356
UCL=7.696
LCL=0
I-MR Chart of Temp
10987654321
108.0
106.5
105.0
103.5
102.0
Observation
Indiv
idual V
alu
e
_X=104.5
UCL=107.751
LCL=101.249
10987654321
4
3
2
1
0
Observation
Movin
g R
ange
__MR=1.222
UCL=3.993
LCL=0
I-MR Chart of TDS
10987654321
5.0
4.5
4.0
3.5
Observation
Indiv
idual V
alu
e
_X=4.135
UCL=4.815
LCL=3.455
10987654321
0.8
0.6
0.4
0.2
0.0
Observation
Movin
g R
ange
__MR=0.2556
UCL=0.8350
LCL=0
I-MR Chart of PH
10987654321
175
170
165
160
155
Observation
Indiv
idual V
alu
e_X=164.78
UCL=176.60
LCL=152.96
10987654321
16
12
8
4
0
Observation
Movin
g R
ange
__MR=4.44
UCL=14.52
LCL=0
I-MR Chart of Mass
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Decaf Starbucks
10987654321
122
120
118
116
114
Observation
Indiv
idual V
alu
e
_X=118.13
UCL=122.36
LCL=113.90
10987654321
4.8
3.6
2.4
1.2
0.0
Observation
Movin
g R
ange
__MR=1.589
UCL=5.191
LCL=0
11
1
I-MR Chart of Temp
10987654321
5
4
3
2
1
Observation
Indiv
idual V
alu
e
_X=2.946
UCL=4.929
LCL=0.963
10987654321
2.4
1.8
1.2
0.6
0.0
Observation
Movin
g R
ange
__MR=0.746
UCL=2.436
LCL=0
I-MR Chart of PH
10987654321
80
70
60
Observation
Indiv
idual V
alu
e
_X=69.81
UCL=84.38
LCL=55.24
10987654321
20
15
10
5
0
Observation
Movin
g R
ange
__MR=5.48
UCL=17.90
LCL=0
I-MR Chart of Mass
10987654321
200
190
180
170
160
Observation
Indiv
idual V
alu
e
_X=168.5
UCL=180.62
LCL=156.38
10987654321
20
15
10
5
0
Observation
Movin
g R
ange
__MR=4.56
UCL=14.88
LCL=0
1
1
I-MR Chart of TDS
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Regular Dunkin Donuts
87654321
144
141
138
135
132
Observation
Indiv
idual V
alu
e
_X=137.77
UCL=143.28
LCL=132.27
87654321
6.0
4.5
3.0
1.5
0.0
Observation
Movin
g R
ange
__MR=2.071
UCL=6.768
LCL=0
I-MR Chart of Temp
87654321
180
165
150
135
120
Observation
Indiv
idual V
alu
e
_X=147.13
UCL=169.16
LCL=125.09
87654321
30
20
10
0
Observation
Movin
g R
ange
__MR=8.29
UCL=27.07
LCL=0
11
1
I-MR Chart of TDS
87654321
3
2
1
0
Observation
Indiv
idual V
alu
e
_X=1.81
UCL=3.273
LCL=0.347
87654321
2.0
1.5
1.0
0.5
0.0
Observation
Movin
g R
ange
__MR=0.55
UCL=1.797
LCL=0
I-MR Chart of PH
87654321
140
130
120
110
100
Observation
Indiv
idual V
alu
e_X=118.22
UCL=135.25
LCL=101.20
87654321
20
15
10
5
0
Observation
Movin
g R
ange
__MR=6.4
UCL=20.91
LCL=0
I-MR Chart of Mass
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Decaf Dunkin Donuts
87654321
122
120
118
116
114
Observation
Indiv
idual V
alu
e
_X=117.988
UCL=122.357
LCL=113.618
87654321
6.0
4.5
3.0
1.5
0.0
Observation
Movin
g R
ange
__MR=1.643
UCL=5.368
LCL=0
I-MR Chart of Temp
87654321
140
135
130
Observation
Indiv
idual V
alu
e
_X=134.25
UCL=140.33
LCL=128.17
87654321
8
6
4
2
0
Observation
Movin
g R
ange
__MR=2.286
UCL=7.468
LCL=0
1
I-MR Chart of TDS
87654321
4.2
4.0
3.8
Observation
Indiv
idual V
alu
e
_X=4.0575
UCL=4.3083
LCL=3.8067
87654321
0.3
0.2
0.1
0.0
Observation
Movin
g R
ange
__MR=0.0943
UCL=0.3081
LCL=0
I-MR Chart of PH
87654321
300
250
200
150
100
Observation
Indiv
idual V
alu
e_X=201.6
UCL=285.9
LCL=117.2
87654321
100
75
50
25
0
Observation
Movin
g R
ange
__MR=31.7
UCL=103.6
LCL=0
I-MR Chart of Mass
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Rutgers Governor School
Mapping The Process
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What is a Process?
