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SQC Guest Lecture

    Introduction
Goals for Today




Show you to see and (perhaps) solve problems differently
•   Academics
                                           About Me
     –   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
Agenda
      18:00        18:20    Introduction
      18:20        18:40    Measure
      18:40        19:00    Define
      19:00        19:20    Brainstorm
      19:20        19:40    Break
      19:40        20:00    Depict the Data
      20:00        20:20    Make Control Charts
      20:20        20:40    Process Mapping
      20:40        21:00    Map the process
      21:00        21:20    Analyze
      21:20        21:55    Conclusion

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So Lets Get Moving
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                                                Outputs
•   People                                            • Products
•   Materials                      Process                • Hardware
•   Methods                        • Sequence of          • Software
•   Mother Nature
                                      Value Added         • Systems
•   Management
•   Measurement
                                      Steps               • People
    System                                            • Services
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
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 Continuous
  Improvement problems
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
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 things
 1. The Average µ
 2. 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 falling         95% chance of falling       99.7% chance of falling
between       and            between        and          between        and
Effect of Changing Parameters


           (a) Changing                                             (b) Increasing
      shifts the curve along the axis                   increases the spread and flattens the curve

                                                                                               1   =6
                                     1   =   2=   6
                                                                                                    2=   12


140                160         180                200    140            160              180              200

              1   = 160     2 =174                                            1   =   2 =170
What is Process Sigma?
      Before                                                Customer
                           Mean                             Specification
       3
                                                                               A 3 process
                                  1                             Defects        (3 standard
                                          2                                    deviations fit
                                              3                                between target and
                                                                               spec)
                       A 6 process
                          Mean                            Customer
                                                          Specification



               After                  1
                                          2                      No Defects!
               6                              3
                                                  4
                                                      5
                                                           6


15
SQC Guest Lecture- Starbucks
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
?
SQC Guest

  Define
What is Quality?
– Dictionary Definition
   1. a distinguishing characteristic, property, or attribute
   2. the basic character or nature of something
   3. a trait or feature of personality
   4. degree or standard of excellence, esp a high standard
   5. (formerly) high social status or the distinction associated
      with it
   6. musical tone colour; timbre
   7. logic the characteristic of a proposition that is dependent
      on whether it is affirmative or negative
   8. 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 Selected
2. Individuals Brainstorm for 10-15 minutes
   without talking. Ideas are written down
3. 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 list
2. Assign a letter to each item
3. 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 Notes
2.   Randomize Ideas Together
3.   Sort Ideas into Related Groups
4.   Create Header Card
5.   Record Results
Affinity Diagram Example
1. Randomize Ideas Together     2. Group Ideas




                              4. Put it Together
   3. Create Headers
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 t
2. At the top of the t, write the issue or problem
3. At the far right of the top of t write the ideal state you wish
   to obtain
4. 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 Goal
2. 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 needed
4. 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 Effect
2. 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 categories
5. Add increasing detail to describe the cause
Cause and Effect Example
Generic 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?”
SQC Guest

 Measure
Types of Data
                                              Variable / Continuous Data
• Attribute    / Discrete Data                      Individual unit can be measured on
– Individual unit categorized into a                 a continuum or scale Examples:
  classification. Examples:                           • Length
    • Counts or frequencies of occurrence             • Volume
      (# of errors, # of units)                       • Time
                                                      • Size
    • Categories (good/bad, pass/fail,
                                                      • Width
      low/medium/high)
                                                      • Pressure
    • Characteristics (locations, shift #,            • Temperature
      male/female)                                    • Thickness
    • Groups (complaint codes, error                Can have almost any numeric value
      codes, problem type)
                                                    Can be meaningfully subdivided
– Finite number of values is possible                into finer increments
– Cannot be subdivided meaningfully




                                                                               Page 110
Data Type – Why is this
                                important?
                                      Data type is a key driver of your Project Strategy
                                                                                                                                                               
