S I G M A
Measure Performance
Introduction and Determine What
to Measure
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S I G M AI G M A
Define
Opportunities
Measure
Performance
Analyze
Opportunity
Improve
Performance
Control
Performance
Business
Opportunity
Document and Analyze
Processes
Define Customer
Requirements
Build Effective Teams
Determine what to
measure
Manage measurement
Understand variation
Determine Sigma
Performance
Excellent team
performance
process stratification
and Analysis
determine root causes
validate root causes
manage creativity
improvement ideas
evaluate and select
solution
present
recommendations
Implement change
Develop and Execute
pilot plan
plan and implement
solution
process integration
closure and
recognition
Define Opportunities
Measure Performance
Analyze Opportunity
Improve Performance
Control Performance
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S I G M AI G M AReview and Transition
• In Section ,we learned how to：
Understand the role of effective teams in process improvement.
Apply team evaluation tools to identify opportunities to improve
team effectiveness.
• Section ，Measure Performance, covers the
following areas:
Business
Opportunity
1 .2 Document and
Analyze
Processes
Build
Effective
Teams
Define
Customer
Requirement
Prepared Team
Determine what
to measure
2 .2
Manage
Measurement
Determine
Sigma
performance
Understand
Variation
Excellent Team
Performance
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S I G M AI G M ASummary of “ Measure Performance”Summary of “ Measure Performance”
• What to Measure
Understand the role that data plays in process improvement
Understand the cause and effect relationships that occur inside the team’s process
Determine the indicators needed to evaluate current process performance
• Measurement
Understand different types of data and how each type can provide the team with different insights and
knowledge of a process
Develop operational definitions and data collection plans that build validity and consistency in the data
which the team gathers
• Variation
Understand the concept of variation and how a process can be evaluated by assessing its variation over
time
Plot and calculate the variation of the team’s business process
Gain hands on experience with the use of the statistical software package MINITABTM
• Sigma Performance
Understand the various calculations associated with determining process sigma
Calculate the sigma performance of the team’s process
Calculate the rolled-up Sigma for the business
• Team Performance
Understand the role of high-performance work teams in process improvement
Use team diagnostics and assessments to evaluate the team strengths and opportunities for
improving its own performance
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S I G M A
Measure
Determine What to Measure
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S I G M AI G M What to Measure
Objective
To identify different types of measures and an understanding of how the
measures relate to critical customer requirements.
Key Topics
•Performance Measurement
•Input, Process,and Output Indicators
•Indicator Relationships
Determine
Sigma
Performance
Determine What
to Measure
Manage
Measurement
Understand
Variation
Excel Team
Performance
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S I G M AI G M APerformance Measures-
Customer Value Achieved?
供货商 流程输入 业务流程 流程产出
关键客户要求
基于联合客户期望和流程
业绩表现的重要决定
输入衡量 流程衡量 产出业绩
表现衡量
客户价值
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S I G M AI G M A
Process Elements and Indicator
Relationships
Input Indicators Process Indicators Output Indicators
Measures that evaluate the degree to which the
inputs to a process, provided by suppliers, are
consistent with what the process needs to
efficiently and effectively convert into
customers-satisfying outputs.
Examples:
•#of customer inquiries
•Type of customer inquiries
•# of orders
•# of positions open
•Type of position open
•Accuracy of the credit analysis
•Timeliness of the contract submitted for review
Measures that evaluate the effectiveness,
efficiency and quality of the transformation
processes-the steps and activities used to
convert inputs into customer-satisfying outputs
Examples:
•Availability of service personnel
•Time required to perform credit review
•%of non-standard approvals required
•#of qualified applicants
•Total cost of service delivery
•Total overtime hours
Measures that evaluate dimensions of the output
-may focus on the performance of the business s
well as that associated with the delivery of
services and products to customers.
Examples：
•#of calls/hour taken by each service rep
•2nd year customer retention figures
•Total # of meals delivered
•%customer complaints
Effective improvement requires information from the entire supplier-
customer,cause and effect relationship.
Customers:Suppliers: Inputs: Outputs:
Process
Start Boundary___________ End Boundary____________
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S I G M AI G M AInput, Process and Output Indicators
Efficiency Measures
• Cost per transaction
• Time per activity
• Amount of rework
• Turnaround time
• Variability of an activity
• Efficiency Measures
• Percent defective
• Number of errors
• Total response time
• Invoice/billing accuracy
• Revenue
Input
Indicators
Process
Indicators
Output
Performance
Indicators
CTQ’S
CTP’S
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S I G M AI G M AProcess Output Indicators include
CTQ’s & CTP’s
VOB-Voice of the Business
CBR-Critical Business Requirements
CTP-Critical to the Process
VOC-Voice of the Customer
CCR-Critical Customer Requirements
CTQ-Critical to Quality
VOB
Business
Issues CBR’S
CTQ’S
CTP’S
Output
Indicators
CCR’S
Customer
Issues VOC
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S I G M AI G M ACTQ & CTP Examples
CTP’S
Cost/Unit
Productivity
Compliance with
Regulations
Changeover Time
Safety
Training Hours
CTQ’S
Price/Unit
Delivery Time
Dimensions
Purity
Reliability
Color
Service Level
Process Output
Indicators
CTQ’S
CTP’S
Critical to:
The Customer
The Market
Critical to:
The Business
The Regulator
The Employees
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S I G M AI G M ASuccess Derived From Project Focus Example:Medical Diagnostic Tube Life
After 8 projects January’96 to May ‘97 average tube life doubled.
Y
y1
Oil Dielectric Quality
GTD-3
y2
Focal Spot Control
GTD-7
y3
Generators Spits
GTD-17
y4
Rotor Failures
GD-14
yn
X4,1 X4,2 X4,3 X4,4 X4,N
X2,N
X3,N
X2,4X2,3X2,2
X3,1 X3,2 X3,3 X3,4
X2,1
X1,NX1,4X1,3X1,2X1,1
Top level Y is big enough to be seen at
OBU level-an operational business
objective.
Frequently the parent project does at least a
verification of this top level Y with the
customer
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S I G M AI G M A
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S I G M AI G M ACCR’s and Multiple Output Indicators
In the previous section, teams translated a
variety of VOC data into critical customer
requirements. Teams were careful to
recognize that some customer feedback and
statements need to be clarified, and that a
process for specifying CCRs involves
considering key issues customers may have
with a product or service. From these issues,
the team was able to specify the critical
customer requirements of the process output.
Some CCRs may be measured in terms of one
specific expectation a customer has. Others
may require several output indicators. The
table shows how one CCR can have one or
several associated output indicators.
Output Indicator
•Product delivery cycle time from the
completion of the customer order to the
delivery of the product
•Number and type of vehicle
specifications delivered correctly
•Actual delivery time VS promised
•Delivery time for each vehicle
•Number of times vehicles were delivered
to location other than what is specified on
agreement
Critical Customer
Requirement
Product is delivered within
three hours of order taken.
Right vehicle is delivered at
the right time to the right
location
Output Indicator
•Number and type of vehicle
specifications delivered correctly
•Actual delivery time Vs
promised delivery time for each
vehicle
•Number of times vehicles were
delivered to location other than
what is specified on agreement
critical Customer Requirement
•The vehicle delivered meets
the vehicle specifications as
described in the contract.
