Lean Six Sigma Analyze Phase Introduction. TECH QUALITY and PRODUCTIVITY in INDUSTRY and TECHNOLOGY

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TECH 50800

QUALITY and PRODUCTIVITY in INDUSTRY and TECHNOLOGY

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Week 11

Lean Six Sigma Basics: Analyze TECH 50800

QUALITY and PRODUCTIVITY in INDUSTRY and TECHNOLOGY

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Lean Six Sigma Analyze Phase

Introduction

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4

LEAN SIX SIGMA PROCESS…

Pilot Study Implement‐

ation Plan

Champion Define Analyze Improve Control

Voice of the Customer

Analysis

Complete Project Charter

Current State Process

Map

Create Basic KPOV

Graphs

Develop/

Evaluate Solutions

Future State Process

Map

Determine Process Control Plan Finalize

KPIVs

Full Implement‐

ation Recognize/

Reward

Finalize Financial Estimates Identify

Opportunities

Select Project

Determine KPOVs

Data Collection

Examine Process and

Data

KPIVs Verified Set Team

Ground Rules

Measure Lean 101

Identify Waste

Lean 201

Quick Hit Improve‐

ments

Identify Constraints

Exploit Constraints

Link KPOVs to CTQs Launch Project Team

Potential KPIVs Identified

Link KPIVs to KPOVs

Initial Financial Estimates

Analyze Phase

Analyze Phase Goals



Use Data Driven Decision Making techniques



Continue to utilize statistical analysis to understand the data.



Appropriately apply advanced graphing techniques

o

Scatter Plots

Analyze Examine Process and

Data KPIVs Verified Link KPIVs to

KPOVs

THE ANALYZE PHASE

5

Analyze Phase Steps



Examine the process/data



Verify or eliminate KPIVs.



Conclusively link KPIVs to KPOVs using data analysis and graphing

techniques.

THE ANALYZE PHASE

6 Analyze

Examine Process and

KPOVs

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Analyze Phase Expected Outcomes



KPIV data collection completed



KPIVs Analysis used to determine critical KPIVs



Critical KPIVs conclusively linked to KPOVs

THE ANALYZE PHASE

Analyze Examine Process and

KPOVs

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Lean Six Sigma Analyze Phase Analyze Tools

LEAN SIX SIGMA TOOLS…

Voice of the Customer

Analysis Project Charter

Process Mapping

Basic Statistics Measurement Systems Analysis Affinity

Diagram

Project Selection Matrix

CTQ Tree Create Data Collection Plan

Process Observation Worksheet

SIPOC Ground Rules

Worksheet

Spaghetti Diagram

5S

Visual Controls

Little’s Law Theory Of Constraints

Variability Principle CTQ Tree

Ishikawa Diagram

Advanced Pivot Tables and

Charts

Advanced Graphing Techniques KPIV Analysis

Pilot Implementatio

n Checklist

Process Modeling and

Simulation Future State Process Map Solution Matrix

Impact Effort Matrix

Process Control Plan

Recognize Improvement

Achieved

ROI Tool

Project Management

Implementatio n Checklist ROI

Tool

Champion Define Measure Lean 101 Analyze Improve Lean 201 Control

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Lean Six Sigma Analyze Phase KPIV Analysis

Data Analysis

Using data to find patterns, trends and other clues to support or reject KPIVs.

Process Analysis

A detailed look at existing processes to identify waste.

BECOMING a ‘DEFECT DETECTIVE’

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Steps

1. Examine the process/data 2. Verify or eliminate KPIVs.

3. Conclusively link KPIVs to KPOVs using data analysis and graphing techniques.

KPIV ANALYSIS

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‘CSI Approach’

…you must create a robust case to ‘convict’ each KPIV….



We suspect that each of the KPIVs have an impact on the KPOVs.



Use your data to build evidence to prove which KPIVs have an impact on the KPOVs.

KPIV ANALYSIS

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Time as a KPIV

• Time (Date/Time of day) should always be considered as a KPIV

• If evidence is found, investigate further into the time‐dependent variables that may be impacting the KPOV

• What are the KPIVs that are typically responsible for time dependencies within a process/service?

