CHAPTER 9:
Management of
Qua ty
Quality
Copyright © 2006 McGraw-Hill Ryerson Limited
9-1
A. Introduction
• What does the term quality mean?
product or service to
• Qualityy is the abilityy of a p
consistently meet or exceed customer
expectations.
• Prior to 1980s, in North America, the focus was
on: quantity, cost, productivity
• It was not that quality was unimportant, it just was
not very important
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9-2
B. Evolution of Quality Management
• Craftsmanship: quality control was the responsibility of each
craftsman.
• Division of labour: quality control shifted to full time quality inspectors
• Taylor: father of scientific management
• Shewhart: introduced statistical process control charts
• After the Second World War: American Society for Quality (ASQ)
• 1950s: quality assurance
– Joseph Juran: cost of quality approach
– Armand Feigenbaum: total quality control (more management involvement)
• 1960s: zero defects
• 1980s: strategic management approach to quality
• Today: TQM, Six Sigma, Black Belts
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9-3
C. Quality: The Basics
1.
2.
3.
4.
Dimensions of Quality
Determinants of Quality
Consequences of Poor Quality
Costs of Quality
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9-4
C1. Dimensions of Quality
• Product quality
• P
Performance,
f
Aesthetics,
A th ti
Special
S
i lF
Features,
t
Safety, Reliability, Durability, Perceived quality,
Service after Sale
• Service quality
• Tangibles, Convenience, Reliability,
Responsiveness Time,
Responsiveness,
Time Assurance,
Assurance Courtesy
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9-5
C1. Examples of Quality Dimensions for
Products: Car
Dimension
Example
1. Performance
Everything works; ride handling, leg room
2. Aesthetics
Interior design, soft touch, fit and finish, grade of
material used
3. Special features
Convenience
High tech
Placement of gauges and controls
GPS, DVD player
4. Safety
Antilock brakes, airbags
5. Reliability
y
Infrequency
q
y of breakdowns
6. Durability
Long life, resistance to rust and corrosion
7. Perceived quality
Top rated car, e.g. Cadillac
8. Service after sale
Warranties, handling of complaints, maintenance
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9-6
C1. Examples of Quality Dimensions for
Services: Car Repair
Dimension
Example
1 Tangibles
1.
Were the facilities clean? Were personnel neat?
2. Convenience
Was the service centre conveniently located?
3. Reliability
Was the problem fixed?
4. Responsiveness
Were customer service personnel willing and
able to answer the questions?
5. Time
How long did the customer have to wait?
6. Assurance
Did the customer service personnel seem
knowledgeable about the repair?
7. Courtesy
Were customer service personnel and the
cashier friendly and courteous?
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9-7
C2. Determinants of Quality
• Design
– Quality of Design: Characteristics designers
specify for a product or service
• Conformity
– Quality of Conformance: The degree to which
goods or services conform to the specifications of
the designers
• Ease of use
– Good instructions and labels
• Service after delivery
– Recall, repair, replacement, refund
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C3. The Consequences of Poor Quality
A recent study showed that, while a satisfied customer will
tell a few people about his or her experience, a dissatisfied
person will tell an average of 19 others
•
•
•
•
Loss of business
Liability
Productivity
Costs
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9-9
Costs of Quality
• A failure to satisfy a customer is
considered a defect
• Prevention costs
• Appraisal costs
• Internal failure costs
• External failure costs
• Ethics and quality
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9-10
C4. Costs of Quality
• Internal Failure Costs
– Costs incurred to fix problems that are detected before
the product/service is delivered to the customer.
• External Failure Costs
– All costs incurred to fix problems that are detected
after the product/service is delivered to the customer.
• Appraisal Costs
– All product and/or service inspection costs.
• Prevention Costs
– All TQ training, TQ planning, customer assessment,
process control, and quality improvement costs to
prevent defects from occurring
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9-11
D. Quality Gurus
Contributor Known for
Deming
14 points; special & common causes of
variation
a at o
Juran
Quality is fitness for use; quality trilogy
(planning, control, improvement)
Feigenbaum
Quality is a total field; the customer defines
quality (GE)
Crosby
Q lit is
Quality
i free;
f
zero defects
d f t (prevention)
(
ti )
Ishikawa
Taguchi
Cause-and effect diagrams; quality circles;
internal customer (Lotek)
Taguchi loss function
Quality
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9-12
Quality Engineering
• Quality engineering is an approach originated by
Genichi Taguchi that involves combining
engineering and statistical methods to reduce
costs and improve quality by optimizing product
design and manufacturing processes.