• A Process
• Remember “Verb-Noun Combination”
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Graphically Presenting a Process
• Six Sigma – SIPOC– Process Mapping
• Lean– Value Stream Map
Let the Picture do the talking
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Suppliers Inputs Process Outputs Customers (SIPOC)
• Is a high-level picture of a process that depicts how the given process is servicing the customer.
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SIPOC Procedure1. Agree to the name of the process. Use a Verb + Noun format (e.g.
Recruit Staff).2. Define the Outputs of the process. These are the tangible things that
the process produces (e.g. a report, or letter).3. Define the Customers of the process. These are the people who receive
the Outputs. Every Output should have a Customer.4. Define the Inputs to the process. These are the things that trigger the
process. They will often be tangible (e.g. a customer request)5. Define the Suppliers to the process. These are the people who supply
the inputs. Every input should have a Supplier. In some “end-to-end” processes, the supplier and the customer may be the same person.
6. Define the sub-processes that make up the process. These are the activities that are carried out to convert the inputs into outputs. They will form the basis of a process map.
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SIPOC Symbols• Suppliers: The individuals, departments, or organizations that
provide the materials, information, or resources that are worked on in the process being analyzed
• Inputs: The information or materials provided by the suppliers. Inputs are transformed, consumed, or otherwise used by the process (materials, forms, information, etc.)
• Process: The macro steps (typically 4-6) or tasks that transform the inputs into outputs: the final products or services
• Outputs: The products or services that result from the process.
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SIPOC Example
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Process Maps
• Are a graphical outline or schematic drawing of the process to be measured and improve.
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Process Map Procedure
1. Identify the process to be studied, identify boundaries and interfaces
2. Determine Various Steps in the process3. Build the Sequence of Steps4. Draw the formal chart with process map5. Verify Completeness
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Process Map Symbols
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Process Map Example
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Value Stream Mapping (VSM)
• Special type of flow chart that uses symbols known as "the language of Lean" to depict and improve the flow of inventory and information
• Purpose– Provide optimum value to the customer through a
complete value creation process with minimum waste
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VSM Procedure
Before doing any steps, determine who owns the process!1. Identify Process Customers (Y Process Output Measures)2. Identify Process Suppliers 3. Map the Material (Process) Flow
• Process General Steps• Queue or Staging Areas
4. Identify Process Information Systems5. Map the Information Flow6. Identify Common Data7. Gather the Data
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Common VSM Symbols
MSD Cust. Srvc.
Customer
MRP
ProductionControl
Electronic Communication Information Flow
Red Box and Rectangle represents information system used.
Dotted Line represents manual process connection
Box with Jagged top represents interaction with customer or supplier.
Block represents a process step that is performed.
Manual Information Flow
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Determine Process Cycle Times & Identify Value Added Steps
VA
NVA
Value Added Steps are anything that the customer is willing to pay for
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VSM Example
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Links to the Videos
• Latte : http://youtu.be/HyAAxMEdB24
• Frap : http://youtu.be/3qk28eEbfc4
• Drip : http://youtu.be/IGuwC1WcjKY
• Clover : http://youtu.be/YtXClUKhLmw
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Now Apply It!
