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The DMAIC Process Detail
The Measure Phase
© Max Zornada (2005)
Slide 1
DMAIC Process Storyboard
DEFINE
TEAM FORMATION
Objective: Select problem/
opportunity theme, select team
members
MEASURE
Objective: Identify and implement the measures required to
establish baseline performance and quantify the opportunity.
Key Steps:Cause and Effect Diagram
Run chart or
Objective: Define the Problem/Opportunity,
Customers, Customer Requirements, and Process.
Team charter
Key Steps:Flowchart
•Determine what to measure
•Understand the measures
•Understand Variation
•Assess measurement system
•Assess process performance
•Develop business case
•Develop project team charter
•Understand Customer Requirements
•Understand the Process.
Output: Problem/Opportunity
selected, Team members selected.
Output: Team Project Charter, Work Plan, Measurable Output: A quantified picture of the current process
Customer Requirements, Process Map/Process Analysis performance, problem impact. The process sigma rating.
ANALYSE
IMPROVE - I : Generate Potential Solutions
Objective: Identify and verify the root cause(s) of the problem.
Key Steps:•Analyse data
•Analyse process
•Determine potential root causes
•Hypothesis Testing
•Verify root causes
Cause and Effect Diagram
(Fishbone)
Checksheet
Pareto Chart
Output: Root cause(s) identified.
IMPROVE - II: Implement and Check
Objective: Implement the preferred solution. Confirm that the
problem and its root cause(s) have been reduced or eliminated.
Key steps:•Implement preferred
After
solution
•Verify effectiveness
•Apply comparative
methods if necessary.
Output: Confirmation that the best solution to eliminate the
problem & its root cause(s) has been implemented.
Before
control chart
Objective: Determine possible solutions that will address the identified root
cause(s) of the problem.
Key Steps:Potential Solutions
Action Plan
•Generate potential solutions
•Assess potential solutions
•Select preferred solution
•Test/Pilot preferred solution
•Develop implementation plan
Output: Preferred solution or countermeasures
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
CONTROL - Standardise
Objective: Prevent the problem and its root
cause from recurring.
Flowchart
Key steps:Standard
procedure
•Standardise the solution
(standards & procedures)
•Document project
•Implement scorecard
•Implement controls
Output: Solution embedded and “routinised” in
relevant process, procedures and standards.
© Max Zornada (2005)
FUTURE PLANS
Objectives: Review team effectiveness,
plan to address remaining issues and
institutionalise the learning.
D
C
Key Steps:Define,
I
M
•Review remaining project
opportunities
•Review other applications
•Review learnings
Measure,
Analyse,
Improve,
Control
A
Output: Recommendations for future projects
and improvements to team processes. Project
documentation and learnings “pack”
Slide 2
Overview of the Measure Phase

Determining what to Measure;

Understanding and Describing Data;

Understanding and Managing Variation;

Statistical Process Control;

Process Capability and Sigma Level;

Overview of Sampling
© Max Zornada (2005)
Slide 3
Determining what to Measure
© Max Zornada (2005)
Slide 4
Y = f(x)

The fundamental equation that drives Six Sigma;

Output (Y) is a function of the Inputs and the
Process
Examples of Y
Examples of x’s - x1, x2, x3 …. xn

Output

Inputs to the process

Outcomes

Leading indicators/Drivers

Effect

Problems and their causes

Symptom

“Noise” factors

A Dependent Variable

Complexity

A Key Performance
Indicator

Independent Variables
Control and “levers”

© Max Zornada (2005)
Slide 5
Approaches to identifying measures
(and what data to collect)

The process scorecard “generic” template;

Cause and effect (fishbone diagram) around the
CTQ outcome of interest;

The Critical-to-Quality (CTQ) Tree approach;

Correlation analysis between measures and
outcomes;

The Measurement Assessment.
© Max Zornada (2005)
Slide 6
Consider a Generic Process
Real Work
Stream
Complexity Stream
Complexity Stream
Customer
© Max Zornada (2005)
Slide 7
Measuring Process Performance
Supplier Interface Measures?
Process
Performance
Measures ?
Customer
Customer Interface Measures?
© Max Zornada (2005)
Slide 8
Consider HTLC: Typical Measures
Things like ….
Supplier Interface
Measures




Incoming stock
delivery performance
Credit check
turnaround time
Backlog of items on
order
Outputs
Process
Inputs
Process Measures

Time to process an
order
Customer Interface
Measures

Customer
Satisfaction

Cost

Number of orders in
the system (work in
progress)

Complaints

Orders not delivered
on time/Late
Order backlog

Overdue orders

Number of orders
filled.

No. of Orders
Received
© Max Zornada (2005)
Slide 9
A Generic Template for Developing
Process Based Performance Measures
Overall Organisation/Business Unit
End-to-End Core Process
Internal Process
Outcomes Measures
•Time
•Cost
•Quality/Waste
© Max Zornada (2005)
Customer Outcomes
Measures
•Delivery
•Quality
•Value
External
Customer
Slide 10
A Scalable Concept
But the specific measures
developed will be different
in each case.
Workgroup A
Subprocess
Internal Supplier
Internal Process
Outcomes Measures
•Time
•Cost
•Quality/Waste
Customer Outcomes
Measures
•Delivery
•Quality
•Value
Workgroup B
Sub-process
Customer Outcomes
Measures
•Delivery
•Quality
•Value
Internal Customer
Internal Process
Outcomes Measures
•Time
•Cost
•Quality/Waste
© Max Zornada (2005)
External
Customer
Slide 11
Inputs, Process and Outcomes Measures
A draft “generic” template for process measurement
Input Measures
Customer Outcomes
Measures (Inputs)
•Delivery
•Quality
•Value
Customer outcomes
the supplier(s) to
the process work to,
in order to meet the
input requirements
for the process
Customer Outcomes
Measures
•Delivery
•Quality
•Value
Process
Internal Process
Outcomes Measures
•Time
•Cost
•Quality/Waste
© Max Zornada (2005)
External
Customer
Slide 12
What can you do about ….