                   Attribute / Discrete Data                                                                                       Variable / Continuous Data
                                       Requires larger sample size                                                                •      More analysis tools available
                                       Usually readily available                                                                  •      Smaller sample size needed
                    To see variation you stratify                                                                                 •      Higher confidence in results
                                                                                                                                   •     To see variation, you can also
                                Pareto Chart
                                      100%
                                      80%
                                                                                                                                        look at the distribution
                                      60%
                                                                                                                                   Dotplot                                                                                                                 Histogram
                                      40%
                                      20%
                                        0%
                                                       FM                     OD           ID     Burr
                                                                                                         Control Chart
       Control Chart
                                      P Chart of Resolved
                                                                                                         for Individuals
                                                                                                          4%
             0.4                                                                                              % Defective      1
                                                                                                                                       Descriptive Statistics
                                                            1
                                                                                                                                                                          Summary for Mystery
                                                                                     UCL=0.3539
                                                                                                         3%
             0.3
                                                                                                                                                                                                                    A nderson-D arling N ormality Test
                                                                                                                                                                                                                         A -S quared
                                                                                                                                                                                                                         P -V alue <
                                                                                                                                                                                                                                           27.11
                                                                                                                                                                                                                                           0.005
                                                                                                                                                                                                                                                           Individuals Chart
Proportion




                                                                                     _                   2%
                                                                                                                                                                                                                         M ean
                                                                                                                                                                                                                         S tDev
                                                                                                                                                                                                                         V ariance
                                                                                                                                                                                                                                           100.00
                                                                                                                                                                                                                                            32.38
                                                                                                                                                                                                                                          1048.78
                                                                                                                                                                                                                                                           4%
             0.2                                                                     P=0.1972                                                                                                                            S kew ness
                                                                                                                                                                                                                         Kurtosis
                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                          0.00716
                                                                                                                                                                                                                                         -1.63184
                                                                                                                                                                                                                                              500
                                                                                                                                                                                                                                                                % Defective      1




             0.1                                                                                         1%                                                                                                              M inimum
                                                                                                                                                                                                                         1st Q uartile
                                                                                                                                                                                                                         M edian
                                                                                                                                                                                                                                           41.77
                                                                                                                                                                                                                                           68.69
                                                                                                                                                                                                                                          104.20
                                                                                                                                                                                                                                                           3%
                                                                                                                                                                                                                         3rd Q uartile    130.81
                                                                                                                                                 40   60         80      100      120            140   160
                                                                                                                                                                                                                         M aximum         162.82
                                                                                     LCL=0.0404                                                                                                                    95% C onfidence Interv al for M ean

             0.0                                                                                         0%                                                                                                              97.15            102.85
                                                                                                                                                                                                                   95% C onfidence Interv al for M edian
                                                                                                                                                                                                                                                           2%
                                                                                                                                                                                                                         82.78            117.66
                   1/29   3/5   4/9   5/14    6/18   7/23       8/27   10/1   11/5
                                                                                                                                                                                                                   95% C onfidence Interv al for S tDev
                                             Week                                                                                                               95% Confidence Intervals


Tests performed with unequal sample sizes
                                                                                                                        Days             Mean
                                                                                                                                                                                                                         30.49             34.53

                                                                                                                                                                                                                                                           1%
                                                                                                                                        Median

                                                                                                                                                 80        90             100              110               120




             44                                                                                                                                                                                                                                            0%
                                                                                                                                                                                                                                                                          Days
So how do we translate our CTQs Into
           Measurements?

• Quality Functional
  Deployment (House of
  Quality)
• “Whats into Hows”


                    Y   into Y into x


From the Customer        Means Something   You Can Measure it`
                         Internally
What is Measurement System Analysis?
• MSA = Measurement System Analysis
• Treats measurement as a process
     – Procedures
     – Gages
     – Fixtures and other equipment
     – People
• Assesses adequacy of the measurement system
• Determines sources of variation

46                                       Page 188
So What are We Going To Measure?
– Taste (what is taste?)
   • pH
   • Total Dissolved Solids
      – Blue Meter
      – Combined Meter
   • Temperature
   • Conductivity
– Consistency
   • Weight of the beverage
Go Measure!
• Create the Following Control Charts
  – Group 1: Starbucks Regular Pike
  – Group 2: Starbucks Decaffeinated
  – Group 3: Dunkin Donuts Regular
  – Group 4: Dunkin Donuts Decaffeinated
  – Group 5: Starbucks Regular Blond
  – Group 6: Starbucks Regular Dark
So How Do We Display the Data?
•   Dot Plot
•   Run Chart
•   Box Whisker Plot
•   CUSUM
•   EWMA
•   Scatter Diagrams
•   Pareto Charts
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
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) + 3 ; LCL = X-bar - 3
     40