•The vehicle is delivered within
the time specified in the
contract.
•The vehicle is delivered at the
location specified in the
contract.
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S I G M AI G M ASelecting the Right Process Indicators
• In addition to making sure that the indicators provide the team with valid and
quantifiable data, teams must be sure that what they are measuring actually
enables them to evaluate the cause and effect relationships occurring inside
the process. Below is a list of questions that each team should review after
identifying output, process, and input indicators.
• Are each of the process indicators true “predictors,”or leading indicators, of at
least one output indicator?
• Do the process indicators evaluate areas of the process that are known to
adversely affect the quality of the process output?
• Has the team identified process indicators for the process variables that most
influence the ability of the process in meeting critical customer requirements
and therefore the output indicators?
• If a critical customer requirement is not met,does the team know why(root
cause)? What additional process indicators may be needed to answer this
question?
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S I G M AI G M ASelecting the Right Input Indicators
• Input indicators allow measurement of the consistency
of the inputs to the process.
Do the input indicators measure the critical requirements we have
of our suppliers’ products or services?
Do the indicators measure elements of the input that are known to
affect the ability of our process to meet critical customer
requirements?
Are the input indicators true “predictors,” or leading indicators,of
at least one process indicator?
Do the indicators measure aspects of the input that would, within a
specified tolerance, eliminate significant inspection, scrap,rework
or excessive cycle time?
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S I G M AI G M AIndicator Relationships
• Link Output Performance to Process and Input Indicators
• First look to establish output indicators because they indicate how
effective your process is at meeting CCRs. Once you understand
the key output performance measures, determine what key input
and process indicators you need in order to meet the desired
outcomes and therefore satisfy customer requirements.
• You can use a relationship matrix to help show the relationship
between the output performance measures and key input and
process measures. The relationship matrix will help prioritize the
most important measures.
• Note: The strength of the relationship is based on how likely
changes in the input of process indicator will cause changes in the
output indicator.
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S I G M AI G M ALink Output Performance to Process
and Input Measures
Example:Call Center
Relationship of Process & Input Measures
Note:The strength of the relationship is based on how likely changes in the
input/process measure will cause changes in the output performance
measure.
process &Input
Output Indicators
Performance Indicators
Answer
Speed
Employee
Experience
First Time
Resolution
Call Abandon Rate
Customer Satisfaction
Strong Relationship weak Relationship
medium Relationship Blank No Relationship
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S I G M AI G M AReview and Transition
• In Determine What to Measure, we learned:
The role that data plays in process improvement
The cause and effect relationships that occur inside the team’s process
How to determine the indicators needed to evaluate current process
performance
• In Management Measurement, we will learn:
The different types of data and how each type can provide the team
with different insights and knowledge of a process
How to develop operational definitions and data collection plans that
build validity and consistency in the data which the team gathers
Determine What
to Measure
Manage
Measurement
Understand
Variation
Determine
Sigma
Performance
Excel Team
Performance
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S I G M A
Measure Performance
Manage Measurement
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S I G M AI G M Manage Measurement
• objective
To establish a discipline and a methodology to be cost-efficient and effective in
collecting data to measure performance.
• Key Topics
Data Collection
Operational Definition
Measurement Plan
Performance Date Versus Cause Data
Sampling
Determine What
to Measure
Manage
Measurement
Understand
Variation
determine
Sigma
Performance
Excel Team
Performance
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S I G M AI G M AData Collection
Measurement
management starts
with a data collection
methodology.
Data Collection Method
Identify
Measures
Step 2
Develop measurement plan
Step 1
Develop operational definitions
for measure
Step 3
Collect data
Step 4
Display and Evaluate data
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S I G M AI G M AOperational Definition
• Step 1:Operational Definition
• An operational definition is a concept that helps guide the team’s thinking on what
they need to measure as well as the key attributes of the measure:what,how,and
who. It provides the foundation for the team to reach agreement and build
consistency and reliability into data collection. This helps ensure any person using
the agreed-on definition will be measuring the same thing.
• Operational Definition
• A precise description of the specific criteria used for the measures(the what),the
methodology to collect the data(the how),the amount of data to collect(how
much),and who has responsibility to collect the data(the who).
Provides everybody with the same meaning.
Ensures that consistency and reliability are built in up front.
Describes the scope of the measure(what is included and what is not included).
“an operational definition puts communicable meaning into a concept。”
------W。Edwards Deming
Example:Operational Definition
Poor:Cycle time for applications.
Good:Collect data from all applications received by fax from January 3,1999 to January 17,1999.
The response time will be determined by the date and time of the fax received as shown on the
faxed application to the time the approval or rejection letter is faxed to the applicant as shown
on the fax log.
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S I G M AI G M ASix Sigma and Operational Definitions
• Operational definitions enable a team to fully agree on how a particular
characteristic of a process is to be measured. It is the process
characteristic that is critical to the satisfaction of the customer.
• Therefore, when developing an operational definition,it is important for
the team to fully understand and agree that the definition reflects exactly
what information the team is attempting to gather on the process.
• Clarity is even more important when developing and selecting the
measures that will be used to determine the sigma performance of a
process.
• Operational definitions may determine if a team is to count all the defects
on an invoice(required to calculate defects per million opportunities) or
the total number of defective invoices(any invoice with any defect) or the
type of defects encountered on an invoice (to eliminate the most common
defects first). Each of these cases may require a very different approach
for gathering the data.
Operational definitions help ensure that the team does it right the first time
when it comes to data collection.
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S I G M AI G M A
Exercise: Operational Definition
• Objective
• To practice developing an operational definition.(20 minutes)
• Instructions
• one of the first three examples below and one from your process.
• an operational definition for each that will be clear to all who need to
understand it .
• to share the definitions with the class.
• -Time Departures. A consumer organization wants to rate airlines on how
successful they are at meeting the departure schedule as put forward by airports.
But before the organization can start it needs an operational definition of when the
airplane departs.
• B. Customer Complaints Reduction. A fast food restaurant wants to reduce the
number of complaints it receives. It needs an operational definition of complaints
before it can start to measure it.
• Staff. A customer service organization wants to be able to assess
how knowledgeable its staff is at meeting the customer needs. It needs an
operational definition to help establish a baseline.
• Process.
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S I G M AI G M AMeasurement Plan
Questions to Answer
What precise data will be collected?
Performance measurement?
Causes of process deficiencies?
Do we analyze all relevant data or a
sample?
What is the right sample size?
What is the right frequency?
What will be the sample selection
method?
What tools are necessary?
What formats will be used?
What logs will be kept?
Do we need a computer?
• Step 2: Measurement Plan
• Determining current process performance usually requires the collection
of data. When developing a measurement plan ensure that:
The data collected is meaningful
The data collected is valid
All relevant data is collected concurrently
What logistical issues are relevant?
Who will collect data?
Where is the data located?
When will it be collected?
What additional assistance is required?
What you want to do with the data?
Used daily, weekly,etc.