A late delivery to ensure its delivered on time - after
its already been delivered late?

A cost over run - after it has already been incurred?

Avoiding dissatisfying a customer - after they have
already been dissatisfied?

We need some predictive measures as well;

These are referred to as leading indicators or
drivers.
© Max Zornada (2005)
Slide 13
Consider our process
The Real Work Stream gives us the
optimum:
Real Work
Stream
Customer

Processing time/order (&
cycle time) and hence
delivery time;

Work input and hence
resources & sost/order;

Nothing goes wrong.
This will be the best this process
can do.
© Max Zornada (2005)
Slide 14
Causes of Outcomes
Drivers or Leading Indicators

What would cause an order to take longer to be
processes?

What would cause an order to cost more to be
processed?

What would cause an order to be delivered late?

What would cause the process to operate other than
perfectly (only real work).
Complexity!
© Max Zornada (2005)
Slide 15
Understanding complexity provides
insight into what the leading indicators
should be
Real Work
Stream
Example: HTLC
Eg. item in stock
measure
Backlog of items on Order
Eg. technician availability
measure
% order rescheduled due to
“technician not available”
Customer
© Max Zornada (2005)
Slide 16
Shortcut method for identifying leading
indicators (x’s)

What are all of the things that could stop the process
( internally)?

What external factors could stop the process from
meeting its customer and process outcomes?

Can you measure these?
© Max Zornada (2005)
Slide 17
The Process Scorecard
A “generic” template for process measurement: Inputs,
Process, Leading Indicator and Outcomes Measures
Customer Outcomes
Measures
•Delivery
•Quality
•Value
Input Measures
Customer Outcomes
Measures (Inputs)
•Delivery
•Quality
•Value
Leading
Indicators (causes
of the outcomes)
Customer
Outcomes
Measures
Process
Customer
Leading Indicators
•Process specific issues
•Key Complexity Issues
•External to process
issues
Internal Process
Outcomes Measures
•Time
•Cost
•Quality/Waste
© Max Zornada (2005)
Internal
Process
Outcomes
Measures
Slide 18
Process Measurement: Y = f(x)
Customer Outcomes
Measures
•Delivery
•Quality
•Value
Input Measures
Customer Outcomes
Measures (Inputs)
•Delivery
•Quality
•Value
Usually
the Y’s
Process
Customer
Leading Indicators
•Process specific issues
•Key Complexity Issues
•External to process
issues
Internal Process
Outcomes Measures
•Time
•Cost
•Quality/Waste
Potential x’s found here
© Max Zornada (2005)
Slide 19
Fishbone Diagram
HTLC Example
Inputs
Customer Outcomes
Complexity Issues
Item not in stock
Customer complaints
Order incorrectly
specified
Promised date too
soon
Refund/Penalty claims
Technician not available
No transport
Delivery
Performance
Supplier didn’t supply
Return trips to same customerTraffic conditions
Processing time too long
Process Lead Time too long
Other
External Impacts
© Max Zornada (2005)
Can we get
measures for
these things ?
Process Outcomes
Slide 20
Identifying Measures

We can potentially generate lots of measures;


Only a small number of measures may actually
matter;


Do we measure everything?
Problem is identifying which ones?
We can focus our measurement and data collection
by considering the relationships between various
potential measures and the CTQ outcome which is
the focus of the improvement effort;

Build a measures correlation matrix.
© Max Zornada (2005)
Slide 21
Measures Correlation Matrix
Potential Input/Process/LI
Measure (x’s)
Outcome Measure (Y)
On-time
delivery
Right Equip Equipment
Delivered
Total
Works
No. of Order with item Out of Stock
10
9
9
3
7
0
12
No. of Orders for Non-Stocked Item
1
3
3
15
No. of Order on Backlog
9
0
1
10
9
0
0
9
No. of Orders with no transport
allocated
9
0
0
9
Time of day order delivered
1
0
0
1
Quoted Lead Time per Order
3
0
0
3
No. of Orders incorrectly specified
3
9
3
15
Processing time
1
0
0
0
Importance
No. of Orders with no tech allocated
© Max Zornada (2005)
Slide 22
Measures Correlation Matrix
Potential Input/Process/LI
Measure (x’s)
Outcome Measure (Y)
On-time
delivery
Right Equip Equipment
Delivered
Total
Works
No. of Order with item Out of Stock
10
9
9
3
7
0
12
No. of Orders for Non-Stocked Item
1
3
3
15
No. of Order on Backlog
9
0
1
10
9
0
0
9
No. of Orders with no transport
allocated
9
0
0
9
Time of day order delivered
1
0
0
1
Quoted Lead Time per Order
3
0
0
3
No. of Orders incorrectly specified
3
9
3
15
Processing time
1
0
0
0
Importance
No. of Orders with no tech allocated
© Max Zornada (2005)
Slide 23
The Tree Diagram Approach to
Identifying Measured
© Max Zornada (2005)
Slide 24
Identifying Measures using a CTQ Tree
HTLC Example
Ontime delivery
performance
The Outcome
Measure (Y)
© Max Zornada (2005)
Slide 25
Identifying Measures using a CTQ Tree
HTLC Example
Brainstorm things
that could affect the
outcome. Refer
previous analysis.
Ontime delivery
performance
The Outcome
Measure (Y)
Credit check
turnaround time
Stock
Availability
Technician
Availability
Transport
Availability
© Max Zornada (2005)
Slide 26
Identifying Measures using a CTQ Tree
HTLC Example
Brainstorm things
that could affect the
outcome. Refer
previous analysis.
Ontime delivery
performance
The Outcome
Measure (Y)
Credit check
turnaround time
Orders received
Stock
Availability
Technician
Availability
Transport
Availability
© Max Zornada (2005)
Orders filled
from stock
Order placed on
backlog
Identify measures for
each of the things
that can affect the
outcome (the x’s)
Slide 27
Deciding what data to collect