SUMMARIZING and DISPLAYING DATA

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DISPLAYING DATA EXAMPLE

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Drive Thru Delays by Category

Food Not ready Waiting

CashierFor Customer

Adds to Order

Line SpeakerAt

Money readyNot

CC Machine

down Customer

Delay Other

KPOV PARETO CHART

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Average Daily Drive Thru Time (minutes)

KPOV RUN CHART

17 CC Machine

Down Cashier

Absent

Additional Cook Hired

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LEAN SIX SIGMA TOOLS…

Additional Analyze Phase Tools:



Measurement Scales – Review



Capability Analysis



Correlation and Regression

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Lean Six Sigma Analyze Phase Measurement Scales

Scale Description Example

Nominal (Categorical)

Data consists of categories only. No ordering scheme possible.

Gender, Ethnicity, Group, Department Ordinal

(Ranking)

Data arranged in some order but differences between values cannot be determined or are meaningless.

Service Arrival, Sequence by Type

Interval

Data arranged in order and the differences between values can be found. However ratios are meaningless.

Satisfaction Scale

Ratio Interval scale with a zero starting point and values that are multiples.

Age, Length of Service, Time

MEASUREMENT SCALES

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MEASUREMENT SCALES

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Scale Center Spread Significance Tests

Nominal

(Categorical) Mode Information Only Chi‐Square Ordinal

(Ranking) Median Percentages Sign or Run Test

Interval Arithmetic Mean Standard Deviation

F test, t test, correlation

analysis

Ratio

Arithmetic Mean Geometric Mean Harmonic Mean

Standard Deviation Percent Variation

F test, t test, correlation

analysis

MEASUREMENT SCALES

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Lean Six Sigma Analyze Phase Capability

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

Capability indices are a statistical measure of process capability:

o

Process capability  The ability of a process to produce output within specification limits.



The concept of process capability only holds meaning for processes that are in a state of statistical control.

CAPABILITY INDICES

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

Capability indices:

o

Measure how much "natural variation" a process experiences relative to its specification limits.

o

Allows different processes to be compared with respect to how well an organization controls them.

o

Are important tools in process improvement efforts.

CAPABILITY INDICES

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VISUALIZING PROCESS CAPABILITY

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Estimates what the process is capable of producing if the process mean is centered between the specification limits

p

U S L - L S L

C 6 ˆ

 

CAPABILITY INDEX C _p

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VISUALIZING C _p

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

Capability indices use short term variation where the standard deviation is estimated ( ).



Capability indices are based on ±3 or where the process falls 99.7% of the time.



If the process mean is not centered within the specifications, C

_p

overestimates process capability.

p

U S L - L S L

C 6 ˆ

 

ˆ 

CAPABILITY INDEX C _p

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

C

_pk

estimates what the process is capable of producing when the process mean is not centered between the specification limits.



C

_pk

can also be used for single sided metrics – upper or lower specification only by selecting the appropriate formula.

p k

U S L - ˆ ˆ - L S L

C m i n ,

3 3 ˆ ˆ  

 

 

    

ADDITIONAL INDICES

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

C

_pL

 Estimates process capability for specifications that consist of a lower limit only.



C

_pU

 Estimates process capability for specifications that consist of a upper limit only.



If the specification is two‐sided, the off‐centered capability index is the smaller of C

_pU

and C

_pL

.

p L p U

- L S L U S L -

ˆ ˆ

C C

3 3 ˆ ˆ

 

 

 

ADDITIONAL INDICES

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C

_pk

Sigma level

(σ) Process yield Process fallout (PPM)

0.33 1 68.27% 317311

0.67 2 95.45% 45500

1.00 3 99.73% 2700

1.33 4 99.99% 63

1.67 5 99.9999% 1

2.00 6 99.9999998% 0.002

EVALUATING CAPABILITY

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C

_p

represents the potential capability C

_pk

represents the current capability If C

_pk

is worse than C

_p

, it can be improved by

centering the process.

When centering is perfect, C

_p

= C

_pk

. C

_pk

can never be better than C

_p

.

EVALUATING CAPABILITY

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

A process is said to be stable when only Common Causes are present and no special cause is active.



A process can be Stable, but still incapable of meeting customer specifications.



Stability has nothing to do with Capability

STABILITY and CAPABILITY

36 Control Limits

Process Limits

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

Process Performance Indices are an estimate of the capability of a process using measured or long term variation () and mean ().