Identify trends in the process data
Identify deficiencies in the process
Demonstrate current process
performance
Identify variation is a process
Identify a cause and effect relationship
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S I G M AI G M ADevelop a Measurement Plan-
Types of Data
• Before data collections starts, classify the data into different types:continuous or
is important because it will:
Provide a choice of data display and analysis tools
Dictate sample size calculation
Provide performance or cause information
Determine the appropriate control chart to use
Determine the appropriate method for calculation of 6s
Continuous
Measured on a continuum
Objective
•Time
•Money
•Weight
•Length
Subjective
•Satisfaction
•Agreement
•Extent
•Type of error
Discrete
Count or categories
Objective
•Count defects
•# approved
•# of errors
•Type of document
Subjective
•Yes / No
•Categories
•Service performance
rating(good,poor)
•Satisfaction
•Agreement
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S I G M AI G M ATwo Basics Types of Data
• Continuous or variable data-measured on a continuum or scale.
Usually continuous measures can be divided into parts and still
make sense. For example:
Time can be divided into days, hours, minutes, or seconds (cycle time)
Money can logically be divided or specified in increments (sales, costs,
losses)
Satisfaction if measured with a continuous scale,( dissatisfied,
dissatisfied, neither satisfied nor dissatisfied, satisfied, very satisfied)can
logically be calculated and expressed in an average level of satisfaction on
a scale.
• Discrete, categorical or attribute data-measured by
example:
Defects(yes/no,approved/disapproved,pass/fail,met customer
requirement/did not meet customer requirement)
Categories(days of the weed, locations, type of customer, type of product,
risk-low/medium/high)
Satisfaction(poor/fair/good/excellent or dissatisfied/satisfied)
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S I G M AI G M ACause Data
Performance Data
• Descriptive
• Focus on Results
• Helps establish a baseline
• Measures performance of a process
• Should be collected first
Cause Data
• Focuses on why process performs the way it does
• Helps identify potential root causes
• Collect this type of data to explain performance
problems
• Cause data, on the other hand, focuses on why the process performs as it does. Cause
data supports problem solving by helping to isolate root causes of problems.
• Don’t assume, however, that you shouldn’t gather cause data and performance data at
the same time. Remember, resourcefulness is one of the keys to effective data collection.
Sometimes, you’ll know enough about potential causes to measure performance and
isolate potential causes at the same time.
• Most of the time, however, you won’t know enough about potential causes until you’ve
determined your processes current performance level. Be prepared to document current
performance first, then brainstorm potential causes and collect additional data related
to those causes at a later date.
Performance and Cause Data
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S I G M AI G M AStep 2: Develop a Measurement Plan
Each Six Sigma improvement team should complete a measurement plan that
contains the following information:
Example:Cycle time for loan application processing
How will data be used? How will data be displayed?
•Identification of the Largest Contributors
•Identifying of Data is Normally Distributed
•Identifying Sigma Level and Variation
•Root Cause Analysis
•Correlation Analysis
•Pareto Chart
•Histrogram
•Control Chart
•Scatter Diagrams
Performanc
e measure
operational
Definition
Data Source
and Location
Sample Size Who Will
Collect the
Data
When Will
Data be
Collected
How Will
Data be
Collected
Other Data
that should
be Collected
at the same
time
Time to
process a
loan
application
Fax date,time
Decision fax
date, time
Loan
applications
Representative
fax center
289 Tim Smith
Dave Mann
During the
first weed of
the month,
10/1/99 to
10/7/99
Randomly
selected from
September ‘99
Type of loan
Amount of
loan Dealer
Time of day
Day of week
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S I G M AI G M A
Step 2: Develop Data Measurement Plan
• Example: Cycle time for loan application processing
Performan
ce measure
operational
Definition
Data Source
and Location
Sample Size Who Will
Collect the
Data
When Will
Data be
Collected
How Will
Data be
Collected
Other Data
that should be
Collected at
the same time
Time to
process a
loan
application
Fax date,time
Decision fax
date, time
Loan
applications
Representative
fax center
289 Tim Smith
Dave Mann
During the first
weed of the
month, 10/1/99
to 10/7/99
Randomly
selected from
September ‘99
Type of loan
Amount of loan
Dealer Time of
day Day of
week
Considerations for other data that should be collected at
the same time:
How will you display the data?
What do you want to do with the data after it is collected?
How do you want to stratify the data?
What data might you need to identify and verify root cause?
Data collection is a balance between time money and accuracy (getting the data you need).
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S I G M AI G M AStep 3: Collect Data
• Follow the plan—note any deviations
from the plan
• Consistency—avoid bias
• Observe data collection
Discussion on Data Collection Experience
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S I G M AI G M AObtaining the Measurements
• The data collected will only be as good as the collection system itself. In order
to assure timely and accurate data, the collection method should be simple to
use and understand. There are several most common are:
Checksheet –a simple log of “tick marks” representing the volume and type of work
Time stamps- a recording of the time that each activity begins and ends.
Example: Checksheet
Applications Returned for Missing Data
• All data can be collected manually(writing in the log, recording the time,
etc.)or automatically. Automatic data collection assures accurate and timely
data, and removes the burden of collection from the operator of the process.
But, it can be very expensive to set up. It usually involves computer
programming and/or hardware. For most initial efforts, a paper log is the most
cost effective form of data collection.
Reason Missing Incorrect
Social Security Number ///// //
Street Address /// /////
Phone Number /////
////
Employment Information /// /
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S I G M AI G M AIdentify Tools to Help You Collect DataIdentify Tools to Help You Collect Data
• Hint: Identify types of data you need to collect before you design the form
Checksheets
Simple data collection form which
helps determine how often
something occurs.
Concentration Diagrams
Pictorial checksheet which helps you
mark where something occurs or the
type of problem.
Wasteful Energy Habits Week 1 Week 2 Week 3 Total
Long showers /// / // 6
Lights left on //// /// //// 11
Windows left open // / 3
AC set below 72° / // // 5
Door left open ///// ///// /// 13
Total 15 12 11 38
Name
Address ///
Telephone//
Type of Loan Needed/////
Income Level///// /////
Other Loan Information/////
Banking Information///// //
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S I G M AI G M AProcess Distribution Checksheet
.4
6
.4
7
.4
8
.4
9
.5
0
.5
1
.5
2
.5
3
.5
4
.5
5.
.5
6
.5
7
.5
8
.5
9
.6
0
.6
1
.6
2
//
//
/
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//
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// //
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//
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2 3 5 8 10 18 14 22 15 13 10 9 5 4 3 1
Totals
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S I G M AI G M AOne-Factor Attribute Checksheet
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S I G M AI G M ASampling
Using a sample of data you draw conclusions about the entire
population of data. This is known as “statistical inference.” Sampling
saves costs and time. Sampling provides a good alternative to collecting
all the data. Identifying a specific confidence level allows us to make
reasonable business decisions.
Entire population
of data sample
Statistical
inference
parameters：
M，S
Statixtics:
X，S，etc.