• Create a SIPOC, Process Map or Value Stream Map for the “make drink” process– Latte– Frappuccino– Drip Coffee– Clover
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Rutgers Governor School
Analyze
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101
What is an Hypothesis Test? Hypothesis Test determines which is more likely to be true:
Null hypothesis (Ho) or Alternative hypothesis (Ha)
Ho always starts with “There is no difference between….”
p-Value: Probability Ho is true given the evidence
If p is low: Reject Ho and accept Ha
Example:
Null hypothesis (Ho): Defendant is guilty (not a Key X)
Alternative Hypothesis (Ha): Defendant is not guilty (A Key X)
p-Value: Probability defendant is not guilty given the evidence
If p is small (reasonable doubt): Reject Ho and conclude defendant is not guilty (Key X!)
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102
Steps in Test of Hypothesis1. Formulate the Null and Alternate Hypothesis2. Determine the appropriate test 3. Establish the level of significance:α4. Determine whether to use a one tail or two tail test5. Determine the degree of freedom6. Calculate the test statistic7. Compare computed test statistic against a tabled/critical
value
• Remember: tests DON’T PROVE anything. – They gather sufficient evidence against the null hypothesis Ho
or fail to gather sufficient evidence against Ho.
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Formulate the null and alternative hypotheses.
a. NULL HYPOTHESIS (H0): H0 specifies a value for the population parameter
against which the sample statistic is tested. H0 always includes an equality.
b. ALTERNATIVE HYPOTHESIS (Ha): Ha specifies a competing value for the
population parameter.
Ha is formulated to reflect the proposition the researcher wants to verify.
Ha always includes a non-equality that is mutually exclusive of H0.
Ha is set up for either a 1-tailed test or a 2-tailed test.
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Determine The Appropriate Test• Z
– is any statistical test for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution.
• T– is any statistical hypothesis test in which the test statistic follows a
Student's t distribution if the null hypothesis is supported• Paired T
– is a test that the differences between the two observations is 0• ANOVA
– Is a test to determine the differences between two or more treatments• Chi Squared
– Is a test to determine the goodness of fit of data to a distribution• Lots of Other Tests
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Choose α, our significance level
It really depends on what we are testing
– α = 0.05
– α = 0.01
– Type I error
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Find the critical value of the test statistic
• Standard normal table
• Student’s t distribution table
• Two-sided vs. one-sided
• F Distribution Table
• Chi Square Distribution Table
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Two-sided tests Zα/2
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One-sided tests Zα
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F Table
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Compare the observed test statistic with the critical value
| Ztest | > | Zcrit | Þ HA
| Ztest | £ | Zcrit | Þ H0
Zcrit-Zcrit
H0HA HA
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| Ztest | > | 1.96 | Þ HA
| Ztest | £ | 1.96 | Þ H0
Compare the observed test statistic with the critical value
1.96-1.96H0
HA HA
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Compare the observed test statistic with the critical value (1 Tail)
Ztest > 1.645 Þ HA
Ztest £ 1.645 Þ H0
1.645H0
HA
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p-value
• p-value is the probability of getting a value of the test
statistic as extreme as or more extreme than that observed
by chance alone, if the null hypothesis H0, is true.
• It is the probability of wrongly rejecting the null
hypothesis if it is in fact true
• It is equal to the significance level of the test for which
we would only just reject the null hypothesis
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The Chi Square Test
• A statistical method used to determine goodness of fit– Goodness of fit refers to how close the observed data
are to those predicted from a hypothesis
• Note:– The chi square test does not prove that a hypothesis is
correct• It evaluates to what extent the data and the hypothesis have
a good fit
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Purpose of ANOVA • Use one-way Analysis of Variance to test when the mean of a
variable (Dependent variable) differs among two or more groups– For example, compare whether systolic blood pressure differs
between a control group and two treatment groups• One-way ANOVA compares two or more groups defined by a
single factor. – For example, you might compare control, with drug treatment with
drug treatment plus antagonist. Or might compare control with five different treatments.