Process and capability indices are formulaically identical. However, the estimated  and  for capability indices have a higher level of uncertainty:

C

_p

 P

_p

C

_pk

 P

_pk

C

_pU

P

pU

C

_pL

 P

_pL

PROCESS PERFORMANCE INDICES

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Lean Six Sigma Analyze Phase Correlation and Regression

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

Regression Analysis includes techniques for modeling and analyzing several variables where the focus is on the relationship between a dependent variable and one or more independent variables.



Regression Analysis attempts to explain how the typical value of the dependent variable changes when any one of the independent variables is varied while the other independent variables are held fixed.

REGRESSION ANALYSIS

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

Regression analysis is used for trend analysis, prediction and forecasting



Regression analysis is also used to understand which among the independent variables are related to the dependent variable, and to explore the forms of these relationships.



Regression Analysis methods include:

o

Linear Regression

o

Non‐Linear Regression

o

Multiple Linear Regression

REGRESSION ANALYSIS

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REGRESSION ANALYSIS

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

Sample is representative of the population.



Error is a random variable with a mean of zero conditional on the explanatory variables.



Independent variable is measured with no error.



Predictors are linearly independent,



Errors are uncorrelated.



Variance of the error is constant across observations (homoscedasticity).

ASSUMPTIONS

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

Linear Correlation Coefficient (r), measures the strength and the direction of a linear relationship between two variables.



Value of r range is ‐1 < r < +1 data.

CORRELATION COEEFICIENT

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

Positive correlation:

o

If x and y have a strong positive linear correlation, r is close to +1.

o

An r value of exactly +1 indicates a perfect positive fit.

o

Positive values indicate a relationship between x and y variables such that as values for x increases, values for y also increase.

CORRELATION COEEFICIENT

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

Negative correlation:

o

If x and y have a strong negative linear correlation, r is close to ‐1.

o

An r value of exactly ‐1 indicates a perfect negative fit.

o

Negative values indicate a relationship between x and y such that as values for x increase, values for y

CORRELATION COEEFICIENT

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

No correlation:

o

If there is no linear correlation or a weak linear correlation, r is close to 0.

o

A value near zero means that there is a random, nonlinear relationship between the two variables.

o

Note that r is a dimensionless quantity; that is, it does not depend on the units employed.

CORRELATION COEEFICIENT

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

A perfect correlation of ± 1 occurs only when the data points all lie exactly on a straight line.



If r = +1, the slope of this line is positive.



If r = ‐1, the slope of this line is negative.



If r = 0, there is no correlation

CORRELATION COEEFICIENT

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

A correlation greater than 0.8 is generally described as strong, whereas a correlation less than 0.5 is generally described as weak.

CORRELATION COEEFICIENT

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

Coefficient of Determination (r

²

) gives the proportion (percentage) of the variance of one variable that is predictable from the other variable.



It is a measure that allows us to determine how certain one can be in making predictions from a certain model/graph.



The Coefficient of Determination is the ratio of the explained variation to the total variation.

COEFFICIENT of DETERMINATION

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

The range of r

²

is 0 < r

²

< 1



The Coefficient of Determination represents the percent of the data that is the closest to the line of best fit.

o

For example, if r = 0.922, then r

²

= 0.850.

o

The value indicates that 85% of the total variation in y can be explained by the linear relationship between x and y.

o

The other 15% of the total variation in y remains unexplained.

COEEFICIENT of DETERMINATION

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COEEFICIENT of DETERMINATION

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

Examples of nonlinear functions include Exponential Logarithmic, Polynomial, Power and Moving Average.



e.g. Exponential  The graph of y = e

^x

is upward‐

sloping, and increases faster as x increases.

NON‐LINEAR REGRESSION

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

e.g. Logarithmic growth describes a phenomenon whose size or cost can be described as a logarithm function of some input. e.g. y = C log

NON‐LINEAR REGRESSION

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

Excel performs Regression Analysis for plotted data using the Trendline option in the Chart Tools:

REGRESSION ANALYSIS

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

Excel performs both linear and non‐linear regression and can calculate the Coefficient of Determination

REGRESSION ANALYSIS

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

Linear Correlation

REGRESSION ANALYSIS

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

5

^th

Power Polynomial Correlation

REGRESSION ANALYSIS

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

When there is more than one independent variable, the regression line cannot be visualized in the two dimensional space