Sampling from a population
analysis
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S I G M AI G M ASampling Situations
Different situations which dictate
sampling techniques:
• To analyze and control a process
• To describe a large
population(., types of
customers and buying behavior)
XXX
sample
Average cycle time(Xbar）
No. of defects
Proportion defedtive
Standard deviation（S）
XXXX
sample
X X X
X
X X
X
Systematic
Process
sampling
Typical
Descriptive
statistics:
Random
sampling
from a
population
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S I G M AI G M ASampling
Types Process-subgroup sampling
XXX
sample
X XX
Day 1 Day 2 Day 3
Sample from a particular step in the process each day(hour, week, month)
Population-stratified random sample
Randomly sampling within a logical category(location,shift,product,ect)
A
A B
B
C
C D
D
A
A
B
B
C
C
D
D
sample
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S I G M AI G M ASampling Considerations
• Where
Location in the process where process steps directly affect outputs (strong
relationship)
Maximize opportunity for problem identification(cause data)
• Frequency
Dependent on volume of transactions and/or activity
Unstable process—more frequently (use systematic or subgroup sampling)
Stable process—less frequently(use sample size formula)
Dependent on how precise the measurement must be to make a meaningful
business decision
• considerations
Is the sample representative of the process or population?
Is the process stable?
Is the sample random?
Is there an equal probability of selecting any data point?
The answer to each of these questions must be yes before we can draw statistically
valid conclusions
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S I G M AI G M ADetermining Minimum Sample Size
Minimum sampling size from a population or a stable process can be
estimated from the following formulas:
Continuous Data Sample Size
For continuous data:
N=minimum sample size required
S=estimate of standard deviation of the population or
process data
D=level of precision desired from the sample in the
same units as the “s” measurement
=constant representing a 95%confidence interval
where
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S I G M AI G M A
Discrete Data Sample Size
For discrete or proportion data:：
where
n=minimum sample size
p=estimate of the proportion of the population of process which is
defective
D=level of precision desired from the sample in units of proportion
=constant representing 95%confidence interval
the highest value of p(1-p) or p=.5
Benefits of Continuous Data
Usually requires a smaller sample
More information for stratification and root cause analysis
Determining Minimum Sample Size
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S I G M AI G M AFormula for Small Populations
• Making adjustments in the minimum sample size required for
small populations:
• Sample size formula assumes:
a 95% confidence interval
A small sample size(n) compared to the entire population size(N)
If n/N is greater than , the sample size should be adjusted to
The proportion formula should only be used when nP≥5
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S I G M AI G M AFormula for Small Populations
Example: Processing loan applications
Given:
• The sample size formula shows that you need a minimum sample size of
289.
• You have only processed 200 units.
Solution: The correct minimum sample size would be:
or 119-minimum sample size required
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S I G M AI G M AMinimum Sample Size
Example:Sample Size Calculation—Continuous
A sigma team samples a loan process to determine the average processing
time,and wishes to estimate the average time within one day. Based on
previous sampling, the team has estimated the standard deviation of the
current loan processing time as 4days.
What is the minimum sample size required to be able to estimate the average
with the required precision?
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S I G M AI G M A
Minimum Sample Size
Example: Sample Size Calculation—Discrete
Another sigma team determines the minimum sample size required
for the proportion of service contracts that require rework at the
client approval meeting. From interviews, the team has concluded
that approximately 25% of the contracts contain errors and require
rework. They wish to determine the % requiring rework within 5%.
n=（)(.1875)=289 contracts
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S I G M AI G M AExample: Sample Size
Objective:
Determine the appropriate sample size.(10 minutes)
Instructions:
Use the room service breakfast example. Breakfast is
scheduled for the time the customer requests delivery.
The customer requirement is +/-10 minutes from the scheduled
delivery time.
Estimated s= and D=2 minutes
Estimated number of defects is 30%（P=；D=5%）
Determine the minimum sample size for both
continuous and discrete data.
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S I G M AI G M AAnswer: Sample Size(continued)
Continuous
Discrete
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S I G M AI G M AExample: Sample Size Formula
• Objective:
Determine the appropriate sample size formula to use.(30 minutes)
• instructions：
At your tables determine the right formula(proportion/discrete or continuous)to use
and calculate the sample size for each situation.
the average cycle time within 2 hours. The estimated standard deviation is
8 hours. What is the minimum number to sample?
team collected 100 observations to determine the proportion defective. They found
20% to be defective. How accurately can they estimate the proportion defective?
have a customer survey with 2 categorical questions and 8 interval statements.
You estimate that at least one option of a categorical question will be answered by
approximately 50% of the respondents and you want to be able to detect a
difference within±5%。For the continuous statements you want to be able to detect
a difference of at least ½ a point. The highest estimated standard deviation for any
of the statements is expect the response rate to be 25%.how many surveys
do you have to send out and how many completed surveys do you need returned?
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S I G M AI G M AAnswers to Sampling Exercise
3Discrete Calculation
Continuous
must send out 4*minimum sample or 4*385= 1,550
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S I G M AI G M AStep 4: Display and Evaluate Data
Display data:look for
data errors and
outliers.
Evaluate the data
collection
methods:determine if
the methods used to
collect data have
provided consistent
and representative
data.
Scatter
HistogramRun
Pareto
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S I G M AI G M AEvaluate Data
• Has your data collection method:
Given you dependable data?
Provided consistent information throughout the data collection period?
Provided a reliable set of data?
Given representative data?
• If you repeat the data collection will you get similar results?
• Does the data collected provide the information you need?
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S I G M AI G M AReview and Transition
• In we learned:
The different types of data and how each type can provide the team with different
insights and knowledge of a process.
How to develop operational definitions and data collection plans that build validity
and consistency in the data which the team gathers.
• In , understand Variation, we will learn:
The concept of variation and how a process can be evaluated by assessing its
variation
How to plot and calculate the variation of the team’s business process
The use of the business statistical software package with hands-on experience
Determine What
to Measure
Manage
Measurement
Understand
Variation
Determine
Sigma
Performance
Excel Team
Performance
Operational Definitions
Data Collection Formats and Plans
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S I G M A
Measure Performance
Understand Variation
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S I G M AI G M Understanding Variation
Objective
To develop an understanding of the importance of variation in
managing processes and how to measure variation.
Key Topics
•What is Variation?
•Charting Variation?
Determine What
to Measure
Manage
Measurement
Understand
Variation
Determine
Sigma
Performance
Excel Team
Performance
Baseline Performance
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S I G M AI G M AVariation
• Variation means that a process does not produce exactly the same result
every time the product or service is delivered.
• Variation exists in all processes.
• Measuring and understanding variation in our business processes helps
identify specifically what the current level of performance is and what needs
to change in order to reduce the variability and therefore reduce the defects
delivered to customers.
Data Variation
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S I G M AI G M AWhat Causes Variation?
Suppliers Process Inputs Business Process Process Outputs
Critical
Customer
Requirements
Variation in the
output of processes
causes defects
Defects
Root cause analysis
of variation leads
to permanent defect
reduction
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S I G M AI G M AWhat is Variation?
Delivery Time
Critical Customer
Requirement = 10 days
Defects:Service
unacceptable to
customer
F
r
e
q
u
e
n
c
y
o
f
D
e
l
i
v
e
r
y
T
i
m
e
s
s = Variation or data spread
x = days
1 2 3 4 5 6 7 8 9 10 11 12
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S I G M AI G M AVariation Reduction
• If we reduce variation, then fewer observations will fall
above the customer requirement of 10 days.