     35                                                        Upper Control Limit
                                                                      (UCL)
     30

     25
                                                                           Center Line
                                                                           (X-bar)
     20
                                                               Lower Control Limit
     15
                                                                         (LCL)
     10


          0           5          10          15         20            25

 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.”
51                                                                               Page 110
Before Using Control Charts Check for Normality
                                                       Histogram of Normal                                                                         Probability Plot of Normal
                         100                                                                                                                                 Normal
                                                                                                                  99.9
                                                                                                                                                                                                 Mean        168.0
                                                                                                                                                                                                 StDev       24.00
                            80                                                                                      99
                                                                                                                                                                                                 N             500
                                                                                                                                                                                                 AD          0.418
                                                                                                                    95                                                                           P-Value     0.328
                                                                                                                    90
                            60
            Frequency




                                                                                                                    80
                                                                                                                    70




                                                                                                      Percent
                                                                                                                    60
                            40                                                                                      50
                                                                                                                    40
                                                                                                                    30
                                                                                                                    20
                            20                                                                                      10
                                                                                                                     5

                                                                                                                     1
                                0
                                          90          120          150        180      210    240
                                                                     Normal                                        0.1
                                                                                                                             50          100               150           200             250
                                                                                                                                                          Normal



                                                      Histogram of Positive
                 200                                                                                                                           Probability Plot of Positive
                                                                                                                                                             Normal
                                                                                                                  99.9
                                                                                                                                                                                               Mean          168.0
                                                                                                                                                                                               StDev         24.00
                 150                                                                                               99
                                                                                                                                                                                               N               500
                                                                                                                                                                                               AD           46.489
                                                                                                                   95                                                                          P-Value      <0.005
Frequency




                                                                                                                   90

                 100                                                                                               80
                                                                                                                   70




                                                                                                     Percent
                                                                                                                   60
                                                                                                                   50
                                                                                                                   40
                                                                                                                   30
                    50                                                                                             20
                                                                                                                   10
                                                                                                                    5


                        0                                                                                           1
                                    150         180          210           240         270     300
                                                                    Positive                                       0.1
                                                                                                                                  100        150          200          250         300
                                                                                                                                                         Positive




                                                      Histogram of Negative                                                                    Probability Plot of Negative
                                                                                                                                                             Normal
                                                                                                                   99.9
                        250                                                                                                                                                                    Mean         168.0
                                                                                                                                                                                               StDev        24.00
                                                                                                                     99
                                                                                                                                                                                               N              500
                        200                                                                                                                                                                    AD          44.491
                                                                                                                     95                                                                        P-Value     <0.005
                                                                                                                     90
     Frequency




                                                                                                                     80
                        150                                                                                          70
                                                                                                        Percent



                                                                                                                     60
                                                                                                                     50
                                                                                                                     40
                        100                                                                                          30
                                                                                                                     20
                                                                                                                     10
                                                                                                                         5
                        50
                                                                                                                         1

                            0                                                                                       0.1
                                     0         30       60          90           120    150    180                                0     50            100        150         200         250
                                                                   Negative
                                                                                                                                                        Negative
                                                                                                                                                                                                                     Page 173
Control Chart Decision Tree
                                    Variable (continuous)                               Attribute (discrete)
                                                                What Type Of Data?

                                                                                                            Counting
                          Data Collected In
                                                                                                            Specific Defects or
                          Groups or Individuals?
                                                                                                            Defective Items?
     GROUPS                                        INDIVIDUAL
     (Averages)                                    VALUES                         Specific                                                 Defective
     (n>1)                                         (n=1)                          Types Of                                                 Items
                                                                                  “Defects”

X-Bar R (Means w/Range)             Individuals (I Chart)
X-Bar S (Means w/St Dev)            With Moving Range (I-MR)                   You can count only                                 You can count how
                                                                               defects                                            many are bad and
                                                                                                                                  how many are good
NOTE: X-Bar S is appropriate
                                                                                 Poisson Distribution                             Binomial Distribution
for subgroup sizes of > 10




                                                                                     Area of
                                                                                                                                         Constant
                                                                                     Opportunity Constant
                                                                                                                                         Sample Size?
                                                                                     In Each Sample
                                                                                     Size?


