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Six Sigma Basic Analysis of DMAIC

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									Six Sigma Green Belt

• Knowledge Discovery Tools
– Root Cause Analysis – Descriptive Statistics – EWMA Charts

• Hypothesis Testing
– F Tests, T Tests, ANOVA, Chi-Square

• Linear Regression
– Correlation – Predictive Equations

• Design of Experiments • Logistic Regression

Where is the Project
• Through Measure Phase, have a good idea of where Process is Now and perhaps some insight where improvement is possible. • Analysis Phase is to “close the gap” between the As Is and To Be look at the process. • Will use Statistical and some Non-Statistical tools to guide the analysis.

Root Cause Analysis
• Pareto Charts and Fish Bone Diagrams used in combination to find Root Cause • Pareto Chart – Bar Chart showing frequency or cost arranged with highest value on left and lowest on right. • During Measurement Phase, frequencies of lost time were recorded: Wait Time, Move Time, Adjusting Parts, Looking for Tools

Pareto Chart

Pareto Chart

Root Cause
• Example continued: Knowing that “adjust” has highest frequency, can then construct fish bone (also termed cause-and-effect diagram or Ishikawa Diagram) • Problem Statement is: Why Adjusting? • Branches: Man, Machine, Method, Mother Nature, Management, Materials, Measurement System, Money

Fish Bone Diagram
• Fishbone Example Adjustment.xls • Complete the Fish Bone through Brainstorming • When you think you have all the possibilities, construct another Pareto.

Root Cause

Root Cause
• Now you know with some level of certainty that the lost time is caused by adjustments which in turn are caused by measurements.
– Pretty Close to determining what needs to be done to eliminate 33% of the Lost Time.

• Can repeat cycle as many times as needed to determine root cause. Or at least have a direction. • Proper Analysis Presents the Improvement

Descriptive Statistics
• Minitab Descriptive Statistics provides quick and easy analysis of data:

Descriptive Statistics

Analysis of SPC
• Check SPC charts for “drift” from Common Causes, especially if process is automated. • Create common cause chart to check the changing level of the process due to built-in process characteristics.
– Processes with drift – Forecast where next process measurement will be – Allow for more process control

Common Cause Charts
• Example: If a process SPC shows an out of control situation which cannot be economically corrected or can be corrected by some type of operator intervention, then using the predictive nature of the chart can keep the process in control (feed forward control). • Common Cause Charts use the Exponential Weighted Moving Average (EWMA) to track the process mean. Charts are often called EWMA Charts.

EWMA Charts
• Construction:
– Determine the process variable most likely to be causing the drift (i.e. temperature of a component) – Determine the weight to be given to historical vs. current observations-Lambda
• Lambda value set between 0 and 1 • Closer to 0, then more weight to historical, more smoothing. • Closer to 1, then more weight to current
– Need to experiment to give best value

EWMA Chart
• Minitab Example: 40 Temperature Readings, Lambda of .9 (heavy weight on current).

EWMA Chart
• Summary
– In Analysis of SPC charts/data if Out of Control Situation Appears:
• Look for Drift: especially if automated process • If bringing process under control is not economical, then look for ways to inject actions into process to bring under control. • Construct EWMA Chart for further analysis and possible correction.
– Experiment with Lambda as historical vs. current data may have an effect.

Hypothesis Testing
• Common approach for analyzing data. • Determine the decision or conclusion that must be made about the data with a specified level of confidence. • Must determine correct test for the analysis • Phrase the hypothesis in two statements; the null hypothesis and the alternate hypothesis. • Determine significance level(confidence level) • Perform the calculations

The Null Hypothesis
• Regardless of the Test, a Null Hypothesis and an Alternate Hypothesis is stated. The test will cause the Null Hypothesis to be either rejected, or fail to be rejected. • Null Hypothesis basically means there is no difference.
– Cannot be proven as true, but can be accepted if not proven untrue.

• Alternative Hypothesis basically means there is a difference

Type I and Type II Errors
• Errors in Statistics basically mean an incorrect decision has been made: • Type I error (designated with Greek letter alpha)
– Saying something happened when it actually didn’t (False Alarm)

• Type II error (designated with Greek letter Beta)
– Not discovering something happened when it actually did (Failure to Alarm) – (Mark J. Anderson and Patrick J. Whitcomb)

Type I and Type II Errors
• Type I and II Errors.xlsx

Hypothesis Testing
• Common uses:
– Did the mean go up or down (i.e. did it change between, for example, different machines, different locations, different processes?) – Did the proportion go up or down (i.e. did it change between, for example, number of defects, number of satisfied customers, number of errors?) – Did the variance go up or down (i.e. did it change between different people, processes, etc.)

Hypothesis Testing
• Different Tests for Different Questions
– F-Tests: Used to test whether or not the variances from two samples (i.e. machines, or before/after) are statistically different.
• Enter Data from samples into Excel. • Use Table for calculated F (n sub 1 sample, and n sub 2 sample) • Divide the first sample variance by the second sample variance to obtain actual F • Compare the Calculate F with the Actual F
– If the actual F is greater than the calculated F, then reject the null hypothesis (variances are the same). – F-Test.xls

Hypothesis Testing
• T Test: Used to determine if sample means have changed. • Same logic as F Test. • Example: t Test.xls • Example Template for t and F Tests:
– t-and-f-test.xls

Hypothesis Testing
• Chi-Square Test: Used to compare a sample variance to a specified value (example: Normal standard deviation is x, adjustment made, now standard deviation is y. Has the variance (standard deviation) statistically changed?
– Is what is expected vs. what is observed statistically different (or just due to chance?) and how much difference can there be before statistical change has occurred.

Hypothesis Testing
• Chi-Square
– Determine Sample Size (Example: 10) – Determine expected standard deviation (Example: 5.5) – Determine Observed standard deviation (Example: 6.3) – Obtain Calculated Chi-Square value from Table. – Calculate Actual Chi-Square from Excel – Chi-Square Test.xlsx

Hypothesis Testing
• Analysis of Variance: ANOVA
– ANOVA is used to determine if the mean (average) has changed or to compare different processes:
• Examples: Brand of toothpaste used vs. number of cavities, different treatments on plants vs. growth, different machines’ outputs, different choices (A vs. B vs. C, etc..)

– ANOVA often times is placed into category of Six Sigma with Design of Experiments and Hypothesis Testing or Both. – Powerful and Complex

• Difference between t-test and ANOVA
– t-Test deals with two means, ANOVA can deal with several means at the same time plus provides information about interactions between input variables and the outcomes.

• Before using ANOVA:
– Must test that data has a normal distribution – Variance is same for all “treatments” (Factor) – Samples are random and independent
• No cheating

• Testing for Normality and Equal Variances
– Can use a Normal probability plot for testing normality –or– Use Bartletts Test for equal variances because the test assumes normality (two for price of one).
• Minitab Example: Four different circumstances are established and tested to determine if the means are statistically different. • Bartletts Test shows P-value of .156 (greater than .05) therefore Null Hypothesis is not rejected and variances are assumed to be equal and normality exists.



• Note the p-value is .008 below the .05 We conclude to reject the null hypothesis and state that, within our levels of confidence, that the circumstances do make a difference. • Another Example: Using One-Way ANOVA
– Output by shift over the course of a week. – Third Shift has the highest output with an average of 83.857 so….should we model everything around third shift and maybe fired Second Shift?


• P Value is .874, which is greater than .05, therefore we fail to reject the null hypothesis and can state with some degree of certainty that there is no statistical difference between the shifts.
– Third shift may insist on bragging rights, but that’s about it.

Two Way ANOVA
• Similar to One-Way ANOVA but allows two factors instead of just one.
– Minitab example: New gages being considered. Four operators used current gages and proposed gages, measuring twice. Determine if there is a difference with 95% confidence level.

Two-Way ANOVA

Two-Way ANOVA
• Because the p value is low, the null hypothesis is rejected, and we assume there is a statistical difference not only with the gages, but also with the operators. • First example used General Linear Model, Second used One-Way Crossed ANOVA, Third used Two-Way ANOVA.