• Some experiments involve more than one factor. These data need to be analyzed by two-way ANOVA or Factorial ANOVA.– For example, you might compare the effects of three different drugs
administered at two times. There are two factors in that experiment: Drug treatment and time.
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What Does ANOVA Do?
• ANOVA involves the partitioning of variance of the dependent variable into different components:– A. Between Group Variability– B. Within Group Variability
• More Specifically, The Analysis of Variance is a method for partitioning the Total Sum of Squares into two Additive and independent parts.
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Test Statistic in ANOVA• F = Between group variability / Within group variability
– The source of Within group variability is the individual differences.
– The source of Between group variability is effect of independent or grouping variables.
– Within group variability is sampling error across the cases – Between group variability is effect of independent groups or
variables
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ANOVA is Appropriate if:• Independent random samples have been taken from each population• Dependent variable population are normally distributed (ANOVA is
robust with regards to this assumption)• Population variances are equal (ANOVA is robust with regards to this
assumption)• Subjects in each group have been independently sampled
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ANOVA Hypothesis
• Ho: 1 = 2 = 3 = 4
Where• 1 = population mean for group 1• 2 = population mean for group 2• 3 = population mean for group 3• 4 = population mean for group 4
• H1 = not Ho
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ANOVA Compare the Computed Test Statistic Against a Tabled Value
• α = .05• If Ftest > FCritcal Reject H0
• If Ftest <= FCritcal Can not Reject H0
Fα is found in table on 374 or using Excel FINV function
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Now we Are going to Apply ANOVA to Your Data
• Is there Difference Between Starbucks and Dunkin Donuts? pH? TDS?
• Is there Difference Between decaffeinated and Regular? pH? TDS?
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Regular vs. Decaf
RegularDecaf
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
Type
pH
Boxplot of pH
Regular_1Decaf_1
200
180
160
140
120
100
Type1
TDS
Boxplot of TDS
SUMMARYGroups Count Sum Average Variance
Decaf 18 61.92 3.44 0.676941Regular 18 55.83 3.101667 1.531838
ANOVASource of VariationSS df MS F P-value F crit
Between Groups1.030225 1 1.030225 0.932846 0.340945 4.130018Within Groups37.54925 34 1.10439
Total 38.57948 35
SUMMARYGroups Count Sum Average Variance
Decaf 18 2759 153.2778 398.5654Regular 18 2222 123.4444 666.3791
ANOVASource of VariationSS df MS F P-value F crit
Between Groups8010.25 1 8010.25 15.04351 0.000458 4.130018Within Groups18104.06 34 532.4722
Total 26114.31 35
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Starbucks vs. Dunkin Donuts
SBUXDND
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
Store
pH
Boxplot of pH
SBUX_1DND_1
200
180
160
140
120
100
Location
TDS
Boxplot of TDS
SUMMARYGroups Count Sum Average Variance
SBUX 20 70.81 3.5405 0.707194DND 16 46.94 2.93375 1.458025
ANOVASource of VariationSS df MS F P-value F crit
Between Groups3.272405 1 3.272405 3.15126 0.084822 4.130018Within Groups35.30707 34 1.038443
Total 38.57948 35
SUMMARYGroups Count Sum Average Variance
SBUX 20 2730 136.5 1153.947DND 16 2251 140.6875 268.8958
ANOVASource of VariationSS df MS F P-value F crit
Between Groups155.8681 1 155.8681 0.204154 0.654258 4.130018Within Groups25958.44 34 763.4835
Total 26114.31 35
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Rutgers Governor School
Conclusion
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Takeaways
• Industrial Engineering is focused on solving problems in:– Manufacturing– Finance– Logistics– Medical– Services (including Education)
• Six Sigma is one of many tools to solve problems
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Please Complete the Survey
• https://www.surveymonkey.com/s/93CJQCV
• Todays slides are available at • http://www.slideshare.net/brtheiss/rutgers-g
overnor-school
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