• The quality loss function is based on the concept
that a service or product that barely conforms to
the specifications
p
is more like a defective service
or product than a perfect one.
9-13
Copyright © 2006 McGraw-Hill Ryerson Limited
Loss (dollars)
Quality Engineering
Lower
specification
Nominal
value
Upper
specification
Figure 5.16 – Taguchi’s Quality Loss Function
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9-14
E. Quality Awards
Baldrige Award
Canada Awards
for Excellence
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The Baldrige Award
• The Malcolm Baldrige National Quality Award promotes,
recognizes, and publicizes quality strategies and
achievements by outstanding organizations
• It is awarded annually after a rigorous application and
review process
• Award winners report increased productivity, more
satisfied employees and customers, and improved
profitability
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9-16
The Baldrige Award
• The seven categories of the award are
1. Leadership
2. Strategic Planning
3. Customer and Market Focus
4. Measurement, Analysis, and Knowledge
g
Management
5. Workforce Focus
6. Process Management
7. Results
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9-17
E. Quality Awards
• The Baldrige Award
– Leadership, Information and Analysis, Strategic
Planning Human Resource Development and
Planning,
Management, Process Management, Business
Results, Customer and Market Focus
• The Canada Awards for Excellence (Administered by
National Quality Institute (NQI)
– Leadership, Planning,
g Customer Focus, People
Focus, Process Management, Supplier/Partner
Focus, Overall Business Performance
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9-18
F. Quality Certification
• ISO 9000 (International Organization for Standardization)
– Set of international standards on quality management and
Qualityy assurance,, critical to international Business
Q
• ISO 9000-2000 is based on eight quality management principles:
– Leadership, Involvement, Process Approach, System
Approach to Management, Continual Improvement, Factual
Approach to Decision Making, Mutually beneficial supplier
relationship
• ISO 14000
– A set of international standards for assessing a company’s
environmental performance based on three major areas:
management Systems, Operations, Environmental Systems
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9-19
International Standards
• ISO 9000:2000 addresses quality management by
specifying what the firm does to fulfill the customer’s
q alit requirements
quality
req irements and applicable reg
regulatory
lator
requirements while enhancing customer satisfaction
and achieving continual improvement of its
performance
• Companies must be certified by an external examiner
• Assures customers that the organization is performing
as they
h say they
h are
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9-20
International Standards
• ISO 14000:2004 documents a firm’s
environmental program by specifying what the
firm does to minimize harmful effects on the
environment caused by its activities
• The standards require companies to keep
track of their raw materials use and their
generation, treatment, and disposal of
hazardous wastes
• Companies are inspected by outside, private
auditors on a regular basis
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International Standards
• External benefits are primarily increased sales
opportunities
• ISO certification is preferred or required by many
corporate buyers
• Internal benefits include improved profitability,
improved marketing, reduced costs, and improved
documentation and improvement of processes
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9-22
G. Hazard Analysis Critical Control Point
• Hazard Analysis Critical Control Point (HACCP)
– A quality control system, similar to ISO 9000,
d i
designed
d ffor ffood
d processors
– Deals with food safety (biological, chemical, and
physical hazards)
• HACCP has three main steps
– Hazard Analysis
– Determination of the Critical Control Points
– Creation of the HACCP Plan
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H. Total Quality Management
TQM: A philosophy that involves everyone in an organization in a
continual effort to improve quality and achieve customer satisfaction
• Continuous Improvement: make never-ending improvements to
critical processes
• Competitive
C
benchmarking: Identifying
f
other organizations that are
the best at a process and studying how they do it
• Employee empowerment: Giving workers responsibility
• Team Approach
• Decisions based on facts rather that opinions
• Training
• Quality at the Source: making each worker responsible for the quality
of his or her work
• Fail-safing: incorporating design element that prevent incorrect
procedures
• Suppliers: encourage partnership and long term relationships
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Total Quality Management
Customer
satisfaction
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Total Quality Management
• Customer satisfaction
– Conformance to specifications
p
– Value
– Fitness for use
– Support
– Psychological impressions
z Employee involvement
‹ Cultural
change
‹ Teams
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9-26
Total Quality Management
• Continuous improvement
– Kaizen
– A philosophy
– Not unique to quality
– Problem solving process
9-27
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The Deming Wheel
Plan
Act
Do
Study
Plan-Do-Study-Act Cycle
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I. Problem Solving and Process Improvement
Plan Do Study Act cycle: a framework for problem solving and improving
activities
9-29
Copyright © 2006 McGraw-Hill Ryerson Limited
Six Sigma
Process average OK;
too much variation
Process variability OK;
process off target
X X
X X
XX XX
X
X
X
X
X
X
X X
X
X
Reduce
spread
Process
on target with
low variability
Center
process
X
XX
X
X
X XX
-Six-Sigma Approach Focuses on Reducing Spread and Centering the Process – different focus than
TQM that is driven by close understanding of customer needs and disciplined use of facts, data, and
statistical analysis and diligent attention to managing, improving and reinventing business processes.