                                                                            NO                    YES                              NO                   YES
                                                                        u Chart               c Chart or                      p Chart            np Chart or
                                                                                              u Chart                                            p Chart

                                                                                                                                               Page 110
I-MR




       Page 317
Interpretation
Now Apply it
• Create the Following Control Charts
  – Group 1: I Chart for pH
  – Group 2: I Chart for Temperature
  – Group 3: I Chart for TDS- blue
  – Group 4: I Chart for Weight
  – Group 5: I Chart for Conductivity
  – Group 6: I Chart for TDS - Combined
SQC Guest

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 Procedure
1.   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 process
3. Build the Sequence of Steps
4. Draw the formal chart with process map
5. 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 Systems
5.   Map the Information Flow
6.   Identify Common Data
7.   Gather the Data
Common VSM Symbols

                  Electronic Communication                     Dotted Line represents
                  Information Flow                             manual process connection


                                                               Box with Jagged top
                                                               represents interaction with
                  Manual Information Flow       Customer       customer or supplier.




                   Red Box and Rectangle                       Block represents a process
     Production
       Control     represents information    MSD Cust. Srvc.   step that is performed.
                   system used.
       MRP




70
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
Now Apply It!
• Graphically Depict the following
  – Group 1: Process Map Latte
  – Group 2: Process Map Frap
  – Group 3: Process Map Drip Coffee
  – Group 4: Process Map Clover
  – Group 5: SIPOC for Frap
  – Group 6: SIPOC for Clover
SQC Guest

  Analyze
Steps in Test of Hypothesis
1.   Formulate the Null and Alternate Hypothesis
2.   Determine the appropriate test
3.   Establish the level of significance:α
4.   Determine whether to use a one tail or two tail test
5.   Determine the degree of freedom
6.   Calculate the test statistic
7.   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.


                                                                        76
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
Compare the observed test statistic with
          the critical value




                               -Zcrit        Zcrit
  | Ztest | > | Zcrit |   HA
  | Ztest |   | Zcrit |   H0            H0
                                   HA                HA



                                                          78
Compare the observed test statistic with
          the critical value




                               -1.96        1.96
                                       H0
   | Ztest | > | 1.96 |   HA
   | Ztest |   | 1.96 |   H0     HA          HA




                                                   79
Compare the observed test statistic with
      the critical value (1 Tail)




    Ztest > 1.645   HA        1.645
    Ztest 1.645     H0   H0

                               HA



                                           80
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


                                                                81
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.
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




                                                                    83
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




                                                                         84
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


                                              85
ANOVA Compare the Computed Test
   Statistic Against a Tabled Value
• α = .05
• If Ftest > FCritcal Reject H0
• If Ftest <= FCritcal Can not Reject H0

              Excel is very nice and does it for us!
Now we Are going to Apply ANOVA to
            Your Data
• Is there Difference Between Starbucks and
  Dunkin Donuts? pH? TDS? Conductivity?
• Is there Difference Between decaffeinated and
  Regular? pH? TDS? Conductivity?
• Is there Difference Between Different
  Starbucks Roasts? pH? TDS? Conductivity?
SQC Guest

 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
SQC Guest Lecture- Starbucks
ASQ Greenbelt
• 100 Multiple Choice Questions
• 4 Hours
• Open Book, Open Notes *No Sample
  Problems*
• No graphing calculators allowed
• Results Posted online 7-10 Days after
Requirements to Sit for the Exam
• Required Experience
   – The Six Sigma Green Belt requires three years* of work experience in
     one or more areas of the Six Sigma Green Belt Body of Knowledge.
• Minimum Expectations for a Certified Six Sigma Green Belt
   – Operates in support of or under the supervision of a Six Sigma Black
     Belt
   – Analyzes and solves quality problems
   – Involved in quality improvement projects
   – Participated in a project, but has not led a project
   – Has at least three years of work experience
   – Has ability to demonstrate their knowledge of Six Sigma tools and
     processes