Delivery Time
Critical Customer
Requirement = 10 days
Defects: Service
unacceptable to
customer
F
r
e
q
u
e
n
c
y
o
f
D
e
l
i
v
e
r
y
T
i
m
e
s
s =Variation or data spread
x = days
1 2 3 4 5 6 7 8 9 10 11 12
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S I G M AI G M AVariation and Mean Reduction
• If we reduce both the average delivery time and the variation in
delivery time, we can further reduce those times that do not meet
customer requirements.
Delivery Time
Critical Customer
Requirement = 10 days
Defects:Service
unacceptable to
customer
F
r
e
q
u
e
n
c
y
o
f
D
e
l
i
v
e
r
y
T
i
m
e
s
x = 6 days
1 2 3 4 5 6 7 8 9 10 11 12
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S I G M AI G M A
What Does Variation Mean to Sigma?
• Measuring variation means that we can clearly define how well we
are meeting customer requirements.
• By observing or measuring the process over time you can
determine the mean and standard deviation, and therefore the
performance of the process against customer requirements.
• Sigma requires that we measure two elements:
Process performance
Customer requirements
• The goals of Sigma Business Improvement are to center the
process well within customer requirements through reducing
variation,first by eliminating special causes of variation,and then
the common causes that are necessary in order to center the
process outputs fully within customer requirements.
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S I G M AI G M A
Charting Variation
Histograms
A histogram is a bar graph that displays the results for a
sample of performance data (daily commuting time, for
example) in picture form. This picture is sometimes called
a frequency distribution because it shows clearly how
frequently each separate value appears in the data.
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S I G M AI G M ACharting Variation-Normal Distribution
single peak equal to average
symmetrical sides continuously declining
on both sides
X
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S I G M AI G M ACharting Variation-Standard Deviation
The standard deviation noted as σ -for the population
s-for the sample
A normal distribution is completely described when we know the x and s of
the data.
Normal Distribution
X Xi
S
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S I G M AI G M ACharting Variation-Standard Deviation
• The standard deviation noted as -for the sample
is an efficient way of expressing the average spread or
variation of a set of data.
Standard deviation for a sample is calculated as:
Where x=the average of all the data
xi=the individual data point value
n=the number of data points
A normal distribution is completely described when we
know the x and s of the data.
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S I G M AI G M A
Standard Variation: Yield &The Normal CurveStandard Variation: Yield &The Normal Curve
• The normal curve can also be partitioned as shown below and
because of its perfect symmetry,the following rules apply:
Number of standard deviations
on either side of the team
% of data between
these limits
1
2
3
4
5
6
X
Number of Standard Deviations form the Mean
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
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S I G M AI G M AExercise:Histogram Interpretation
Objective
To practice interpreting
histograms.(15 min.)
Instructions
Analyze the following
Histograms and answer
the corresponding questions
below.
What type of distribution is this?
What may this represent?
What type of distribution is this?
What may this represent?
10 23 36 49 62 75 88 101 114 127
3 6 9 12 15
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S I G M AI G M ACharting Variation-Run Charts
Three Different Run Charts with the Same Distribution
26
25
24
23
22
21
20
19
18
17
16
15
14
26
25
24
23
22
21
20
19
18
17
16
15
14
26
25
24
23
22
21
20
19
18
17
16
15
14
16 17 18 19 20 21 22 23 24
X X X X X X XXX
X X X X X
X X X
X
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S I G M AI G M ACharting Variation-Control Charts
26
25
24
23
22
21
20
19
18
17
16
15
14
UCL
CL
LCL
M T W TH F M T W TH F M TH F M T W TH F M T W TH F M
Days
C
om
m
ut
in
g
T
im
e(
m
in
s)
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S I G M AI G M AControl charts-Basics
Control charts
• Help manage variation
• Help monitor the process
• Provide an easy to understand visual indicator of process
performance
• Help sigma improvement teams understand the root cause
of the variation in a process
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S I G M AI G M AControl charts-Basics
• Steps to building an appropriate control chart
• the type of data
• data consistently with control charting in mind
• the appropriate control chart
• the control chart
• process performance
• corrective action
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S I G M AI G M AControl Chart Theory
• The control chart, invented by is a
common sense way to determine if a process is
exhibiting common cause or special cause variation.
• This is another way of asking, is the process “in
control”or “out of control?”
• Common Cause Variation:Variation that is random
and inherent in the system.
• Special Cause Variation:Variation that is
unpredictable, intermittent and usually related to only
one element of the process.
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S I G M AI G M AControl Chart Theory
• Another definition used in manufacturing is that common cause
variation is due to all the following categories or elements of a process
collectively.
While special cause variation is that caused by only one of these categories.
Service and sales versions of these categories may include the following:
Service/Sales Categories
measurement Methods machines
Material Mother Nature People
People Marketing Location
Products Distribution Mother Nature
Procedures Policies Service
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S I G M AI G M ARationale for the Three Sigma Limits
• Dr. Shewhrt determined that selecting the three sigma
limits for a control chart would help people improve the
process profitably… That is plus or minus 3 sigma from
the average was a good balance between the two types of
statistical errors.
1）Type I, Finding a special cause when there is not one and,
2）TypeⅡ, not finding a special cause when there is one
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S I G M AI G M ASelecting the Appropriate Control Chart
*Proportion Defective:The entire unit is either good or bad. A proportion can be
calculated-binomial assumptions apply.
**Count of Defects:There is no limit to the number of defects that can be counted. It
is not possible to count the non-defects. Poisson assumptions apply.
Type of Data
Discrete Continuous
C Chart
Constant sample size
U Chart
Variable sample size
NP Chart
Constant sample size
P Chart
Variable sample size
Individuals, Moving Range & EWMA
Sample size=1
Sample size<6
X-bar and R
Sample size>=6
X-bar and S
Count of defects** Proportion of defective*
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S I G M AI G M AThe Central Limit Theorem
The central limit theorem states:
“The shape of the sampling distribution of X-Bar will be a
normal curve, no matter what the shape of the population
distribution.” Koosis
The conclusion is that X-Bar Charts will almost always
reflect a normal distribution regardless of the distribution
of the individual data points.
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S I G M AI G M A
*Proportion Defective:The entire unit is either good or bad. A proportion can be
calculated-binomial assumptions apply.
**Count of Defects:There is no limit to the number of defects that can be counted. It
is not possible to count the non-defects. Poisson assumptions apply.
Type of Data
Discrete Continuous
C Chart
Constant sample size
U Chart
Variable sample size
NP Chart
Constant sample size
P Chart
Variable sample size
Individuals, Moving Range & EWMA
Sample size=1
Sample size<6
X-bar and R
Sample size>=6
X-bar and S
Count of defects** Proportion of defective*
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S I G M AI G M AThe Binomial Assumptions are as Follows:
1）The count of discrete data comes from a distinct subgroup N.
This subgroup is usually more than 50 items.
2）There are two possibilities of result:conformance of non-conformance
3）Each result is independent of the other.
The assumption is that both the total number of units and the total
number of non-conforming units are this case the unit or
item is either conforming or non-conforming,and the proper control
chart is either the NP-Chart if the sample size is constant, or the P
Chart if the sample size is not.
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S I G M AI G M ABinomial Measurements Have Two Possible Outcomes
Defective,Not Defective
Yes, No
Conforming,Not Conforming
Satisfied, Not Satisfied
Example: Loan Approval Process
Note:
Not all percentage are
discreet or count
.%yield. If both the
numerator and the
denominator are determined
by measuring, the % is
considered continuous data
file C:\6Sigma\Control Charts\
STAT>CONTROL CHART>P
variable to be charted <Loans Approved>
column number containing the subgroup size in
“Subgroups in”<Total Loans>
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S I G M AI G M A
P Chart for Loans Not Approved
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S I G M AI G M A
*Proportion Defective:The entire unit is either good or bad. A proportion can be
calculated-binomial assumptions apply.
**Count of Defects:There is no limit to the number of defects that can be counted. It
is not possible to count the non-defects. Poisson assumptions apply.
Type of Data
Discrete Continuous
C Chart
Constant sample size
U Chart
Variable sample size
NP Chart
Constant sample size
P Chart
Variable sample size
Individuals, Moving Range & EWMA
Sample size=1
Sample size<6
X-bar and R
Sample size>=6
X-bar and S
Count of defects** Proportion of defective*
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S I G M AI G M A
The Poisson Assumptions are as Follows:
1）The chance of an error or incident is small (less than
five percent)
2）Events occur independently of one another
3）The area of opportunity for the error or event is
constant for each subgroup.
Think about this as counting the number of errors where
the opportunity for error is unlimited. For instance
there would be no limit to the number of blemishes that
could be found on an automobile,or the number of
accidents that could occur in a population of workers.
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S I G M AI G M APoisson Distributions are Characterized by the Poisson Distributions are Characterized by the
Following:Following:
Probability of defect is low
Opportunity for defect is high
You cannot count the non-defects
Data are characterized by the number of occurrences in a sample
Example:Automobile Warranty Claim Process
file C:\6Sigma\Control Charts\u-
STAT>CONTROL CHART>U
variable to be plotted and,
denote sample size by
selecting.“Subgroups in” cars delivered
15201501December 8
16275601November 7
19270770October 6
22600870September 5
15770595August 4
18420776July 3
246751000June 2
16020630May1
1ST6MONTHS
No OF CARS
DELIVERED
No OF
CLAIMS
Month
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S I G M AI G M AU Chart for No. Of Claims
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S I G M AI G M A
C Chart for Errors in 100 Applications
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S I G M AI G M AExponentially Weighted Moving Average
Control Charts
• When the process average changes slowly over time, a potentially
more sensitive control chart is the exponentially weighted average
chart. This control chart is sensitive to small shifts in data and is
useful when early detection of a process shift is critical to the
business process owners.
Example
EWMA Calculation
Historical Mean=100
()+.2(81)817
()+.2(71)716
()+.2(82)825
()+.2(102)1024
(1000)+.2(120)1203
()+2(89)892
()+2(114
)
1141
EWMA
(WEIGHT=)
CALCULATIONINDIVIDU
AL DATA
SEQUENCE
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S I G M AI G M AControl Chart Maintenance
• Control charts should be based on common cause
this reason special causes should be investigated and removed
from the data. This maximizes the possibility of detecting special
cause variation.
• The minimum number of data points to construct a control chart
should be 20-30.
• Question:Under what circumstances should the limits on a control
chart be changed?
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S I G M AI G M AGuidelines for Recalculating
Control Limits
Do the data display a pattern clearly different than the past?
Is the reason for the change known?
Do we expect the new process results to continue?
OK to calculate limits from new data.
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S I G M AI G M AⅠChart for Cycle Av for Chart M1
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S I G M AI G M AⅠChart for Cycle Av for Chart M2
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S I G M AI G M AI Chart for Cycle Average
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S I G M AI G M A
Should customer specifications be placed on
the control chart?
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S I G M AI G M ARelating “Voice of Customer” to
“Voice of Process”
State
of Process
Control
Within Spec Outside Spec
In control
O
ut of control
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S I G M AI G M AIntroduction to Statistical Comparison
• Hypothesis tests answer the question “Is Group 1significantly
different from Group 2”. Groups 1&2 could be the cycle time of a
process before and after a process improvement, or defects at one
location 1 and location 2.
• Hypothesis tests include continuous and discrete data and could
include more than two groups. Test included are:
t-Tests
ANOVA tests
Correlation
Regression
Chi-squared tests
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S I G M AI G M A
Introduction to Statistical Comparison-Is Sample Introduction to Statistical Comparison-Is Sample
A different from Sample B? A different from Sample B?
Entire
Population
of data
Sampl
e
Entire
Population
of data
Sampl
e
Parameters:
μσ
Parameter：
μσ
Sample A
X and S
Sample B
X and S
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S I G M AI G M AIntroduction to Statistical Comparison
• We are hypothesizing that there is no difference
between the populations being tested. We are testing
the null hypothesis that the groups being compared are
not different.
A p-value is reported for each hypothesis test.
The p-value has a range between and .
The closer the p-value is to the more likely the groups being
are different.
A p-value less than is considered significant since we are
testing to prove that there is a difference.
The p-value is the probability that the observed difference could be
caused by sampling variation alone.
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S I G M AI G M AIntroduction to Statistical Comparison
• We are hypothesizing that there is no difference
between the populations being tested. We are testing
the null hypothesis that the groups being compared are
not different.
A p-value is reported for each hypothesis test.
The p-value has a range between and .
The closer the p-value is to the more likely the groups
being are different.
A p-value less than is considered significant since we are
testing to prove that there is a difference.
The p-value is the probability that the observed difference
could be caused by sampling variation alone.
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S I G M AI G M AHypothesis Tests Assumptions
• Sufficient samples must have been drawn
randomly from a population
Statistical independence assumption
• That the data are normally distributed
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S I G M AI G M AHypothesis Testing
• Suppose a six sigma team wished to compare the average salaries
of employees from two different departments. First they collect a
random sample of people from the population of each department.
Next they plotted the histograms from each department.。
1
3
6
5
1
33
2
1
XCS=Average Salary=
3
2
3
4 4
3 3
1
2
Xm= Average Salary =
Marketing
F
re
qu
en
cy
F
re
qu
en
cy
Customer Service
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S I G M AI G M AHypothesis Test Interpretation
Our hypothesis test,often,will be to “disprove the null hypothesis.”
To accomplish this,we will return to the concept of p-value stated earlier.
This time we will define P as follows:
If p≤,we declare a significant difference exists.
“the p-value is the probability that the observed difference between Xcs and
Xm is caused by sampling variation.”
Another way to state this is:
“The p-value is the probability that these two samples came from the same
population.”
The conclusion here is that we will not declare a statistically significant
difference exists unless there is less than a 5% chance we have made a
mistake.
0 P
Not Different
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S I G M AI G M ATypes of Error
Hypothesis Test Result
Not Different Different
OK
OK
TypeⅠerror
α=probability of
TypeⅡerror
β=probability ofDo not take
action or make
decision when
should have.
Take action or
make decision
when should not.
D
if
fe
re
nt
N
ot
D
if
fe
re
nt
Actual
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S I G M AI G M AHypothesis Tests
Discrete Continuous
Chi Square
Regression
T-Test
ANOVA
DOE
Logstic
Regression
Y
X
C
on
ti
nu
ou
s
D
is
cr
et
e
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S I G M AI G M ASummary of Statistical Tools 1
Tool What Type of Data When to Use How to apply this
Tool in my work
Histogram Visual display of one variable
showing data center, spread,shape
and outliers.
Continuous or discrete large amounts of data
get a ‘feel for the data’
compare actual description to
customer specs
Multivari Charts Bar chart comparison of sub-groups
on one variable.
Continuous or discrete To visually compare sub-groups by
individual data points and the mean. In
MINITAB 12 only. To identify major
source of variation.
Box Plots Visual display of the summary of Y
data grouped by category of X.
Y=continuous
X=discrete or categorical
Summary display to visualize
differences in data center, spread and
shape across categories.
Run Charts Plots observation is time sequence Y=continuous or discrete To view process performance over time
for trends,sifts or cycles.
Control Charts Plots observations in time sequence
against a mean and control limits.
Y=continuous or discrete To monitor the process in order to
control and improve process
performance over time for trends, shifts
or cycles. To identify special causes.
Scatter
Diagram(Plot)
Plots a response Y versus a predictor
X.
Y=continuous
X=continuous
To understand the possible relationships
between two variables. To identify
possible root causes which are related to
Y. Do not use with special
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S I G M AI G M ASummary of Statistical Tools 2
Tool What Type of Data When to Use How to apply this
Tool in my work
Behaviorally
Anchored
Scales
A response scale on which specific
points are named or described to
clarify the differences between
points.
Discrete/Categorical:
Nominal (name)
Ordinal (order)
To translate subjective or qualitative issues into
data (discrete or continuous).To reduce
variation in the response measured.
t-Test Determine if there is a difference
between two groups.
Y=continuous
X=discrete or categorical
if sample average=specified value
if 2 sample means are equal
t: to reduce variation when comparing
two sample averages
Analysis of
Variance
Determine if there is a difference
among many groups.
Y=continuous
X=discrete or categorical
（2 or more Xs)
Determine of there is a statistically significant
difference among the groups.
Discrete
Data:
Chi Square
Determine if there is a difference for
observed frequencies of 2 discrete
variables.
Y= discrete or categorical
X= discrete or categorical
Determine if there are relationships between
two discrete variables.
Regression(Linear
& Multiple)
Summarizes, describes, predicts and
quantifies relationships.
Y=continuous
X=continuous or discrete
if there is evidence of a
relationship between Xs and Ys.
data to develop a mathematical
equation to quantify the relationship.
root causes.
predictions using the model.
Logistic
Regression
Summarizes, describes, predicts and
quantifies relationships.
Y=discrete
X=continuous or discrete
if there is evidence of a
relationship between Xs and Ys.
data to develop a mathematical
equation to quantify the relationship.
root causes.
predictions using the model.
Design of
Experiments（DO
E）
Systematic and efficient proactive
approach to testing relationships.
Y=continuous or discrete
X=continuous or discrete
To establish cause and effect relationship
between Ys and Xs. To identify ‘vital few’ Xs. Version Nov 2002103Page
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S I G M AI G M AReview and Transition
In Understanding Variation, we learned:
The concept of variation and how a process can be evaluated by assessing its variation.
How to plot and calculate the variation of the team’s business process.
How to use a business statistical software package.
• In Determine Sigma Performance, we will learn:
The various calculations associated with determining process sigma.
How to calculate the sigma performance of the team’s process.
Determine What
to Measure
Manage
Measureme
nt
Understan
d
Variation
Determine
sigma
Performan
ce
Excel
Team
Performance
Baseline Performance
Version Nov 2002104Page
S I G M A
Measure Performance
Determine Sigma Performance
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S I G M AI G M Determine Sigma Performance
Objective
To determine the right method for calculating Sigma performance.
Calculate process sigma performance using the appropriate method.
Key Topic
Calculating Sigma Defined
Continuous Data Calculations
Discrete Data Calculations
Rolled-up Sigma Calculations
Determine What
to Measure
Manage
Measuremen
t
Understand
Variation
Determine
sigma
Performanc
e
Excel
Team
Performance
Process Performance Based
on Customer Requirements
Version Nov 2002106Page
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S I G M AI G M ASteps for Calculating Sigma
• The method to be used for calculating sigma
performance depends on the type of process
performance data used(continuous or discrete).
• Steps in Calculating Sigma Performance
• Critical Customer Requirements (CCRs)
• types of variable and output measures to
be collected
• nature of data collected (short term/long
term)
• Sigma Performance
Version Nov 2002107Page
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S I G M AI G M ACalculating Sigma Defined
Critical Customer Requirements (CCRs)
Critical customer requirements must be determined by/from the
customer and defined as key output variables or CTQs
The level of performance required on these key output measures
define the critical customer requirement that the Sigma
Calculation is based on. For example, cycle time<5 days
Determine sigma calculation method required. Identify
and collect data on each, based on Critical Customer
Requirements.
the type of data for each performance
measure to be used to calculate sigma.
Continuous
Discrete
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S I G M AI G M ACollect Data
•Identify the specific measures required
•Develop an operational definition
•Determine minimum sample size
•Collect data
The output measure are derived from critical customer requirements
as described in section . Often more than one output measure is
important to customers. For example, time of delivery (cycle time)and
quality of the product or service may both be important to customers.
You could have different Sigma performance levels for each of these
measures.(See Sigma Roll-up calculations.)
Version Nov 2002109Page
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S I G M AI G M of Data
Short-Term and Long-Term Data
Output measures tend to vary over time due to many internal and
external example, supplier quality may vary, affecting the
quality of information required for your process. New competitors
may emerge affecting the marketplace and customer expectations. It
is important to separate short term performance from long term in
order to determine the potential for the current process. Classify the
nature of the data measured as either short term or long term.
•Short term
30-50 data points minimum
no special causes or shifts in performance
•Long term
100-200 data points minimum
includes special causes or possible shifts in performance
Version Nov 2002110Page
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S I G M AI G M AShort-term versus Long-term Data
A
B
C
D
E
A+B+C+D+E
Long-term Data
includes the effects of
special cause variation
Time
Short-term Data
generally dose not
include special cause
variation
Version Nov 2002111Page
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S I G M AI G M Sigma Performance
Following are the basic methods for calculating Sigma
• All methods require the minimum sample size for 95% confidence.
• Data should be randomly selected to represent the population.
Method Type of Data Comments
Ⅰ.Z-Score Continuous The data must be roughly normally
distributed. Calculate the Z-score and
yield of the process.
Ⅱ.DPMO (Defects per Million
Opportunities)
Discrete N>1000 Must have at least 5 defects or 5 non-
defects.
Ⅲ.Discrete(High Volume) Discrete N>1000 Less than 5 defects
Ⅳ.Discrete (Low Volume) Discrete N≤1000 Less than 5 defects
Ⅴ.Sigma Roll-up Discrete or Continuous Combine yields from a business point
of view.
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S I G M AI G M Sigma Performance
Select the appropriate method
Calculating process Sigma
Ⅰ
Continuous
Ⅱ
DPMO Method
Discrete
Ⅴ
Sigma Roll-up
Ⅲ
High Volume
Ⅳ
Low Volume
Version Nov 2002113Page
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S I G M AI G M AThe concept of Six Sigma
Area Under the Standard Normal Curve
Defects
-3 -2 -1 0 1 2 3
0
10
20
30
40
50
60
70
80
Process Yield
.6794
Z or sigma=
Z Process
Version Nov 2002114Page
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S I G M AI G M ACalculating Sigma for Continuous DataCalculating Sigma for Continuous Data-Example-Example
Example:
• A customer service counter processes applications for credit cards
at the store location. The average time for processing application
or ‘Xbar’ is minutes; the standard deviation of ‘s’ is
minutes; and critical customer requirement or CCR is 10 minutes.
CCR
Cumulative Probability or Yield
S=
Credit Card Application Processing Time
10minutes
Z10=
X-Xbar
S
=
Z10=
0
Version Nov 2002115Page
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S I G M AI G M ASigma Calculation Table
*note:
This table does not include a
shift. If you enter this
table with long-term data
then you calculate long-term
Sigma and if you enter with
short-term data then you
calculate short-term Sigma
Both Motorola and GE Capital
assume that you enter their A
bridged Sigma Table with long
-term data and exit with a
short-term Sigma. In order to
do this,they assume a shift
of Sigma between short-
and long-term Sigma.
Therefore,if long-term yield
equates to a standard normal
area of Sigma(or
DPMO)then they assume a
shift and report short-term
Sigma of .
*
*
Version Nov 2002116Page
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S I G M AI G M AUpper and Lower CCRs
Defects
Defects
0 10-10
Delivery Time
Version Nov 2002117Page
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S I G M AI G M ACombine into a single yield
Calculations
Defects greater than USL=(%)
Area from zero to USL==((%)
Defects less than LSL=(%)
Area from zero to LSL=(%)
Yield==(70%)
Look up Yield of in Sigma Table
Z=(approximately)
-3 -2 -1 0 1 2 3
0
10
20
30
40
50
60
70
80 USLUSLUSL
.013
.70 or
yield=70%
Standard Normal Values of Delivery Time
Version Nov 2002118Page
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S I G M AI G M Sigma Performance
I
Continuous
II
DPMO Method
Discrete
V
Sigma Roll-up
III
High Volume
IV
Low Volume
Calculating Process sigma
Select the
appropriate
method
Version Nov 2002119Page
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S I G M AI G M ABreakfast Example
• Now let’s review an example of how process
outputs, critical customer requirements,and the
standard normal distribution are combined to
determine the process sigma. A hotel provides
room service meals to its guests,and from
numerous guest surveys and research, has
designed a service that guarantees a breakfast
meal delivery within 10 minutes of the time
requested by its guest. They have determined an
early delivery will inconvenience the guest as
well as a late delivery, especially in the morning.
• Data from a one week operation has been
gathered and is shown here. What is the process
sigma of the breakfast delivery?
50
-10 0 10 20 30
100
0
Fr
eq
ue
nc
y
Delivery Time Deviation
Low
Customer
Limit
Upper
Customer
Limit
Target
Defects
Version Nov 2002120Page
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S I G M AI G M ACalculating Sigma with Discrete Data
• Taking another look at the “Breakfast Delivery” data we’ve been
using, let’s examine a very direct way to calculate process yield.
• By examining the raw data, we can count the number of delivery
times that do not meet customer requirements and translate that
directly into a defect calculation referred to as Defects Per Million
Opportunities, or DPMO。
Version Nov 2002121Page
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S I G M AI G M ADPMO Defined
• DPMO=Defects Per Million Opportunities
• =1M x
where：D*=total number of defects counted in the sample: a defect
defined as failure to meet a CCR or Critical Customer Requirement
• N=number of units of product or service
• O=number of opportunities per unit of product or service for a
customer defect to occur
• M=million
*There must be at least 5 defects and 5 non-defects to use the DPMO
formula.
Version Nov 2002122Page
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S I G M AI G M ADPMO Example
Using the previous example, let’s calculate the DPMO and the process sigma
Using this method from the data set on breakfast delivery times:
D=205
N=725
O=1（There is only one opportunity for a defect per breakfast delivery. Either the
delivery is within the customer limits or not.）
DPMO=
Using the Sigma Calculation table, enter the DPMO column and look up the process
sigma directly.
The relationship between DPMO and process sigma is as follows:
Process Yield=1-DPU
Where DPU=Defects/unit
In our example,
Process Yield == or % sigma=.058
Version Nov 2002123Page
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S I G M AI G M A
Sigma Calculation for Breakfast Example
Objective:
To practice calculating Sigma
Information Provided:
Mean=5minutes
Standard=10minutes
USL=+10minutes
LSL= -10minutes
the Sigma for continuous data
Version Nov 2002124Page
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S I G M AI G M AReview and Transition
• In Determine Sigma Performance, we
learned:
The various calculations associated with determining process sigma.
How to calculate the sigma performance of the team’s process.
• In , Excel Team Performance, we will learn:
The role of high-performance work teams in process improvement.
How to use team diagnostics and assessments to evaluate the team
strengths and opportunities for improving its own performance.
Determine What
to Measure
Manage
Measurement
Understand
Variation
Determine
Sigma
Performance
Excel Team
Performance
Process Performance
Based on Customer Requirement
Version Nov 2002125Page
S I G M A
Measure Performance
Excel Team Performance
Version Nov 2002 Page
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S I G M AI G M Excel Team Performance
Objective
To enable the team to reach a high level of performance fully utilizing
team member skills, knowledge, and experience working
collaboratively.
Key Topics
• Norming Stage
• Teaming Techniques
• Performing Stage
Determine What
to Measure
Manage
Measurement
Understand
Variation
Determine
Sigma
Performance
Excel Team
Performance
Productive Team Atmosphere
Version Nov 2002127Page
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S I G M AI G M ASummary of “Measure Performance”
• Determine What to Measure
Understand the role that data plays in process improvement
Understand the cause and effect relationships that occur inside the team’s process
Determine the indicators needed to evaluate current process performance
• Measurement
Understand different types of data and how each type can provide the team with different insights and
knowledge of a process
Develop operational definitions and data collection plans that build validity and consistency in the data which
the team gathers
• Variation
Understand the concept of variation and how a process can be evaluated by assessing its variation over time
Plot and calculate the variation of the team’s business process
Gain hands on experience with the use of the statistical software package MINITAB TM
• Sigma Performance
Understand the various calculations associated with determining process sigma
Calculate the sigma performance of the team’s process
Calculate the rolled-up Sigma for the business
• Team Performance
Understand the role of high-performance work teams in process improvement
Use team diagnostics and assessments to evaluate the team strengths and opportunities for improving its own
performance
Version Nov 2002128Page
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S I G M AI G M A
$$
CCRsCCRs
Teams
Focus
What is the
process？
Q
ui
ck
W
in
O
pp
or
tu
ni
ty
？
What Part of the Gap Does My
Customer Care About Most？
Current Performance
Gap
Gap
Desired Sigma Level
Customer
Suppliers
Strategy
Technology
Regulation
Competitors
Validated Area
of Focus
What Indicators do We Need to
Evaluate the Current Process？
Input Process Output CCR
Input Indicator
Output Indicator
Process Indicator
CCR’s
VOC
Define Opportunities & Measure Performance Define Opportunities & Measure Performance
Cartoon StoryboardCartoon Storyboard
Process Indicator
g
g
Version Nov 2002129Page