Two basic uses of data:

Monitoring:


Aggregate data: data used to tell you at what
level the process is operating and to indicate
when something has changed;
Improvement:

Disaggregate or Stratify: need to be able to
identify specific linkages between data
elements and sources;
© Max Zornada (2005)
Slide 28
Using a Measurement Assessment Tree
Questions we want
to answer about
the process
Output (Y)
Stratification
Factors
(x variables)
Measures
Y
By time period
N
Y
# late, by hour of day
Y
# late, regular contract
By type of customer
# late, casual sales
Y
How many are late?
Are there trends of patterns?
# late, by day of week
Y
No. of late deliveries
How much is it costing?
Does this metric potentially help
predict the output Y?
By location
By value
Does data exist to obtain this
metric
N
Y
Y
Y
Y
© Max Zornada (2005)
# late, by region
# late, by suburb
Y
Y
Y
Y
# late, by distance from w/h
# late, small orders
# late, large orders
Slide 29
N
N
N
Operational Definitions

A measurement must give consistent results no
matter who does the measuring;

An Operational Definition gives a description of
what something is and how it is measured;

Therefore, before data is collected, we must agree
on the operational definition of all terms and on the
measurement criteria to be used.
© Max Zornada (2005)
Slide 30
Normalisation

Correcting for different scales of measurement is
called normalisation;

Normalisation allows us to compare two groups of
data, where the raw data may have been collected in
different ways;


e.g. different time frame, different units, different
sample size.
Data are usually normalised by time, volume or
task.
© Max Zornada (2005)
Slide 31
Understanding Data and Variation
© Max Zornada (2005)
Slide 32
Hi-Tech Leasing Corporation
Monitoring the performance of the Order
Fulfillment Process
© Max Zornada (2005)
Slide 33
The Funnel Experiment
H
A
G
F
E
Flip chart paper
B
Target
C
Radius of circle = 4 cm
Defines on time delivery zone
Result of an individual pencil
drop
D
Late deliveries zone (outside
the circle)
Distance from centre in cm = days to fill the order
© Max Zornada (2005)
Slide 34
The funnel experiment







The Funnel experiment is used to simulate the performance
and an order fulfillment process;
The company promise customers delivery within 4 days;
Each pencil drop through the funnel represents an order
going through the process;
The distance the drop lands from the target is measured in
centimeters. This represents how long that particular order
took to fill in days.
Orders landing inside the inner circle of radius 4 cm
represent orders delivered within the service standard;
Order landing outside the inner represent late deliveries;
The zones labeled A, B, C, D, E, F, G, H represent the
different reasons for which the delivery was late.
© Max Zornada (2005)
Slide 35
The funnel experiment
The Rules

Group 1: Aim for the target, lock in the settings and
take 50 shots for the target without re-targeting.

Group 2: Same as group 1, except if you miss, you
can re-target to improve your chances next time.

Group 2: Aim each shot where the last one landed.
Measure the 1st 25 shots and record the measurement on the worksheet.
Note: Measurements must be made in the order in which they occur.
© Max Zornada (2005)
Slide 36
Data Collection Sheet: The Funnel Experiment
Drop Value (X)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Drop
16
17
18
19
20
21
22
23
24
25
Value (X)
Type the information directly
into an Excel Worksheet to
simplify calculations.
Total
Average
© Max Zornada (2005)
Slide 37
Types of Data


Continuous or variables data is data that is measured on a
continuous scale and can take any value i.e. can take values
that are not whole numbers (e.g. 3.1, 7.5, 8.9 etc.);
 Examples include measure such as:- time, weight,
temperature, length, money etc.;
Discrete data is data that is measured by counting things. It
can only assume a countable number of values. Can also be
referred to as attribute data when used to count items with a
particular characteristic or attribute;
 Examples include: Percent defective, number of errors,
customer satisfaction ratings on 1-5 scale, models of car.
© Max Zornada (2005)
Slide 38
Populations and Samples



A population is the body of data that we want
information about;
 In our case, all of the orders processed by HTLC;
From the population we select a sample;
 In our case, our sample is the number of orders
for which we collected data about (25 orders);
The idea is to be able to analyse the sample to get
information about the population.
© Max Zornada (2005)
Slide 39
Collecting and Displaying Discrete Data
© Max Zornada (2005)
Slide 40
The Anatomy of a Check Sheet
Example: Lost Time Injury Data for a Security Firm
Progressive “Tally” count of each
occurrence, collected from raw
data or directly from the field
Note: = 1,
=5
The categories in
which the data
occurs
Category
Numerical frequency
count or summary of
the “tally” or
occurrences in each
category
Frequency
Tally
1
Allergy
8
2
Broken limb
12
3
Back/Neck
6
4
Concussion
14
5
Contusion
7
6
Heart Attack
1
7
Sprains
23
8
Other
3
Total
Overall Total
© Max Zornada (2005)
78
Slide 41
Frequency/ Number of Occurrences
Check Sheet Data can be displayed using a
Pareto Chart
30
23
20
14
12
10
8
7
6
3
© Max Zornada (2005)
1
Slide 42
The Pareto Principle
(Also know as the 80/20 Rule):
“A few causes account for most of the effect”
Trivial
Many
20% of the causes
account for 80% of
the effect!
Critical
Few
Causes
Effect
© Max Zornada (2005)
Slide 43
Check Sheet for Funnel Experiment
Reason category
1
A
2
B
3
C
4
D
5
E
6
F
7
G
8
H
Tally
© Max Zornada (2005)
Frequency
Slide 44
Pareto Chart Proforma
© Max Zornada (2005)
Slide 45
Displaying Continuous Data
© Max Zornada (2005)
Slide 46
Representing Data Graphically
Data can be represented graphically by using tools such as
Dot Plot
Histogram
Individual data points
20
17
15
13
10
10
1 2 3 4 5 6 7
5
Scale of allowable values
0
2
2
1-12
13-24
Y-Axis:
Magnitude
scale
3
25-36
3
37-48
49-60
61-72
73-84
Individual data points
Run Chart
© Max Zornada (2005)
X- Axis: Time based scale
Slide 47
Histogram
20
17
15
13
10
10
5
2
0
1-12
2
3
3
13-24 25-36 37-48 49-60 61-72 73-84
Determining the number of class intervals
Class intervals
Number of data values Number of Class Intervals
Under 50
5 to 7
50 to 100
6 to 10
100 to 250
7 to 12
Over 250 1
0 to 20
© Max Zornada (2005)
Slide 48
Exercise: Displaying Data