* The Body of Knowledge is very broad it can be accessed at
(http://prdweb.asq.org/certification/control/six-sigma-green-
belt/bok). For Juniors and Seniors in ISE your course work counts.
Others consider course work, internships and work experience to
meet the requirement.
About the Course
• 11 Weekly Sessions starting the Week of 9/17
  for the December 1st exam
• Purpose is to train students to pass the exam
• Currently Schedule for Monday Nights. If > 25
  students register additional sections will be
  added on Wednesday or Thursday
• Text Book
  – Certified Six Sigma Handbook
Certification Cost
• Exam Preparation = $296 includes
  – ASQ Student Membership - $27
  – Six Sigma Greenbelt Course- $179
  – Textbook - $90
• Exam Fee = $199
• Total Certification Cost $495

  More Information @ www.ASQPrinceton.org
My Contact Information
• Brandon Theiss
  – Brandon.Theiss@gmail.com
  – Connect to me on LinkedIn
Please Complete the Survey
• https://www.surveymonkey.com/s/39N9Y9X

• Todays slides are available on Sakai

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SQC Guest Lecture- Starbucks

  • 1. SQC Guest Lecture Introduction
  • 2. Goals for Today Show you to see and (perhaps) solve problems differently
  • 3. Academics About Me – 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
  • 4. Agenda 18:00 18:20 Introduction 18:20 18:40 Measure 18:40 19:00 Define 19:00 19:20 Brainstorm 19:20 19:40 Break 19:40 20:00 Depict the Data 20:00 20:20 Make Control Charts 20:20 20:40 Process Mapping 20:40 21:00 Map the process 21:00 21:20 Analyze 21:20 21:55 Conclusion Todays slides are available on Sakai Also Please Complete the Online Feedback Survey https://www.surveymonkey.com/s/39N9Y9X
  • 5. So Lets Get Moving
  • 6. 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 Outputs • People • Products • Materials Process • Hardware • Methods • Sequence of • Software • Mother Nature Value Added • Systems • Management • Measurement Steps • People System • Services
  • 7. Lean Tool Kit • 5S- – Sort – Straighten – Shine – Standardize – Sustain • Value Stream Mapping • Kanban • Poka-yoke • Kaizen <- mean continuous improvement
  • 8. Six Sigma Tool Kit • DMAIC – Define – Measure – Analyze – Improve – Control • SIPOC Diagrams • Statistical Process Control • 5 Whys
  • 9. 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?
  • 10. 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 Continuous Improvement problems
  • 11. 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
  • 12. 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 things 1. The Average µ 2. The Standard Deviation σ Page 143
  • 13. 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 falling 95% chance of falling 99.7% chance of falling between and between and between and
  • 14. Effect of Changing Parameters (a) Changing (b) Increasing shifts the curve along the axis increases the spread and flattens the curve 1 =6 1 = 2= 6 2= 12 140 160 180 200 140 160 180 200 1 = 160 2 =174 1 = 2 =170
  • 15. What is Process Sigma? Before Customer Mean Specification 3 A 3 process 1 Defects (3 standard 2 deviations fit 3 between target and spec) A 6 process Mean Customer Specification After 1 2 No Defects! 6 3 4 5 6 15
  • 17. 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
  • 18. 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
  • 19. ?
  • 20. SQC Guest Define
  • 21. What is Quality? – Dictionary Definition 1. a distinguishing characteristic, property, or attribute 2. the basic character or nature of something 3. a trait or feature of personality 4. degree or standard of excellence, esp a high standard 5. (formerly) high social status or the distinction associated with it 6. musical tone colour; timbre 7. logic the characteristic of a proposition that is dependent on whether it is affirmative or negative 8. phonetics the distinctive character of a vowel, – Joseph Juran - > "fitness for intended use" – W. Edwards Deming -> "meeting or exceeding customer expectations."
  • 22. 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.
  • 23. 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