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Six Sigma Improvement Model
Define
Measure
Analyze
Improve
Control
Six Sigma Improvement Model
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J. Six Sigma Tools
Six Sigma: a more advanced and effective version of TQM
• Six Sigma Tools
– Flow diagram: shows steps in the process
– Check sheet: a tool for recording and organizing data to identify
problems
– Histograms: a chart of empirical frequency distribution
– Pareto Analysis: technique for focusing on the most important
problem
– Scatter Diagram: a plot that shows the degree and direction of the
relationship between two variables
– Control
C
C
Charts: a statistical plot off time-ordered values off a
sample statistic
– Cause and Effect Diagrams: used to search for the causes of a
problem
– Run Charts: tool for tracking results over a period of time
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J. Six Sigma Tools
9-33
Copyright © 2006 McGraw-Hill Ryerson Limited
J. Six Sigma Tools
Type of defect
Day
Time
Missing
labels
Monday
8-9
IIII
Monday
9-10
Monday
10-11
Monday
11-12
Monday
12-13
Monday
13-14
Total
Off
centre
I
Smear Loose or
ed print
faded
II
6
III
3
III
I
I
I
6
Copyright © 2006 McGraw-Hill Ryerson Limited
Other
5
I
I (torn)
I
3
2
III
I
II
12
3
3
6
1
25
9-34
J. Six Sigma Tools
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J. Six Sigma Tools
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9-36
K. Methods for Generating Ideas and
Reaching Consensus
• Brainstorming
– Technique for generating a free flow of ideas in a group of people
• Quality Circles
– Groups of workers who meet to discuss ways of improving
products or processes
• Interviewing
– Technique for identifying problems and collecting information
• Benchmarking
– Process of measuring performance against the best in the same
or another industry
• The 5W2H Approach
– A method of asking questions about a process/problem that
include what, why, where, who, how, and how much
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Example Problem (#2, page 342)
• An air-conditioning repair department
manager has
h compiled
il d d
data
t on th
the
primary reason for 41 service calls during
the previous week. Using the data, make
a check sheet for the problem types for
each customer type, and then construct a
Pareto chart for each customer.
Copyright © 2006 McGraw-Hill Ryerson Limited
9-38
2.
Checksheet
Equipment Problem
Customer Type
Noisy
Failed
Odour
Warm
Totals
Residential
10
7
5
3
25
Commercial
3
2
7
4
16
Totals
13
9
12
7
41
Residential customers
Commercial customers
10
7
7
5
4
3
3
2
Noisy
Failed
Odour
Warm
Odour
Warm
Noisy
Failed
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9-39
Example Problem (#3, pg 343)
• Prepare a run chart for the number of
occurrences off defective
d f ti computer
t
monitors based on the following data,
which an analyst obtained from the
process for making monitors. Workers are
given a 15-minute break at 10:15 am and
3:15 pm and a lunch break at noon. What
can you conclude?
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9-40
3.
3
2
1
0
•
•
•
•
•
• •
•
• •
•
• •
•
•
•
•
• • •
break
• •
• •
lunch
•
•
•
•
• •
break
The run chart shows a pattern of errors just before the
break times, lunch, and the end of the shift. Perhaps
p
workers are becoming fatigued. If so, perhaps two 10
minute breaks in the morning and again in the afternoon
instead of one 20 minute break could reduce some
errors.
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9-41
5.
Example (#5, page 344)
Suppose that a table lamp fails to light when
turned on. Prepare a simple cause-andeffect diagram to analyze possible causes.
Use categories such as lamp, chord, etc.
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9-42
Example Problem (#7, pg 344)
• Prepare a scatter diagram for each of the
f ll i d
following
data
t sets
t and
d th
then express iin
words the apparent relationship between
the two variables. Put the first variable on
the horizontal axis and the second variable
on the vertical axis.
9-43
Copyright © 2006 McGraw-Hill Ryerson Limited
7.