Construct a Dot Plot of your Data manually;

Use Excel to construct a Histogram and a Run chart.
© Max Zornada (2005)
Slide 49
Order Fulfillment Process Performance – Dot Plot
© Max Zornada (2005)
Slide 50
Describing Data

Location – where is it?
 Measured by:




Spread – how spread out are the points? (Variation)
 Measured by:




Mean
Median
Mode
Range
Interquartile Range
Standard Deviation
Shape – what does it look like?



Bell shape
Skewed
Uniform
© Max Zornada (2005)
Slide 51
Some Common Data Shapes
Bell Shaped
Skewed "Right"
"Toothlike"
Bi-Modal
© Max Zornada (2005)
Slide 52
Measures of Location
Refer Tools and Techniques Guide Book Appendix

Mean or Average

Median

Mode
Exercise:

Calculate the above three measures of location for
your data.
© Max Zornada (2005)
Slide 53
The Median

The Median is the Middle Value in an Ordered Sequence

If odd number of values = middle value of sequence
If even number of values = average of 2 middle values

Position of Median in Sequence is = (n+1)/2
For an odd number of data points

Raw Data:
9, 6, 4, 2, 4, 2, 4, 7, 2, 4, 3
 Ordered Data:
2, 2, 2, 3, 4, 4, 4, 4, 6, 7, 9

Position:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
Median = the 6th point = 4

Even number of data points

Raw Data:
9, 6, 4, 2, 3, 2, 4, 7, 2, 3, 3, 9

Ordered Data:
2, 2, 2, 3, 3, 3, 4, 4, 6, 7, 9, 9

Position:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
Median = the average of 6th & 7th points = (3+4)/2 = 3.5
© Max Zornada (2005)
Slide 54
Mean/Median - Advantages/Disadvantages
Advantages of the mean:
 Easy to calculate and interpret
 Based on all of the data
Disadvantages of the mean:
 Only gives good indication of location for symmetrical data
 Not a good indicator of location if there are extreme points
in the data or is the data distribution is skewed.
Advantages of the median:
 Easy to obtain and interpret
 Unaffected by extreme points and skewed distributions
Disadvantages of the median:
 Only based on the “middle” data point(s)
© Max Zornada (2005)
Slide 55
Measures of Spread or Variation

Range

Inter-quartile Range

Variance

Standard Deviation
© Max Zornada (2005)
Slide 56
Understanding process performance I

Calculate the range for your data.

Review the graphical representations and measures
of location from previous exercises.

What performance would you be prepared to
guarantee your customers?
© Max Zornada (2005)
Slide 57
Consider the outputs from 3 different systems
Range





Mean
The systems producing these
outputs are obviously different;
However, the mean, median and
range of each are the same;
These summary measures do not
allow us differentiate between
these distributions;
We need another measure that
does.
The Standard Deviation!
Median
© Max Zornada (2005)
Slide 58
The Standard Deviation
Mean
The standard deviation can be thought of as a measure
that represents the average of the distance of all of the
points from the mean.
© Max Zornada (2005)
Slide 59
Getting a little more sophisticated:
The Standard Deviation

Is a measure of the degree to which average process
performance represents typical process performance
n
Standard Deviation (S)



i 1
The Greek symbol Sigma
is used to refer to the
population standard deviation.


(X  X)
1
2

(X
2
(X
i
 X)
2
n  1
 X)
2
 ....
(X
n
 X)
2
n  1
s
2
Where S2 is called the Variance
© Max Zornada (2005)
Slide 60
The Interquartile Range

The interquartile range - IQR, (or hinge spread) is
the spread of the middle 50% of the data;

IQR = UQ - LQ

where LQ is the lower quartile, or the middle of
the lower half of the data,

and, UQ is the upper quartile, or middle of the
upper half of the data.
© Max Zornada (2005)
Slide 61
Calculating the Interquartile Range for an
Even Number of Data Points
Lower Half of Data


Ordered Data:
Position:
Upper Half of Data
2, 2, 2, 3, 3, 3, 4, 4, 6, 7, 9, 9
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
LQ = Middle or Median of
the lower half of the data
= (2+3)/2 = 5/2
LQ = 2.5
UQ = Middle or Median of
the upper half of the data
= (6+7)/2 = 13/2
UQ = 6.5
IQR = UQ - LQ = 6.5 - 2.5
IQR = 4
© Max Zornada (2005)
Slide 62
Calculating the Interquartile Range for an
Odd Number of Data Points
Upper Half of Data


Lower Half of Data
Ordered Data:
2, 2, 2, 3, 4, 4, 4, 4, 6, 7, 9
Position:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
UQ = Middle or Median of
the upper half of the data
= (4+6)/2 = 10/2
UQ = 5
LQ = Middle or Median of
the lower half of the data
= (2+3)/2 = 5/2
LQ = 2.5
IQR = UQ - LQ = 5.0 - 2.5
= 2.5
© Max Zornada (2005)
Slide 63
Exercise

