Six Sigma

1
Six Sigma

• Beth Cudney
• Society of Manufacturing Engineers
• November 11, 2002

2
What is Six Sigma

• Six Sigma is a customer focused continuous
  improvement strategy and discipline that
  minimizes defects and variation towards an
  achievement of 3 defects per million
  opportunities in product design, production, and
  administrative processes.
• Focused on customer satisfaction and results by
  reducing variation in processes.
• Methodology
• Metric based on standard deviation.
• Aggressive goals.

3
Why Use Six Sigma?

• Increase capacity
• Reduce cost
• Improve yields
• Reduce the impact of a Hidden Factory

4
The Hidden Factory

• Each defect must be detected, repaired and placed
  back in the process. Each defect costs time and
  money.

Inspect
First Time Yield
Pass
Inputs
Operation
Fail
Rework
Hidden Factory
Time, Cost, People
Scrap
Increased Cost - Lost Capacity
5
Six Sigma Introduction

• Goals
• Benefits
• Roles
• Strategy
• Six Sigma Levels

6
Agenda

• Six Sigma culture
• Six Sigma concepts for continuous improvement
• Role of statistics in process improvement
• Graphical tools and charting techniques
• Relationship between variation and the cost of
  poor quality
• Process control and process capability
• Measurement System Analysis
• Steps required for successful experimentation

7
Six Sigma Goals

• Develop a world class culture
• Develop leaders
• Support long range objectives

8
Six Sigma Benefits

• Stronger knowledge of products and processes
• Reduced defects
• Increased customer satisfaction - generates
  business growth and improves profitability
• Increased communication and teamwork
• Common set of tools

9
Six Sigma Roles

• Champion
• Team
• Green Belt
• Black Belt
• Master Black Belt

10
Champion

• Provide top-down commitment to the Six Sigma
  goals
• Selection and monitoring of projects
• Deliver support
• Assume a mentorship role

11
Green Belt

• Fundamental Six Sigma tools
• Specific tools that relate to their project

12
Black Belt

• Lead major projects
• Mentor, consult and teach Green Belts
• Promote out-of-the-box and critical thinking
• Challenge the old ways of doing business
• Approximate 1-2 of the population (10-20
  per 1000 employees)

13
Master Black Belt

• Drive major projects
• Train and mentor black belts
• Work with champions to select projects
• Typically 1 per business unit or site
  (1 per 1000 employees)

14
Six Sigma Strategy

• Measure
• Analyze
• Improve
• Control

15
Measure

• What processes are involved?
• Who is the process owner?
• Who are the team members?
• Which processes are the highest priority to
  improve?
• What data supports the decision? (Metric)
• How is the process performed?
• How is the process performance measured?
• Is your measurement system accurate and precise?

16
Measure (Cont.)

• What are the customer driven specifications for
  the performance measures?
• What are the improvement goals?
• What are the sources of variation in the process?
• What sources of variability are controlled and
  how?
• Tools Process Flow
• Process Failure Mode and Effects Analysis
  (FMEA)
• Measurement System Analysis

17
Analyze

• What are the key variables affecting the average
  and variation of the performance measures?
• What are the relationships between the key
  variables and the process output?
• Is there interaction between any of the key
  variables?
• Tools Hypothesis Test

18
Improve

• What are the key variable settings that optimize
  the performance measures?
• At the optimal setting for the key variables,
  what variability is in the performance measure?
• Tools Multiple Regression
• Design of Experiments

19
Control

• How much improvement has the process shown?
• How much time and/or money was saved?
• Long term metric.

20
Cost of Poor Quality

• Costs from
• Internal Failure Costs (Rework, Scrap)
• External Failure Costs (After Delivery)
• Appraisal Costs (Inspection, Test)
• Prevention Costs (Where you should spend)
• Lost Opportunity Costs (Sales, Competition)

21
Process Flow Diagram Benefits

• Allows a team to identify the actual flow or
  sequence of events.
• Shows problem areas, redundancy, unnecessary
  steps, and areas for simplification and
  standardization.
• Compares actual versus the ideal flow.
• Allows a team to identify activities that may
  impact performance.
• Identifies locations where additional data can be
  collected and identified.

22
Cause and Effect Diagram

• Structured approach to identifying root causes.
• Focuses the team on the content of the problem,
  not the history of the problem.
• Creates a collective knowledge and consensus of
  the team around the problem.
• Focuses the team on the causes, not the symptom.
• Identifies the factors to be held constant (C),
  noise factors (N), and critical factors for
  possible experimentation (X).

23
Cause and Effect Diagram Layout
Person
Materials
Environment
Causes
Effect
Methods
Machines
24
Pareto Diagram

• A bar chart whose bars are in descending order.
• Focuses efforts on the problems that offer the
  greatest potential for improvement by showing
  their relative frequency or size.
• Based on the Pareto principle 20 of the sources
  cause 80 of the problem.
• Displays the relative importance of a problem in
  a easily interpreted, visual format.

25
Pareto Diagram Format
26
Histogram

• Summarizes data from a process that has been
  collected over time.
• Graphically presents the frequency distribution
  in bar form.
• Displays large of amounts of data that are
  difficult to interpret in tabular form.
• Shows the relative frequency of occurrence of the
  various data values.
• Reveals centering, variation, and the shape of
  the data.
• Illustrates the distribution of the data.
• Helps indicate if there has been a change in the
  process.