Days
absent
♦
7
6
5
4
3
2
1
0
♦♦
♦♦
♦
♦♦
♦♦
♦ ♦
♦♦
0
20
40
Error
rate
♦
5
4
3
2
1
0
♦♦
♦
♦
♦
♦
♦
♦ ♦
60
Age
0
14
20
25
30°C
30
C
a.
•Age and Days absent are inversely related. Old employees
missed fewer days.
•b.
Error rate is non-linearly related to temperature. It
increases in cold or hot temperatures. The lowest
error rate occurs around 20 degrees Celsius.
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9-44
CHAPTER 10:
Quality Control
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9-45
A. Introduction
• What does the term quality control mean?
y Control is an activity
y that evaluates
• Quality
quality characteristics relative to a
standard, and takes corrective action
when they do not meet standards
• How is quality control accomplished?
• b
by monitoring
it i and
d iinspecting
ti th
the product
d t
during process
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9-46
A. Phases of Quality Assurance
Inspection
before/after
production
Acceptance
sampling
Corrective
action during
production
Process
control
The least
progressive
p
g
Quality built
into the
process
Continuous
improvement
The most
progressive
9-47
Copyright © 2006 McGraw-Hill Ryerson Limited
B. Inspection
Inspection: appraisal of goods or services against
standards
• How Much/How Often
• Where/When
• Centralized vs. On-site
Inputs
Acceptance
sampling
Transformation
Process
control
Copyright © 2006 McGraw-Hill Ryerson Limited
Outputs
Acceptance
sampling
9-48
B. How Much to Inspect and How Often?
Cost
Total Cost
Cost of
inspection
Cost of passing
defectives
Optimal
Amount of Inspection
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9-49
B. Where to Inspect in the Process
•
•
•
•
•
Raw materials and purchased parts
Finished products
Before a costly operation
Before an irreversible process
Before a covering process
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9-50
B. Examples of Inspection Points
Type of
business
Inspection
points
Characteristics
Fast Food
Server
Eating Area
Kitchen
Appearance, friendliness
Appearance
Cleanliness
Cleanliness, purity of food, food
storage, health regulations,
availability of ingredients, hygiene
Supermarket
Cashiers
Aisles, stockrooms
Shelf stock
Accuracy, courtesy, waiting time
Uncluttered layout
Ample supply, rotation of
perishables, appearance
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Acceptance Sampling
pp ca o o
of sstatistical
a s ca techniques
ec ques
• Application
• Acceptable quality level (AQL)
• Linked through supply chains
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9-52
Acceptance Sampling
Firm A uses TQM or Six
Sigma to achieve internal
process performance
Buyer
Manufactures
furnaces
Motor inspection
Yes
Accept
motors?
Supplier uses TQM or Six
Sigma to achieve internal
process performance
Firm A
Manufacturers
furnace fan motors
TARGET: Buyer’s specs
Supplier
Manufactures
fan blades
TARGET: Firm A’s specs
No
Blade inspection
Yes
Accept
blades?
No
Interface of Acceptance Sampling and Process Performance Approaches in a Supply Chain
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Statistical Process Control
•
•
•
•
•
•
Used to detect process change
Variation of outputs
Performance measurement – variables
Performance measurement – attributes
Sampling
Sampling distributions
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9-54
Sampling Distributions
1. The sample mean is the sum of the observations
divided byy the total number of observations
n
x=
∑x
i =1
i
n
where
xi = observation of a quality characteristic (such as time)
n = total number of observations
x = mean
9-55
Copyright © 2006 McGraw-Hill Ryerson Limited
Sampling Distributions
2. The range is the difference between the largest
observation in a sample and the smallest. The
standard de
deviation
iation is the sq
square
are root of the variance
ariance of
a distribution. An estimate of the process standard
deviation based on a sample is given by
∑ (x − x )
2
σ=
i
n −1
or σ =
∑x
2
i
( x)
− ∑
2
i
n −1
n
where
σ = standard deviation of a sample
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9-56
Sample and Process Distributions
Mean
Distribution of
sample means
Process
distribution
25
Time
Relationship Between the Distribution of Sample Means and the Process Distribution
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C. Statistical Process Control
Statistical Process Control: Statistical evaluation of the output
of a process during production
1.
1
2.
3.
4.
5.