From your data calculate of the performance of the
order fulfillment process. Calculate the following:

Variance

Standard Deviation

Lower Quartile

Upper Quartile

Interquartile Range
© Max Zornada (2005)
Slide 64
The Box Plot
Displaying measures of location and spread as a
complete package

A boxplot is a graphical way of displaying
information about the spread and location of data;

A boxplot focuses attention on certain features of
the data without having to plot all the values. E.g.
the presence of extreme points or skewness in the
data;

Box can provide a quick way of assessing data for
which the team may be considering developing a
control chart.
© Max Zornada (2005)
Slide 65
Box Plot Example
Waiting times at a medical clinic

Waiting time (in minutes) at a
medical clinic is measured by
taking 5 samples at random during
the mid-morning of each day for a
week.
Cumulative sum
Frequency

Time
Tally
1
2
3
4
5
6
7
8
9
10
12
15
Total
1
2
2
3
5
2
2
3
2
1
1
1
25
1
3
5
8
13
15
17
20
22
23
24
25
Sample 1
Sample 2
Sample 3
Sample 4
Sample 5
Mon
Tues
Wed
Thurs Fri
6
4
5
15
5
1
10
2
7
3
2
6
9
5
8
12
8
7
4
3
4
9
4
8
5
Total time = 153 minutes
Lower quartile (Q1) = 7th point = 4
Median = 13th point = 5
Upper quartile (Q3) = 19th point = 8
IQR = UQ - LQ = 8 - 4 = 4 minutes
Mean = 153/25 = 6.1 minutes
© Max Zornada (2005)
Slide 66
The Anatomy of a Box Plot
The Box Plot for Waiting time data
Lowest data
point inside
the Lower
Inner Fence
Highest data
point inside
the Lower
Inner Fence
Whiskers
IQR
“Outlier”
*
-2
-1
0
1
2
3
4
5 6
7
8
9 10 11 12 13 14
1.5 X IQR = 6
1.5 X IQR = 6
LQ = 4
Median = 5
Lower Inner Fence
= LQ - (1.5 X IQR)
= 4 - 6 = -2
15
UQ = 8
Mean = 6.1
Upper Inner Fence
= UQ + (1.5 X IQR)
= 8 + 6 = 14
© Max Zornada (2005)
Slide 67
The Box Plot for Waiting time data
Conclusions
*
-2
-1
0
1
2
3
4
5 6
7
8
9 10 11 12 13 14

Box Plot suggests that the data distribution is skewed to the right

Evidence:

15

Mean is not equal to the Median

The Median is less than the Mean

The Whiskers are not equal, the right one is longer than the left one.
There is an outlier - the 15 minute point. This represents an unusual point
which is not typical for the system.
© Max Zornada (2005)
Slide 68
Presenting Data with Box Plot
Vertical Presentation
Horizontal Presentation
*
-2 -1 0
1
2 3 4
5
6 7 8 9 10 11 12 13 14 15
© Max Zornada (2005)
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
-1
-2
*
Slide 69
Exercise: Box Plots

Construct a Box Plot the Order Fulfilment delivery
data simulated by the funnel experiment.
© Max Zornada (2005)
Slide 70
Box plots

Are a graphical representation of data that show,
location, spread, symmetry or skewness and whether
there are any outliers;

Need to have at least 5 distinct data values to draw a
box plot.

Box plots can be used to compare two or more
samples of data;

If the boxes do not overlap, then there are
statistically significant differences between
samples (need at least 10 data points for each box
plot for comparisons).
© Max Zornada (2005)
Slide 71
The Normal Distribution
Average = Median
2s = 68.26 % of Data
4s = 95.44 % of Data
s = Sample Standard Deviation
6s = 99.73 % of Data
σ = Population Standard Deviation
© Max Zornada (2005)
Slide 72
The Box Plot interpretation
The Normal Distribution
The Whiskers are equal in
length.
The Mean = Median and is
in the Middle of the Box
A box plot can be used as a test of whether data is
normally or close enough to normally distributed.
© Max Zornada (2005)
Slide 73
Understanding Variation

Dr. W.A. Shewhart 1920's, found:

All processes display variation;

Some display controlled variation;

Some display uncontrolled variation.
© Max Zornada (2005)
Slide 74
Common vs Special Causes

Dr. W. Edwards Deming called this:

Variation due to common causes. Due to the random
interaction of the many variables in the system or
process. These were purely random and are built in
to the system. People working in the system have no
control over these. They are effectively "prisoners"
of the process.

Variation due to special causes. Not a natural part of
the system. These could be traced to a specific event,
person, machine or localised condition.
© Max Zornada (2005)
Slide 75
Sources of Variation


Common Causes:

Variation caused by the random interaction of all of the
variables that are built in to or are a “normal” part of the
process. This represents “business as usual” performance
for the process;

Adjusting the process increases this type of variation.
Special Cause:

Non-random variation. May exhibit a pattern;

Due to something happening that is not a normal for the
process - a problem, event, a specific cause that can be
found and explained;

Adjusting the process decreases this type of variation.
© Max Zornada (2005)
Slide 76
The Normal Distribution
Average = Median
2s = 68.26 % of Data
4s = 95.44 % of Data
s = Sample Standard Deviation
σ = Population Standard Deviation
6s = 99.73 % of Data
© Max Zornada (2005)
Slide 77
The Path to Continuous Improvement


The path to continuous improvement in quality and
productivity, is to:

Train and empower employees to identify and remove
special causes from work processes;

Train management in Variation principles and
management change or reengineer processes and
systems to reduce variation from common causes;
Alternately: - Management empowers teams to work on
changing the system and processes to remove common
causes - continuously.
© Max Zornada (2005)
Slide 78
Characteristics of Stable Processes

Processes that are free of special causes are referred to as
stable or in statistical control;

Future outcomes of the process can be predicted to occur
within the defined (natural) limits of the process, based
on past results. Therefore, the process capability to meet
customer expectation can be predicted;

At any given time, the outcome is random within the
defined limits;

Because process performance is known and stable,
process costs can be reliably predicted.
© Max Zornada (2005)
Slide 79
Characteristics of Stable Processes

Effects resulting from changes to the processes can be
measured reliably and quickly;

Once in control, some processes are capable of meeting
the customer requirements, while others are incapable;

Once in control, process improvement activities should
focus on making processes capable by reducing the
common causes;

If specification limits are to be changed, the necessary
data is available to understand the likely implications.
© Max Zornada (2005)
Slide 80
A Control Chart
Upper Control Limit (UCL)
Process Mean or Average
Lower Control Limit (LCL)
UCL = Mean + 3 Standard Deviations
LCL = Mean - 3 Standard Deviations
© Max Zornada (2005)
Slide 81
Stable & Unstable Processes
A Stable Process
An Unstable Process
UCL
Mean
LCL
© Max Zornada (2005)
Slide 82
Process Improvement by Managing Variation
Customer Requirement
Process Performance
Special cause
Special cause
USL = Upper Specification Limit
LSL = Lower Specification Limit
(These are customer specified)
USL
% of output meeting
customer requirements
(unpredictable because
of presence of special
causes)
Special cause

Process Unstable and Incapable

Process Unstable - special causes present

Variation too wide

Off-target (not “centred”)
Target
LSL
Bad
Good
© Max Zornada (2005)
Slide 83
Process Improvement by Managing Variation
Step 1. Make the process stable i.e. remove special causes
Process Performance
Customer Requirement
USL
Target
LSL

Process Stable but Incapable

Variation too wide

Off-target (not “centred”)
© Max Zornada (2005)
% of output meeting
customer requirements
(predictable because of
absence of special
causes)
Slide 84
Process Improvement by Managing Variation
Step 2. Re-target to aim at customer target (shift the average)
Process Performance
Customer Requirement
USL
Target
LSL

Process Stable but Incapable

Variation too wide

Now On-target (“centred”)
© Max Zornada (2005)
% of output meeting
customer requirements
(predictable because of
absence of special
causes)
Slide 85
Process Improvement by Managing Variation
Step 3. Reduce variation to make process capable
Process Performance
Customer Requirement
USL
Target
LSL

Process Stable and Capable

Variation Less than Customer
limits

On-target (“centred”)
© Max Zornada (2005)
100 % of output meets
customer requirements
I.e. a “Zero Defects”
process!
Slide 86
Exercise :The Funnel Experiment

Construct a control chart of the performance of the
order fulfilment data.

What can you say about the performance of the
process.
© Max Zornada (2005)
Slide 87
The Shewhart Tests: Test 1-to-4
Test 1. One point beyond zone A
Test 2. Nine points in a row in Zone C or
beyond
A
B
C
C
B
A
A
B
C
C
B
A
Test 3. Six points in a row steadily
increasing or decreasing
A
B
C
C
B
A
Test 4. Fourteen points in a row
alternating up and down
A
B
C
C
B
A
© Max Zornada (2005)
Slide 88
The Shewhart Tests: Test 5-to-8
Test 5. Two out of three point in a row
in zone A or beyond.
Test 6. Four out of five points in a row
in zone B or beyond.
A
B
C
C
B
A
A
B
C
C
B
A
Test 7. Fifteen point in a row in zone C (above
& below the centreline)
A
B
C
C
B
A
Test 8. Eight points in a row on both sides of
centreline with none in zone C.
A
B
C
C
B
A
© Max Zornada (2005)
Slide 89
A 6 Sigma Control Chart?
Customer Specification
A Six Sigma Process
Upper Specification Limit (USL)
UCL
Mean
LCL
Target Level of Performance
Lower Specification Limit (LCL)
UCL = Mean + 6σ
LCL = Mean - 6σ
Probability of getting a defect when process in control
= 3 in a Million
© Max Zornada (2005)
Slide 90
Process Capability and Sigma
© Max Zornada (2005)
Slide 91
Process Capability
Cp
= Specification Width
Process Width
 = Process Standard Deviation
= USL - LSL
6
USL = Upper Specification Limit
LSL = Lower Specification Limit

A measure of a process's ability to meet or exceed the customer's
specification;

A capable process must have a Cp of at least 1.0

Does not look at how well the process is centered in the
specification range;

Target value of Cp = 1.33. Allows for off-center processes

Six Sigma quality requires a Cp = 2.0
© Max Zornada (2005)
Slide 92
Process Capability
For processes know to be not centred
C pk = Min (USL - m , m - LSL)
3
3
USL = Upper Specification Limit
LSL = Lower Specification Limit
 = Process Standard Deviation
m  Process Average

A capable process must have a Cpk of at least 1.0

A capable process is not necessarily in the center of
the specification, but it falls within the specification
limit at both extremes.
© Max Zornada (2005)
Slide 93
Interpreting Cpk
Cpk = negative number
Cpk = zero
Cpk = between 0 and 1
Cpk = 1
Cpk > 1
© Max Zornada (2005)
Slide 94
A Capable and Stable Process
Customer target
Upper Specification Limit
Lower Specification Limit
Process mean
0.135%
1,350 ppm
0.135%
1,350 ppm
3
3
= 99.73% of data inside the limits (Cp=1)
0.27% of points will be outside of the specification limits ie. defects
(= 3/1000 or 2,700 parts per million (ppm) out of spec.)
© Max Zornada (2005)
Slide 95
A Capable, Stable, 6 Sigma Process
Customer target
Upper Specification Limit
Lower Specification Limit
0.00017%
1.7 ppm
0.00017%
1.7 ppm
6
6
= 99.99966% of data inside the limits (Cp = 2)
0.00034% of points will be outside of the specification limits ie. defects
(= 3.4 parts per million out of spec.)
© Max Zornada (2005)
Slide 96
A closer look at Defects

Unit: The entity that is transformed by value-adding
activities.

Defect: A countable failure associated with a single unit. A
single unit can be found defective as a result of having one
or more defects;

Defects Per Unit (DPU) = Defects/Units produced

Defectives: Completed units of work that are classified as
“bad”. A single unit can be found “defective” regardless of
the number of defects.

Yield = Non-defectives/Total Unit
© Max Zornada (2005)
Slide 97
FSG Revisited
Customer Support
Operations
Assume customer support receive calls re: 8% of transactions
6% they fix, 2% get passed onto PIT.
This means 8% defects must be getting through the CC Team and
onto the customer.
2% or transactions
Customer
Support (Call
Centre)
Problem
Investigation
Team
2% internal errors
Document
Receiving
Team
Customer
Communications
Team
Transaction
Processing
Team
8% rework
© Max Zornada (2005)
Slide 98
Yields


The process’s Final Yield is 92% - the is the percentage of
good units making it to the customer;
However, of the work done by the processing team they find:

2 defectives internally;

8 come back from CCT

6 get fixed by Call Centre

2 Come back from PIT.

First Pass Yield = 82%
© Max Zornada (2005)
Slide 99
Six Sigma and DPMO

Defects Per Million Opportunities is the key Six
Sigma Metric
DPMO
=
Total Defects
Total Opportunities
© Max Zornada (2005)
X
1,000,000
Slide 100
DPMO

An opportunity is any opportunity to produce a
defect


e.g. a ten step process with one activity at each
step, provides 10 opportunities to get something
wrong;
Allows us to compare products and processes of
differing complexity.
© Max Zornada (2005)
Slide 101
Calculating Sigma Level
Select the process, unit and requirements:

Identify the process you want to evaluate?
(Process)

What is the “thing” produced by the process?
(Unit)

What are the customer requirements for the thing?
Define what a “defect” is and the number of opportunities:

Possible defects:

How many defects could be found on a single unit?
Collect Data and Calculate DPMO

Collect end-of-process data.
No. of Units counted

Total defects counted
Determine total opportunities in data collected:
Units counted X Opportunities/Unit = Total Opportunities
Calculate DPMO = (Defects/Total Opportunities) X 106 =

DPMO
Convert to a Sigma Level using a conversion table.
Estimated Sigma Level =
© Max Zornada (2005)
Slide 102
Sigma Conversion Table
© Max Zornada (2005)
Slide 103
Statistical Process Control
© Max Zornada (2005)
Slide 104
Types of Control Charts
Measuring
Not much data
available
i and mr Charts
Lots of data
available
X and R Charts
Continuous Data
Are you counting or
measuring ?
Constant Sample Size
Counting
Categorical Data
No
Can you have more
than one count per unit
np Chart
Sample size not constant
p Chart
Constant Sample Size
Yes
Occurrence Data
c Chart
Sample size not constant
© Max Zornada (2005)
u Chart
Slide 105
X and R Charts

Use for continuous data, when degree of normality
of process is uncertain;

Relies on taking samples and plotting sample
averages;

We plot 2 charts together:

The X chart to monitor variation in location;


Plot the average of each sample X.
The R chart to monitor variation in spread.

Plot the range of each sample R.
© Max Zornada (2005)
Slide 106
The Central Limit Theorem

The Central Limit Theorem says that averages of
groups of data will be more normally distributes
that the individual data points;

The more points you sample, the closer those
averages will be to the normal distribution;

If you sample up to 30 points, the distribution of
those 30 points will effectively be normal;

This means that even non-normal data can be
plotted using control charts, by taking averages of
sub-groups of data.
© Max Zornada (2005)
Slide 107
X and R Charts
The X Chart:
Centreline = X =
=
Average of the sample averages
X1 + X2 + …. Xn
Total number of samples taken (m)
We plot the sample averages - X as the individual data points
Upper and Lower Control Limits
UCL
=
X
+
A2R
LCL
=
X
-
A2R
The average of the Ranges
A constant we look up in a table
© Max Zornada (2005)
Slide 108
X and R Charts
The R Chart:
Centreline = R =
=
Average of the sample ranges
R1 + R2 + …. Rn
Total number of samples taken (m)
We plot the sample averages - R’s as the individual data points
Upper and Lower Control Limits
UCL
=
D4R
LCL
=
D3R
D3 and D4 are constants
we look up in a table
© Max Zornada (2005)
Slide 109
Values of Constants for X & R Charts
Sub-group
size
(n)
2
3
4
5
6
7
8
9
10
X Chart
A2
2.66
1.023
0.729
0.577
0.483
0.419
0.373
0.337
0.308
R Chart LCL R Chart UCL
D3
0
0
0
0
0
0.076
0.136
0.184
0.223
© Max Zornada (2005)
D4
3.267
2.574
2.282
2.114
2.004
1.924
1.864
1.816
1.777
Slide 110
Chebyshev’s Rule

Regardless of the shape of the distribution:

At least 75% of the distribution will fall within 2
standard deviations of the mean;

At least 8/9ths (88.89%) of the distribution will fall
within 3 standard deviations of the mean;.

Chebyshev’s rule is generally used when the
underlying distribution is unknown, except for the
mean and the variance.
© Max Zornada (2005)
Slide 111
Data Collection Sheet: Attributes Data
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
np
c
No.
np
c
16
17
18
19
20
21
22
23
24
25
Total
Average
© Max Zornada (2005)
Slide 112
The np-chart (Number Defective)

Use when we are measuring the number of nonconforming or “defective” items in each sample;

The number of defective items in each sample is np;

The individual data points we plot on the control
chart are the np’s;

Sample size must be constant.
© Max Zornada (2005)
Slide 113
The np-chart (Number Defective)
Average proportion defective:
np
=
Total number of defectives
Number of samples
Average proportion defective:
p=
Total defective=
Total inspected
Snp
Sn
Upper and Lower Control Limits
UCL
=
np + 3 np(1-p)
LCL
=
np - 3 np(1-p)
n
© Max Zornada (2005)
Slide 114
The p-chart (Proportion Defective)

If sample size will not be constant, makes more
sense to plot % defective;

Convert the individual data points (np) to p (%) by
dividing each by the sample size (n).


Plot the p’s.
If sample size changes, we need to recalculate the
control limits for each new value of sample size;

Therefore, control limits will only be straight
lines if the sample size remains constant.
© Max Zornada (2005)
Slide 115
The p-chart (Proportion Defective)
Average proportion defective:
p=
Total defective=
Total inspected
Snp
Sn
Upper and Lower Control Limits
UCL
=
p + 3 p(1-p)
n
LCL
=
p - 3 p(1-p)
n
© Max Zornada (2005)
Slide 116
Categorical Data

Categorical data tends to follow the Binomial
Distribution:

Finite - known number of identical samples
collected under identical circumstances;

Only two possible outcomes e.g. OK/Not OK

Probability remains constant

Data points are independent;

If np > 5 and n(1-p) > 5: The approximately
Normal.
© Max Zornada (2005)
Slide 117
The c-chart

Used to count occurrences when we don’t know the nonoccurrences eg.



Record customer complaints but don’t know how many
customers didn’t complain (ie. we can’t work out a %)
When we can get multiple counts per unit of measure;


We can count defects but not non-defects;
e.g. a form may be counted as defective because someone
made one error or several errors.
The sample “frame” must be remain constant:

e.g. complaints/day - for 8 hour day sample frame.
© Max Zornada (2005)
Slide 118
The c-chart
Average non-conformities:
c=
Sum of all data points =
Number of samples
c1 + c2 + …. cn
number of samples
Upper and Lower Control Limits
UCL
=
c+3 c
LCL
=
c-3 c
© Max Zornada (2005)
Slide 119
The u-chart

The same as a c - chart when the sample “frame” is not
constant:


e.g. complaints/day - but not all days are 8 hours long,
due to late night shopping on some days and shorter
opening hours on week ends.
Every time the sample frame changes, we have to recalculate
the control limits.
© Max Zornada (2005)
Slide 120
The c-chart
Average non-conformities:
u=
Sum of all data points =
Number of units sampled
c1 + c2 + …. cn
n1 +n2 + ….. nn
Upper and Lower Control Limits
UCL
=
u + 3 u/n
LCL
=
u - 3 u/n
© Max Zornada (2005)
Slide 121
Occurrence Data

Occurrence data tends to follow the Poisson
Distribution:

Average number of events is proportional to the
length of the interval;

Two events are unlikely to occur together;

Events are independent;

Mean = Variance

If c > 5, approximately Normal
© Max Zornada (2005)
Slide 122
Sampling
© Max Zornada (2005)
Slide 123
Types of Sampling

Population sampling vs. process sampling;

Population sampling:


Conducting a customer survey;

Quality Control Acceptance sampling;

Compiling reasons for calls to call centre
Process Sampling:

Tracking process performance on a daily,
weekly, monthly basis;

Recording hourly call volumes to call
centre.
© Max Zornada (2005)
“Snapshots”
Ongoing
monitoring
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Sampling
Population or Process
Population mean =
Population std dev =
Sample
m

Statistical Inference
Conclusions about
the population or
process
© Max Zornada (2005)
Sample Statistics
Sample mean = X
Sample std dev = s
etc., etc., ….
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Approaches to Sampling

Systematic Sampling:

Taking data at regular intervals;

Random Sampling:

Stratified Sampling:

Stratify the population into significant subgroups
of interest, then use random or systematic
sampling.
© Max Zornada (2005)
Slide 126
Bias

Bias is the difference between the data in the sample
and the true nature of the population or process;

Sampling bias can arise due to:

Convenience sampling: sampling the data that is
convenient to get, rather than what is needed;

Judgement sampling: where sampling is driven
by judgements regarding what is important and
what is not.
© Max Zornada (2005)
Slide 127
Daily Processing Quantity
Sample Size Selection – Daily Data
Minimum Daily Sample Size
© Max Zornada (2005)
Slide 128
Weekly Processing Quantity
Sample Size Selection – Weekly Data
Minimum Weekly Sample Size
© Max Zornada (2005)
Slide 129
Sample Size Formula for populations
The general form of the “sample size” equation.
Z = the Z-Value corresponding to the
2
2
level of confidence required.
Z x
95%: Z= 2
n
2
99.7%: Z = 3
Error
Error = +/- accuracy required
e.g. if error +/- 10%, error = 10%
x2 = variance of the population
For categorical data specifically:
p = proportion expected
n = 36 p (1 - p)
Range = 2 X Error (or Total
2
(Range)
Absolute Error)
© Max Zornada (2005)
Slide 130
Tollgate Review: Measure Phase
© Max Zornada (2005)
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Toll Gate Review: Measure

Determined what we need to know about the process and where in the
process we can get the data.

Identified the types of measures we want to collect and have a balance
of input, process, output and leading indicators.

Developed clear operational definitions of the things we want to
measure.

Clarified stratification factors we need to identify to facilitate data
analysis.

Identified what data needs to be collected as new data vs utilising data
that is already recorded.

Identified appropriate sample sizes, subgroup quantities and sampling
frequencies to ensure we get an adequate representation of the process.

Used our data to establish the process baselines - stability, capability,
sigma level and yield.
© Max Zornada (2005)
Slide 132
End of Module
© Max Zornada (2005)
Slide 133
© Max Zornada (2005)
Slide 134