27
Histogram Format
28
Taguchi Loss Function

• Old way of looking at quality
• New way of looking at quality

Scrap and Rework
Scrap and Rework
No Loss
Lower Spec Limit
Upper Spec Limit
Large Loss
Medium Loss
No Loss
LSL
Target
USL
29
Using the Data

• Location
• Variation
• Quality Measures
• Run Chart
• Control Chart
• Scatter Diagram
• Correlations

30
Location

• Used to describe the middle of the data set.
• sample mean x x1x2x3 . . . xn
• n
• sample median x middle value, if n is odd
• the average of the two middle
  values, if n is even

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Location Example

• Data set 8, 7, 3, 9, 4, 6, 4, 5, 3, 6, 7
• sample mean x 5.63
• sample median x 6

1 2 3 4 5 6 7
8 9 10 11
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Variation

• Used to describe the range of a data set.
• n
• sample variance s2 ? ( xi - x )2
• i1
• n-1
• sample standard deviation s sqrt (s2)

33
Variation Example (Cont.)
x
1 2 3
4 5
y
1 2 3
4 5
z
1 2 3
4 5
34
Quality Measures

• DPM (PPM) defects per million
• total number of defects x 1,000,000
• total number of units
• ?level number of standard deviations between
  the center of the process and the nearest
  specification limit
• minimum USL - x, x - LSL
• ? ?

35
Quality Measures (Cont.)

• ?capability worst case shift of ?level 1.5
• Cpk process capability index
• Cp process potential index
• FPY first pass yield

36
Run Chart

• A graphical tool that records data collected over
  time and displays trends.

37
Run Chart Example
38
Control Chart

• A run chart that includes statistically
  determined upper and lower control limits and a
  center line.

39
Control Chart Example
40
Scatter Diagram

• Used to display data that is associated with more
  than one variable
• Most commonly, bivariate data (data associated
  with two variables)
• Shown as ordered pairs
• first value is one variable
• second value is the second variable
• Purpose is to visually show the relationship
  between the two variables

41
Scatter Diagram Example
42
Failure Mode and Effects Analysis

• A proactive, systematic method for identifying,
  analyzing, prioritizing and documenting potential
  failure modes, their respective effects and
  potential causes of failures.
• Recognize and evaluate potential failures in
  processes and products.
• Reduce or eliminate the potential of a failure.

43
FMEA

• Spending time up-front can reduce costs.
• Product and process changes are easier to make
  and less expensive to implement.
• It is a continuous improvement tool applied
  properly.

1 Design
10 Prototype

100 Production
1000 By the Customer
44
Hypothesis Testing

• A statistical hypothesis is a statement or claim
  about some unrealized true state of nature.
• The actual hypothesis to be tested consists of
  two complementary statements about the true state
  of nature.
• H0 null hypothesis
• H1 alternative hypothesis
• The true state of nature is rarely known with
  100 accuracy.
• Examples
• Average gas mileage differs depending on type A
  or B gas.
• Variability of machined thickness of a part
  depends on they type of tool.
• Type of aspirin determines the amount of pain
  relief.

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Hypothesis Test Decision Table

• H0 Defendant is Innocent
• H1 Defendant is Guilty
• Probability of committing a Type 1 error is
  defined as ? (0 lt ? lt 1).
• Probability of committing a Type II error is
  defined as ? (0 lt ? lt1).

46
Gage Repeatability Reproducibility

• Variability in the way we measure product and
  performance
• The purpose is to asses how much variation is
  associated with the measurement system and to
  compare it to the total process variation
• Three properties
• Accuracy - the ability to produce an average
  measured value which agrees with the true value
  or standard being used
• Precision - the ability to repeatedly measure the
  same product or service and obtain the same
  results
• Stability - the ability to repeatedly measure the
  same product or service over time and obtain the
  same average measured value

47
Gage Repeatability Reproducibility

• Variability in the way we measure product and
  performance
• The purpose is to asses how much variation is
  associated with the measurement system and to
  compare it to the total process variation
• Three properties
• Accuracy - the ability to produce an average
  measured value which agrees with the true value
  or standard being used
• Precision - the ability to repeatedly measure the
  same product or service and obtain the same
  results
• Stability - the ability to repeatedly measure the
  same product or service over time and obtain the
  same average measured value

48
Definition of a Process
Inputs
Outputs
Process Various inputs blended together to
achieve a specified output
Material People Equipment Methods/Procedures Equip
ment Environment
Service Product Task completed
49
Definition of DOE

• A scientific approach in which purposeful changes
  of inputs (factors) to a process are made to
  determine the corresponding changes in the
  outputs (responses).

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Why Use DOE?

• Identify key input factors
• Gain an understanding between input factors and
  responses
• Build a mathematical model that relates response
  to the input factors
• Determine the settings for input factors that
  optimize the response
• Scientific method for setting tolerances

51
Objectives

• To find factor(s) that improve a response
  variable to some optimal value.
• To find a less expensive way to provide
  equivalent or improved performance.
• To gain a better understanding of your process
• Define the magnitude of an effect
• Identify how factors react together
• To systematically demonstrate that the current
  process is optimal.

52
Steps In Designing an Experiment
Define the Objective
Developing a product or process / Product or
process problem
Select Testing Equipment
Lab or production
Select Response Variable
Max, Min, or Nominal / Quantitative vs.
Qualitative
Select Factors and Interactions
Brainstorming, Flowcharts, Review Existing Data
Select Factor Levels
Linear vs. Nonlinear
Linear graphs, Triangular tables, Assign factors
and interactions to columns of the array
Select Orthogonal Array
If not satisfied with confounding scheme, review
design for restructure
Determine Confounding Scheme
Randomize Test Order
Sequence concerns, Additional tests