The Quality Control Steps
Type of Variations
Control Charts
Designing Control Charts
Individual Unit and Moving
g Range
g
Charts
6. Control Charts for Attributes
7. Managerial Considerations
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C1. The Quality Control Steps
1. Define the q
quality
y characteristics to
monitor
2. Measure the characteristics
3. Compare to a standard and evaluate
4. Take corrective action if necessary
5 Evaluate corrective action
5.
9-59
Copyright © 2006 McGraw-Hill Ryerson Limited
C2. Types of Variations
• Random variation: Natural variations in the output of process,
created by countless minor factors (Deming: common)
• Assignable variation: A variation whose source can be identified
((Deming:
g special)
p
)
Sampling
distribution
Process
distribution
Mean
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9-60
C2. Normal Distribution
σ = Standard deviation
−3σ
−2σ
Mean
95 44%
95.44%
+2σ
+3σ
99.74%
If the process has only random variability, then the sample mean
should most likely fall between 2σ or 3σ standard deviations of the
process mean)
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Causes of Variation
• Common causes
– Random,
Random unavoidable sources of variation
– Location
– Spread
– Shape
z Assignable causes
‹ Can
be identified and eliminated
‹ Change
‹ Used
in the mean, spread, or shape
after a process is in statistical control
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Assignable Causes
Average
(a) Location
Time
Effects of Assignable Causes on the Process Distribution for the Lab Analysis Process
9-63
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Assignable Causes
Average
(b) Spread
Time
Effects of Assignable Causes on the Process Distribution for the Lab Analysis Process
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9-64
Assignable Causes
Average
Time
(c) Shape
Effects of Assignable Causes on the Process Distribution for the Lab Analysis Process
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C3. Control Charts
• Control Chart: A time ordered plot of sample
statistics, used to distinguish between
random and non random variability
• Control Limits: The dividing lines between
random and nonrandom deviations from the
mean of the sampling distribution
• Type I error: concluding that a process has
changed
g when it has not
• Type II error: concluding a process is in
control when it is actually not
• Using a larger standard deviation may make it more difficult
to detect non-random errors
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9-66
Control Charts
• Two types of error are possible with control
charts
• A type I error occurs when a process is thought
to be out of control when in fact it is not
• A type II error occurs when a process is thought
to be in control when it is actually out of
statistical control
• These errors can be controlled by the choice of
control limits
9-67
Copyright © 2006 McGraw-Hill Ryerson Limited
C2. Control Limits
Sampling
distribution
Process
distribution
Mean
Lower
control
limit
Copyright © 2006 McGraw-Hill Ryerson Limited
Upper
control
limit
9-68
C3. Type I Error
α/2
α/2
Mean
α = Probability
of Type I error
LCL
UCL
There is a small probability that a value will fall outside the limits
even though only random variations are present; a risk is the sum of
the probabilities of the two tails
9-69
Copyright © 2006 McGraw-Hill Ryerson Limited
C3. Control Chart
Abnormal variation
due to assignable sources
Out of
control
UCL
Mean
Normal variation
due to chance
LCL
Abnormal variation
due to assignable sources
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15
Sample number
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9-70
C3. Observations from Sample Distribution
UCL
LCL
1
2
3
4
Sample number
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Control Charts
• Time-ordered diagram of process
performance
– M
Mean
– Upper control limit
– Lower control limit
z Steps for a control chart
1. Random sample
p
2. Plot statistics
3. Eliminate the cause, incorporate improvements
4. Repeat the procedure
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Control Charts
UCL
Nominal
LCL
Assignable
causes likely
1
2
3
Samples
How Control Limits Relate to the Sampling Distribution: Observations from Three Samples
9-73
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Control Charts
Variations
UCL
Nominal
LCL
Sample number
(a) Normal – No action
Control Chart Examples
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9-74
Control Charts
Variations
UCL
Nominal
LCL
Sample number
(b) Run – Take action
Control Chart Examples
9-75
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Control Charts
Variations
UCL
Nominal
LCL
Sample number
(c) Sudden change – Monitor
Control Chart Examples
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9-76
Control Charts
Variations
UCL
Nominal
LCL
Sample number
(d) Exceeds control limits – Take action
Control Chart Examples
9-77
Copyright © 2006 McGraw-Hill Ryerson Limited
Control Charts for Attributes
• p-charts are used to control the proportion defective
• Sampling involves yes/no decisions so the underlying
distribution is the binomial distribution
• The standard deviation is
σp =
p (1 − p ) / n
p = the center line on the chart
and
UCLp = p + zσp and LCLp = p – zσp
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9-78
Using p-Charts
•
•
•
•
Periodically a random sample of size n is taken
The number of defectives is counted
The proportion defective p is calculated
If the proportion defective falls outside the UCL, it is
assumed the process has changed and assignable
causes are identified and eliminated
• If the proportion defective falls outside the LCL, the
process may have improved and assignable causes are
identified and incorporated
Copyright © 2006 McGraw-Hill Ryerson Limited
9-79
Using a p-Chart
EXAMPLE
z Hometown Bank is concerned about the number of wrong customer
account numbers recorded
z Each week a random sample of 2,500 deposits is taken and the
number of incorrect account numbers is recorded
z The results for the past 12 weeks are shown in the following table
z Is the booking process out of statistical control?
z Use three-sigma control limits, which will provide a Type I error of
0.26 percent.
Copyright © 2006 McGraw-Hill Ryerson Limited
9-80
Using a p-Chart
Sample
Number
Wrong Account
Numbers
Sample
Number
Wrong Account
Numbers
1
15
7
2
12
8
24
7
3
19
9
10
4
2
10
17
5
19
11
15
6
4
12
3
Total
147
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Copyright © 2006 McGraw-Hill Ryerson Limited
Using a p-Chart
Step 1: Using this sample data to calculate
p=
Total defectives
Total number of observations
σp = √p(1 – p)/n
=
147
= 0.0049
12(2,500)
= √0.0049(1 – 0.0049)/2,500 = 0.0014
0 0049 + 3(0
3(0.0014)
0014) = 0.0091
0 0091
UCLp = p + zσp = 0.0049
LCLp = p – zσp = 0.0049 – 3(0.0014) = 0.0007
Copyright © 2006 McGraw-Hill Ryerson Limited
9-82
Using a p-Chart
Step 2: Calculate the sample proportion defective. For sample 1, the
proportion of defectives is 15/2,500 = 0.0060.
Step 3: Plot each sample proportion defective on the chart
chart, as
shown in Figure 5.12.
Fraction Defective
X
.0091
X
UCL
X
X
X
.0049
X
Mean
X
X
X
.0007
|
|
|
1
2
3
X
X
|
|
4
5
X
|
|
|
|
|
|
|
6
7
Sample
8
9
10
11
12
LCL
The p-Chart from POM for Windows for Wrong Account Numbers, Showing That Sample 7
is Out of Control
9-83
Copyright © 2006 McGraw-Hill Ryerson Limited
Application Example
A sticky scale brings Webster’s attention to whether caulking tubes are
being properly capped. If a significant proportion of the tubes aren’t
beingg sealed,, Webster is placing
p
g their customers in a messy
y situation.
Tubes are packaged in large boxes of 144. Several boxes are inspected
and the following numbers of leaking tubes are found:
Sample
Tubes
Sample
Tubes
Sample
Tubes
1
3
8
6
15
5
2
5
9
4
16
0
3
3
10
9
17
2
4
4
11
2
18
6
5
2
12
6
19
2
6
4
13
5
20
1
7
2
14
1
Total =
72
Copyright © 2006 McGraw-Hill Ryerson Limited
9-84
Calculate the p-chart three-sigma control limits to assess whether the
capping process is in statistical control.
p=
Total number of leaky tubes
72
=
= 0.025
Total number of tubes
20(144 )
σp =
p(1 − p )
=
n
0.025 (1 − 0.025 )
= 0.01301
144
UCL p = p + zσ p = 0.025 + 3(0.01301) = 0.06403
LCL p = p − zσ p = 0.025 − 3(0.01301) = −0.01403 = 0
The process is in control as the p values for the samples all fall
within the control limits.
9-85
Copyright © 2006 McGraw-Hill Ryerson Limited
Control Charts for Attributes
• c-charts count the number of defects per unit of
service encounter
• The underlying distribution is the Poisson distribution
• Assumes that defects occur over some continuous
region and that the probability of more than one defect
at any particular spot is negligible.
UCLc = c + z√c and
Copyright © 2006 McGraw-Hill Ryerson Limited
LCLc = c – z√c
9-86
Using a c-Chart
The Woodland Paper Company produces paper for the newspaper
industry. As a final step in the process, the paper passes through a
machine that measures various product quality characteristics
characteristics.
When the paper production process is in control, it averages 20
defects per roll.
a. Set up a control chart for the number of defects per roll. For this
example, use two-sigma control limits.
b. Five rolls had the following number of defects: 16, 21, 17, 22, and
24,, respectively.
p
y The sixth roll,, using
gp
pulp
p from a different
supplier, had 5 defects. