Rutgers Governor School - Six Sigma

Rutgers Governor School

Introduction

Goals for Today

Show you to see and (perhaps) solve problems differently

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

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

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So Lets Get Moving

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.”

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

So How do Make “it” Better

• Statistics• Lean• Six Sigma• Modeling

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

Population Parameters

p̂x

Size = N

Mean = mStd. Dev. = sProportion = p

Sample StatisticsSample Statistics

Size = n Mean = Std. Dev.= s Prop. =

Key Descriptive Statistical Terms

Page 143

Lean Tool Kit

• 5S- – Sort– Straighten– Shine– Standardize– Sustain

• Value Stream Mapping• Kanban• Poka-yoke• Kaizen <- mean continuous improvement

Six Sigma Tool Kit

• DMAIC– Define– Measure– Analyze– Improve– Control

• SIPOC Diagrams • Statistical Process Control • 5 Whys

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

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?

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

16

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”.

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

Page 6

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).

19

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)

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

Page 143

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

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

23

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

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

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

?


Define

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."

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.

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

Nominal Group Technique

• A brainstorming technique that is used when some group members are more vocal then others and encourages equal participation

Page 114

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

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

Page 87

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

Multi-Voting Example

Affinity Diagrams

• A tool that gathers large amounts of language data (ideas, opinions, issues) and organizes them into groupings based on their natural relationships

Page 92

Affinity Diagram Procedure

1. Record Ideas on Post It Notes2. Randomize Ideas Together3. Sort Ideas into Related Groups4. Create Header Card5. Record Results

Affinity Diagram Example1. Randomize Ideas Together 2. Group Ideas

3. Create Headers4. Put it Together

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.

Page 109

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

Force Field Example

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.

Page 124

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

Tree Diagram Example

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.

Page 97

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

Cause and Effect ExampleGeneric Format 1. Identify Categories

2. Add Causes 3. Add Details

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?”


Measure

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

Page 110

52

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

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”

So What are We Going To Measure?

– Taste (what is taste?)• pH• Total Dissolved Solids• Temperature

– Consistency• Weight of the beverage• Taste

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

So How Do We Display the Data?

• Dot Plot• Run Chart• Box Whisker Plot• CUSUM• EWMA• Scatter Diagrams• Pareto Charts

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

Page 164

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.

Page 166

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.

Page 164

CUSUM(Cumulative Sum Chart)

• Is a sequential analysis technique used for monitoring changes

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

Scatter Diagrams

• Is used to display a relationship or association between two variables

Page 167

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.

Page 136

64

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

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

Page 173

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

Page 110

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

Page 313

X-Bar S

𝑈𝐶𝑙=𝐵4𝑆

𝐿𝐶𝑙=𝐵3𝑆

𝑈𝐶𝑙=𝑋+ 𝐴3 𝑆

L

Page 315

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.


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

Page 319

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 ¿

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.

Page 321

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

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


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

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.

Page 325

𝑈𝐶𝐿=𝑐+3√𝑐

𝐿𝐶𝐿=𝑐−3√𝑐

U Chart

used to monitor "count"-type data where the sample size is greater than one, typically the average number of nonconformities per unit

Page 323

𝑈𝐶𝐿=𝑢+ 3√𝑢√𝑛

𝐿𝐶𝐿=𝑢− 3√𝑢√𝑛

Interpretation

Page 369

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

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

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

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

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


Mapping The Process

What is a Process?

• A Process

• Remember “Verb-Noun Combination”

Graphically Presenting a Process

• Six Sigma – SIPOC– Process Mapping

• Lean– Value Stream Map

Let the Picture do the talking

Suppliers Inputs Process Outputs Customers (SIPOC)

• Is a high-level picture of a process that depicts how the given process is servicing the customer.

Page 51

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.

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.

SIPOC Example

Process Maps

• Are a graphical outline or schematic drawing of the process to be measured and improve.

Page 128

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

Process Map Symbols

Process Map Example

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

Page 24

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

95

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

Determine Process Cycle Times & Identify Value Added Steps

VA

NVA

Value Added Steps are anything that the customer is willing to pay for

VSM Example

Links to the Videos

• Latte : http://youtu.be/HyAAxMEdB24

• Frap : http://youtu.be/3qk28eEbfc4

• Drip : http://youtu.be/IGuwC1WcjKY

• Clover : http://youtu.be/YtXClUKhLmw

http://youtu.be/HyAAxMEdB24

http://youtu.be/3qk28eEbfc4

http://youtu.be/3qk28eEbfc4

http://youtu.be/IGuwC1WcjKY

http://youtu.be/YtXClUKhLmw

http://youtu.be/YtXClUKhLmw

Now Apply It!

• Create a SIPOC, Process Map or Value Stream Map for the “make drink” process– Latte– Frappuccino– Drip Coffee– Clover


Analyze

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!)

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.

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.

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

105

Choose α, our significance level

It really depends on what we are testing

– α = 0.05

– α = 0.01

– Type I error

106

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

107

Two-sided tests Zα/2

108

One-sided tests Zα

F Table

110

Compare the observed test statistic with the critical value

| Ztest | > | Zcrit | Þ HA

| Ztest | £ | Zcrit | Þ H0

Zcrit-Zcrit

H0HA HA

111

| 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

112

Compare the observed test statistic with the critical value (1 Tail)

Ztest > 1.645 Þ HA

Ztest £ 1.645 Þ H0

1.645H0

HA

113

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

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

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.

116

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.

117

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

118

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

119

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

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

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?

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


Decaf 18 2759 153.2778 398.5654Regular 18 2222 123.4444 666.3791



Total 26114.31 35

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


SBUX 20 70.81 3.5405 0.707194DND 16 46.94 2.93375 1.458025



Total 38.57948 35


SBUX 20 2730 136.5 1153.947DND 16 2251 140.6875 268.8958



Total 26114.31 35


Conclusion

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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• https://www.surveymonkey.com/s/93CJQCV

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overnor-school





My Contact Information

• Brandon Theiss– [email protected]– Connect to me on LinkedIn

mailto:[email protected]

Rutgers Governor School - Six Sigma

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