• There are other ANOVA cases:
– Two-Way ANOVA with Replication-Interaction Effects – Nested ANOVA – Analysis of Means – Main Effects Plots – Interval Plots – Balanced ANOVA

Regression Analysis
• Often combined with Correlation Analysis-Will look at both:
– Designed to help in determining cause and effect – Predict future output, number of defects, resource requirements (i.e. budgets), predict cycle times, manpower, etc.
• A look into the future

– Understand the relationship between some input variable (x) and an output variable (y). – Several types of Regression Models

Linear Analysis
• Most Basic: Start with look at Correlations: • Correlation Analysis:
– Measurement and determination of Linear (Straight Line) strength between two variables (continuous). – Start with a Scatter Plot for the two variables under consideration, x and y
• Example: Number of SAT scores vs. GPA (Minitab)

Correlation Analysis
• Scatter Plot:

Correlation Analysis
• The Correlation Matrix will calculate the strength of the Linear Relationship from -1 to 1. The closer the number to a -1 or 1 indicates a linear relationship. A value of zero indicates there is no correlation.

Correlation Analysis
• To Determine Significance, run the Analysis with P values.

Correlation Analysis
• In Example all the P values are greater than .05, therefore be suspicious that a correlation exists.
– Sample size can play a large role in analysis, make sure it is large enough (generally greater than 20 samples).

Linear Regression
• After determining Correlation is Linear, can conduct a Simple Linear Regression Analysis

Linear Regression
• Check Correlation

Linear Regression
• Obtain Linear Regression Formula:

Linear Regression
• Can now use the formula to determine number of calls vs. people.

Design of Experiments
• An entire body of knowledge built around the manipulation of process and product design factors to discover the combination that is most effective, efficient, and/or robust in actual operating conditions. (Michael L. George) • Several Models: Classical, Taguchi, Evolutionary Operations… • Entire course can be built around DOE (like some other Six Sigma Tools)

Design of Experiments

A System or Process

Design of Experiments
Controllable Factors = X

A System or Process

Design of Experiments
Controllable Factors = X

A System or Process

Uncontrollable Variables = Z

Design of Experiments
Controllable Factors = X

A System or Process

Response Measures = Y

Anderson/Whitcomb Uncontrollable Variables = Z

Design of Experiments
• Definitions:
– Output Variable is the Response – Controllable Input Variables are the Factors – Settings for each Factor are the Levels
• Usually two levels are adequate for the experiment, one high and one low.

– Definitions for experiment, what factors, what levels, are called Runs or Treatments

Design of Experiments
• Procedure (Tague)
– Identify the Process to be studied – Determine measurement precision and accuracy
• Can use Repeatability and Reproducibility

– Identify the Variables or Factors – Determine settings or Levels for Factors – Specify and Document the Experiment’s Design
• Combinations (Runs or Treatments) • Number of Runs: called Replications • Sequence of Runs: called Randomization

Design of Experiments
• Procedure
– Attempt to identify other variables that could interfere with experiment (eliminate or monitor) – Run the Experiment – Analyze the Data: Wide variety of Software, Minitab, Excel available – If conclusions show process can be improved, make changes, verify, and standardize new process. – Conduct more experiments

Design of Experiments Minitab Example
– Three Factors are used: Time, Temperature and type of Catalyst (Material) used for some Chemical output, or product. Question is what combination produces the highest and best output. – The experiment will use the Factorial Method or Model.
• Allows for examination of several factors at a time.

– The experiment will be using two levels

Design of Experiments Minitab Example
• Need to Create Design and determine number of runs:

Design of Experiments Minitab Example

Design of Experiments Minitab Example
– Decide to use Full Factorial with 8 runs and 2 replications – Set Levels for Factors:
• Temperature: Low at 20, High at 40 • Pressure: Low at 1, High at 2 • Catalyst Material: Low A, High B

Design of Experiments Minitab Example

Design of Experiments Minitab Example

Design of Experiments Minitab Example
– Run the Experiments and enter Yield (Results) in C8.

Design of Experiments Minitab Example
Analyze Results

Design of Experiments Minitab Example

Design of Experiments Minitab Example
– Look for Low P Values <.05
• Pressure, Catalyst, and Pressure*Catalyst appear to be significant.
– The Pressure*Catalyst is known as an Interaction

– Use Normal Probability Plot and Pareto Graphs to see which effects have influenced the response (Yield or Result).

Design of Experiments Minitab Example

Design of Experiments Minitab Example

Design of Experiments Minitab Example
• Normal Probability Plot:
– Active Effects (important) don’t fit the Plot very well

• Pareto Chart:
– Graphs those effects with highest importance

• Both Charts show Pressure, Catalyst, and the interaction of Pressure*Catalyst to be important, or Active Effects.

Design of Experiments Minitab Example
• Minitab allows testing of the model choosen and allows tests of residuals. (Not included in this Example). • Use information and data gathered to determine main effects for results and interactions. • Obtain Main Effects Graph.

Design of Experiments Minitab Example

Design of Experiments Minitab Example
• Interpretation of Main Effects Graph:
– Catalyst has larger main effect than Pressure
• Steeper slope

– Yield increases as Pressure Increases – Yield for Catalyst A is much larger than Catalyst B – Conclusion (without any interaction) is to use higher pressure (4) and Catalyst B to increase Yield – Need to look at Interaction

Design of Experiments Minitab Example

Design of Experiments Minitab Example
• Interpretation of Interaction Graph:
– Shows impact of changing one factor has on another factor.
• Can magnify or diminish Main Effects

– Pressure and Catalyst show different slopes
• Generally, if lines of interaction are parallel, indicates no interaction.

– Regardless of Pressure Yield with Catalyst A are higher than with Catalyst B. – There is a significant difference however in yield with Catalyst A between Pressures of (1) and (4)

Design of Experiments Minitab Example
• Drawing Conclusions:
– Based on Main Effects Graph and Interaction Graph, Yield can be, if not maximize, then improved using Catalyst A and Pressure 4.

Design of Experiments
• Different Designs
– ANOVA (One Way, Two Way) – Factorial (Full or General) – Fractional Factorial (save money by running fewer trials – OFAT (One Factor at a Time) – Plackett-Burman (Number of runs always a multiple of Four) – Response-Surface (Detecting curvature in the Response) – Taguchi Design (Factor settings to minimize response variation)

Design of Experiments
• The Two Level, Full Factorial is considered the basic, building block, model. • Why Use DOE
– Uses Real Time Data rather than Historical Data – Statistically Sound – Helps to identify and maximize the critical x’s which are producing the y’s (inputs, outputs of process) – 3-factor-doe.xls

Lean Tools Overview of Lean
• Merge of Six Sigma with Lean
– Six Sigma reduction in Variation – Lean = Speed – A.K.A. Just-In-Time, TPS

• Readings:
– The Machine that Changed the World, James P. Womack, Daniel T. Jones, and Daniel Roos – Lean Thinking, James P. Womack and Daniel T. Jones – The Toyota Way, Jeffrey K. Liker

Lean Tools Overview of Lean
• Principles of Lean
– Eliminate Waste (muda) – Specify Value via the Value Stream – Create Flow – Customer Pull – Perfection – lean pyr.jpg – History: lean_timeline.jpg

Lean Tools
• • • • 5’s and Visual Management Kaizen and Kaizen DMAIC Kanban Takt Time and Measurements of System (OEE and DFT) • The 14 Principles of Lean

• •



• •

The 5S's are: Phase 1 - Seiri (整理) Sorting: Going through all the tools, materials, etc., in the plant and work area and keeping only essential items. Everything else is stored or discarded. Phase 2 - Seiton (整頓) Straighten or Set in Order: Focuses on efficiency. When we translate this to "Straighten or Set in Order", it sounds like more sorting or sweeping, but the intent is to arrange the tools, equipment and parts in a manner that promotes work flow. For example, tools and equipment should be kept where they will be used (i.e. straighten the flow path), and the process should be set in an order that maximizes efficiency. Phase 3 - Seisō (清掃) Sweeping or Shining or Cleaniness: Systematic Cleaning or the need to keep the workplace clean as well as neat. At the end of each shift, the work area is cleaned up and everything is restored to its place. This makes it easy to know what goes where and have confidence that everything is where it should be. The key point is that maintaining cleanliness should be part of the daily work - not an occasional activity initiated when things get too messy. Phase 4 - Seiketsu (清潔) Standardizing: Standardized work practices or operating in a consistent and standardized fashion. Everyone knows exactly what his or her responsibilities are to keep above 3S's. Phase 5 - Shitsuke (躾) Sustaining the discipline: Refers to maintaining and reviewing standards. Once the previous 4S's have been established, they become the new way to operate. Maintain the focus on this new way of operating, and do not allow a gradual decline back to the old ways of operating. However, when an issue arises such as a suggested improvement, a new way of working, a new tool or a new output requirement, then a review of the first 4S's is appropriate.

• Phase I • Red Tag:

• Phase II • Shadow Boards

Visual Management
• Form of Communication:
– Locations – Activities – Resources – Responsiblities – Where does the team, group, department, facility stand? What are the Goal? What is being Worked On?

Visual Management
• Examples:
– – – – color-coded pipes and wires painted floor areas for good stock, scrap, trash, etc. indicator lights workgroup display boards with charts, metrics, procedures, etc. – production status boards – direction of flow indicators

• Use your Imagination: Where-ever and Whatever needs to be communicated

• Continuous Improvement • Several Different Approaches
– Team Oriented, Results Oriented – Short Term – Designed towards specific area, or problem – Great for “Low Hanging Fruit” – Cost/ Benefit
• Low Cost

Kaizen DMAIC Michael L. George
• Define (Week prior to event-Preparation Week)
– Clearly define the Kaizen objectives – Select a Kaizen leader (probably a Green Belt) – Select and notify participants
• • • • • 6 to 8 team members 2 people directly from project area 1 person who supervisors or leads in project area People from Upstream and Downstream processes People who support the processes in project area

Kaizen DMAIC Michael L. George
• Define (Week prior to event-Preparation Week)
– Prepare any training and materials
• Manuals and/or posters

– Assemble background information – Complete logistics planning
• Meeting rooms, Supplies, Lunch?

– Arrange for coverage during participants’ absence from their workplace or disruptions

Kaizen DMAIC Michael L. George
• Measure (Preparation Week and Monday of Event)
– Validate the value stream map of process – Complete flow layout (include people, paper, material, machines, and information)

• Analyze (Tuesday-Wednesday)
– Validate root cause (fishbone) – Identify sources of waste – Brainstorm process improvements for eliminating non-value added tasks and reduction of variation

Kaizen DMAIC Michael L. George
• Improve (Wednesday-Thursday)
– Create action item list to accomplish improvements – Implement process improvements, train employees then test, fine-tune, and ensure the process is capable

• Control (Thursday-Friday)
– Create Standard Operating Procedures to document and sustain improvements – Present results to management team, complete follow-up, develop plan to monitor results over time

Kaizen DMAIC
• Tips and Tricks
– Don’t get “hung up” with procedures – get the ideas out on the table, and start working to refine them – If you are the leader, walk and study the process during the preparation – Dot the i’s and cross the t’s after the event – Make sure everything is documented and visible – Reward participants – Communicate closely with sponsor during event

Takt Time
• Powerful, Simple Measurement:
– Takt time is the amount of available work time divided by the customer demand during the time period
• 8 available hours or 480 minutes during shift • 60 orders for customers need to be completed • Takt Time is 480/60 or every 8 minutes an order needs to be completed.

– Important Point: Takt time sets the pace

OEE Over-all Equipment Effectiveness
• Series of Measurements designed to pin-point lost time in process
– Planned Production Time (shift length less breaks) – Operating Time (Planned Production Time less Down Time) – Good Output (Total Output less Rejected Output) – Ideal Run Rate (Output expected under Good Conditions)

OEE Over-all Equipment Effectiveness
• Measurements
– Availability: Operating Time/Planned Production Time – Performance: Total Output/Operating Time/Ideal Run Rate – Quality: Good Output/Total Output – Overall OEE: Availability x Performance x Quality

OEE Over-all Equipment Effectiveness
• World Class OEE:
– Availability: 90% – Performance: 95% – Quality: 99.9% – Overall OEE: 85%

• Model helps to identify areas where lost time and waste occurs (down time, rejects, loss of efficiency, maintenance issues, operator issues)

Demand Flow Technology DFT
• Math for Flow Processes developed by John R. Costanza • Measurements for Demand at Capacity
– Demand at Capacity equals Targeted Monthly Volume divided by Work Days per Month

• Flow Rate
– Daily Flow Rate equals Specific Daily Rate divided by Effective Work Hours times Number of Shifts

Demand Flow Technology DFT
• Operational Cycle Time (What each operation needs to complete to maintain Flow)
– Work Hours times Number of Shifts divided by Demand at Capacity

• Total Product Cycle Time
– Analysis of Flow Path
• Start at completion of process, work backwards along critical path. Goal is to find longest path from start of process (feeders) to finish. Compare to what is required to determine where improvements are required.

Demand Flow Technology DFT
• Product Synchronization
– Visual representation of Product (i.e. a “goes into” chart) which allows for clues in establishing the flow lines to complete process or product (i.e. where the feeder processes need to be located for best flow line towards completion). – Think in terms of Natural Flow, eliminate Batches

• Sequence of Events
– Something like a routing except more detailed and includes total quality check

Demand Flow Technology DFT
• Kanban
– Communicates a demand to pull materials without scheduling
• Flexibility in people, machines, processes
– Cross Training of people performing process – Rapid Set-ups (SMED) – Superior Communications between process and Customer

• Essential to Demand Flow

• Linear Planning
– Leveling of Production to a Daily (or other time frame)
• Uses Market Demand Forecasts, Consumption of Forecast

The Fourteen Principles of Lean Jeffrey K. Liker
• Base Your Management Decisions on a LongTerm Philosophy, Even at the Expense of Short-Term Financial Goals • Create Continuous Process Flow to Bring Problems to the Surface • Use “Pull” Systems to avoid Overproduction • Level Out the Workload (Heijunka) • Build a Culture of Stopping to Fix Problems to get Quality Right the First Time

The Fourteen Principles of Lean Jeffrey K. Liker
• Standardize Tasks are the Foundation for Continuous Improvement and Employee Empowerment • Use Visual Controls So No Problems are Hidden • Use Only Tested, Reliable Technology • Grow Leaders who Thoroughly Understand the Work, Live the Philosophy, and Teach It to Others

The Fourteen Principles of Lean Jeffrey K. Liker
• Develop Exceptional People and Teams Who Follow Your Company Philosophy • Respect Your Extended Network of Partners and Suppliers by Challenging Them and Helping Them Improve • Go and See for Yourself • Make Decisions Slowly by Consensus, Thoroughly Considering All Options, Implement Decisions Rapidly

The Fourteen Principles of Lean Jeffrey K. Liker
• Become a Learning Organization Through Relentless Reflection (Hansei) and Continuous Improvement (Kaizen)

Fujio Cho, President, Toyota Motor Corporation, 2002
• “We place the highest value on actual implementation and taking action. There are many things one doesn’t understand and therefore, we ask them why don’t you just go ahead and take action; try to do something? You realize how little you know and you face your own failures and you simply can correct those failures and redo it again and at the second trial you realize another mistake or another thing you don’t like so you can redo it once again. So by constant improvement, or, should I say, the improvement based on action, one can rise to the higher level of practice and knowledge.”

Analysis Phase
• Key Deliverables:
– Process Map; Value Stream Map – Data Analysis
• Quantify Process Performance
– Sound and Verified Measurements and Data Collection – Statistically, and Graphically

– Identify Cause and Effect
• Narrow focus to significant Few

– Positive and Negative Effects on Process
• What x’s are affecting the y’s and to what degree

Analysis Phase
• Key Deliverables:
– Talking to Your Process and It Will Talk Back to You.
• Asking Questions, Gathering the Data, Analyzing the Data is communications.

“When I took math class, I had no problem with the questions, it was the answers I couldn’t give.” -Rodney Dangerfield

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