  • 24. Nominal Group Technique • A brainstorming technique that is used when some group members are more vocal then others and encourages equal participation Page 114
  • 25. Nominal Group Procedure 1. Team Leader Selected 2. Individuals Brainstorm for 10-15 minutes without talking. Ideas are written down 3. 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
  • 26. 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
  • 27. Multi-Voting Procedure 1. Develop a Large Group Brainstormed list 2. Assign a letter to each item 3. 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
  • 29. 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
  • 30. Affinity Diagram Procedure 1. Record Ideas on Post It Notes 2. Randomize Ideas Together 3. Sort Ideas into Related Groups 4. Create Header Card 5. Record Results
  • 31. Affinity Diagram Example 1. Randomize Ideas Together 2. Group Ideas 4. Put it Together 3. Create Headers
  • 32. 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
  • 33. Force Field Procedure 1. Draw a large letter t 2. At the top of the t, write the issue or problem 3. At the far right of the top of t write the ideal state you wish to obtain 4. Fill in the chart – List internal and external factors advancing towards the ideal state – List forces stopping you from obtaining the ideal state
  • 35. 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
  • 36. Tree Diagram Procedure 1. Identify the Goal 2. 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 needed 4. Record the results
  • 38. 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
  • 39. Cause and Effect Procedure 1. Identify and Define the Effect 2. 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 categories 5. Add increasing detail to describe the cause
  • 40. Cause and Effect Example Generic Format 1. Identify Categories 2. Add Causes 3. Add Details
  • 41. 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?”
  • 43. Types of Data  Variable / Continuous Data • Attribute / Discrete Data  Individual unit can be measured on – Individual unit categorized into a a continuum or scale Examples: classification. Examples: • Length • Counts or frequencies of occurrence • Volume (# of errors, # of units) • Time • Size • Categories (good/bad, pass/fail, • Width low/medium/high) • Pressure • Characteristics (locations, shift #, • Temperature male/female) • Thickness • Groups (complaint codes, error  Can have almost any numeric value codes, problem type)  Can be meaningfully subdivided – Finite number of values is possible into finer increments – Cannot be subdivided meaningfully Page 110
  • 44. Data Type – Why is this important? Data type is a key driver of your Project Strategy   Attribute / Discrete Data Variable / Continuous Data  Requires larger sample size • More analysis tools available  Usually readily available • Smaller sample size needed  To see variation you stratify • Higher confidence in results • To see variation, you can also Pareto Chart 100% 80% look at the distribution 60% Dotplot Histogram 40% 20% 0% FM OD ID Burr Control Chart Control Chart P Chart of Resolved for Individuals 4% 0.4 % Defective 1 Descriptive Statistics 1 Summary for Mystery UCL=0.3539 3% 0.3 A nderson-D arling N ormality Test A -S quared P -V alue < 27.11 0.005 Individuals Chart Proportion _ 2% M ean S tDev V ariance 100.00 32.38 1048.78 4% 0.2 P=0.1972 S kew ness Kurtosis N 0.00716 -1.63184 500 % Defective 1 0.1 1% M inimum 1st Q uartile M edian 41.77 68.69 104.20 3% 3rd Q uartile 130.81 40 60 80 100 120 140 160 M aximum 162.82 LCL=0.0404 95% C onfidence Interv al for M ean 0.0 0% 97.15 102.85 95% C onfidence Interv al for M edian 2% 82.78 117.66 1/29 3/5 4/9 5/14 6/18 7/23 8/27 10/1 11/5 95% C onfidence Interv al for S tDev Week 95% Confidence Intervals Tests performed with unequal sample sizes Days Mean 30.49 34.53 1% Median 80 90 100 110 120 44 0% Days
  • 45. So how do we translate our CTQs Into Measurements? • Quality Functional Deployment (House of Quality) • “Whats into Hows” Y into Y into x From the Customer Means Something You Can Measure it` Internally
  • 46. What is Measurement System Analysis? • MSA = Measurement System Analysis • Treats measurement as a process – Procedures – Gages – Fixtures and other equipment – People • Assesses adequacy of the measurement system • Determines sources of variation 46 Page 188
  • 47. So What are We Going To Measure? – Taste (what is taste?) • pH • Total Dissolved Solids – Blue Meter – Combined Meter • Temperature • Conductivity – Consistency • Weight of the beverage
  • 48. Go Measure! • Create the Following Control Charts – Group 1: Starbucks Regular Pike – Group 2: Starbucks Decaffeinated – Group 3: Dunkin Donuts Regular – Group 4: Dunkin Donuts Decaffeinated – Group 5: Starbucks Regular Blond – Group 6: Starbucks Regular Dark
  • 49. So How Do We Display the Data? • Dot Plot • Run Chart • Box Whisker Plot • CUSUM • EWMA • Scatter Diagrams • Pareto Charts
  • 50. 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
  • 51. 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) + 3 ; LCL = X-bar - 3 40 35 Upper Control Limit (UCL) 30 25 Center Line (X-bar) 20 Lower Control Limit 15 (LCL) 10 0 5 10 15 20 25  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.” 51 Page 110
  • 52. Before Using Control Charts Check for Normality Histogram of Normal Probability Plot of Normal 100 Normal 99.9 Mean 168.0 StDev 24.00 80 99 N 500 AD 0.418 95 P-Value 0.328 90 60 Frequency 80 70 Percent 60 40 50 40 30 20 20 10 5 1 0 90 120 150 180 210 240 Normal 0.1 50 100 150 200 250 Normal Histogram of Positive 200 Probability Plot of Positive Normal 99.9 Mean 168.0 StDev 24.00 150 99 N 500 AD 46.489 95 P-Value <0.005 Frequency 90 100 80 70 Percent 60 50 40 30 50 20 10 5 0 1 150 180 210 240 270 300 Positive 0.1 100 150 200 250 300 Positive Histogram of Negative Probability Plot of Negative Normal 99.9 250 Mean 168.0 StDev 24.00 99 N 500 200 AD 44.491 95 P-Value <0.005 90 Frequency 80 150 70 Percent 60 50 40 100 30 20 10 5 50 1 0 0.1 0 30 60 90 120 150 180 0 50 100 150 200 250 Negative Negative Page 173
  • 53. Control Chart Decision Tree Variable (continuous) Attribute (discrete) What Type Of Data? Counting Data Collected In Specific Defects or Groups or Individuals? Defective Items? GROUPS INDIVIDUAL (Averages) VALUES Specific Defective (n>1) (n=1) Types Of Items “Defects” X-Bar R (Means w/Range) Individuals (I Chart) X-Bar S (Means w/St Dev) With Moving Range (I-MR) You can count only You can count how defects many are bad and how many are good NOTE: X-Bar S is appropriate Poisson Distribution Binomial Distribution for subgroup sizes of > 10 Area of Constant Opportunity Constant Sample Size? In Each Sample Size? NO YES NO YES u Chart c Chart or p Chart np Chart or u Chart p Chart Page 110
  • 54. I-MR Page 317
  • 56. Now Apply it • Create the Following Control Charts – Group 1: I Chart for pH – Group 2: I Chart for Temperature – Group 3: I Chart for TDS- blue – Group 4: I Chart for Weight – Group 5: I Chart for Conductivity – Group 6: I Chart for TDS - Combined
  • 58. What is a Process? • A Process • Remember “Verb-Noun Combination”
  • 59. Graphically Presenting a Process • Six Sigma – SIPOC – Process Mapping • Lean – Value Stream Map Let the Picture do the talking
  • 60. 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
  • 61. SIPOC Procedure 1. 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.
  • 62. 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.
  • 64. Process Maps • Are a graphical outline or schematic drawing of the process to be measured and improve. Page 128
  • 65. Process Map Procedure 1. Identify the process to be studied, identify boundaries and interfaces 2. Determine Various Steps in the process 3. Build the Sequence of Steps 4. Draw the formal chart with process map 5. Verify Completeness
  • 68. 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
  • 69. 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 Systems 5. Map the Information Flow 6. Identify Common Data 7. Gather the Data
  • 70. Common VSM Symbols Electronic Communication Dotted Line represents Information Flow manual process connection Box with Jagged top represents interaction with Manual Information Flow Customer customer or supplier. Red Box and Rectangle Block represents a process Production Control represents information MSD Cust. Srvc. step that is performed. system used. MRP 70
  • 71. Determine Process Cycle Times & Identify Value Added Steps VA NVA Value Added Steps are anything that the customer is willing to pay for
  • 73. Links to the Videos • Latte : http://youtu.be/HyAAxMEdB24 • Frap : http://youtu.be/3qk28eEbfc4 • Drip : http://youtu.be/IGuwC1WcjKY • Clover : http://youtu.be/YtXClUKhLmw
  • 74. Now Apply It! • Graphically Depict the following – Group 1: Process Map Latte – Group 2: Process Map Frap – Group 3: Process Map Drip Coffee – Group 4: Process Map Clover – Group 5: SIPOC for Frap – Group 6: SIPOC for Clover
  • 75. SQC Guest Analyze
  • 76. Steps in Test of Hypothesis 1. Formulate the Null and Alternate Hypothesis 2. Determine the appropriate test 3. Establish the level of significance:α 4. Determine whether to use a one tail or two tail test 5. Determine the degree of freedom 6. Calculate the test statistic 7. 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. 76
  • 77. 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
  • 78. Compare the observed test statistic with the critical value -Zcrit Zcrit | Ztest | > | Zcrit | HA | Ztest | | Zcrit | H0 H0 HA HA 78
  • 79. Compare the observed test statistic with the critical value -1.96 1.96 H0 | Ztest | > | 1.96 | HA | Ztest | | 1.96 | H0 HA HA 79
  • 80. Compare the observed test statistic with the critical value (1 Tail) Ztest > 1.645 HA 1.645 Ztest 1.645 H0 H0 HA 80
  • 81. 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 81
  • 82. 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.
  • 83. 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 83
  • 84. 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 84
  • 85. 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 85
  • 86. ANOVA Compare the Computed Test Statistic Against a Tabled Value • α = .05 • If Ftest > FCritcal Reject H0 • If Ftest <= FCritcal Can not Reject H0 Excel is very nice and does it for us!
  • 87. Now we Are going to Apply ANOVA to Your Data • Is there Difference Between Starbucks and Dunkin Donuts? pH? TDS? Conductivity? • Is there Difference Between decaffeinated and Regular? pH? TDS? Conductivity? • Is there Difference Between Different Starbucks Roasts? pH? TDS? Conductivity?
  • 89. 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
  • 91. ASQ Greenbelt • 100 Multiple Choice Questions • 4 Hours • Open Book, Open Notes *No Sample Problems* • No graphing calculators allowed • Results Posted online 7-10 Days after
  • 92. Requirements to Sit for the Exam • Required Experience – The Six Sigma Green Belt requires three years* of work experience in one or more areas of the Six Sigma Green Belt Body of Knowledge. • Minimum Expectations for a Certified Six Sigma Green Belt – Operates in support of or under the supervision of a Six Sigma Black Belt – Analyzes and solves quality problems – Involved in quality improvement projects – Participated in a project, but has not led a project – Has at least three years of work experience – Has ability to demonstrate their knowledge of Six Sigma tools and processes * The Body of Knowledge is very broad it can be accessed at (http://prdweb.asq.org/certification/control/six-sigma-green- belt/bok). For Juniors and Seniors in ISE your course work counts. Others consider course work, internships and work experience to meet the requirement.
  • 93. About the Course • 11 Weekly Sessions starting the Week of 9/17 for the December 1st exam • Purpose is to train students to pass the exam • Currently Schedule for Monday Nights. If > 25 students register additional sections will be added on Wednesday or Thursday • Text Book – Certified Six Sigma Handbook
  • 94. Certification Cost • Exam Preparation = $296 includes – ASQ Student Membership - $27 – Six Sigma Greenbelt Course- $179 – Textbook - $90 • Exam Fee = $199 • Total Certification Cost $495 More Information @ www.ASQPrinceton.org
  • 95. My Contact Information • Brandon Theiss – Brandon.Theiss@gmail.com – Connect to me on LinkedIn
  • 96. Please Complete the Survey • https://www.surveymonkey.com/s/39N9Y9X • Todays slides are available on Sakai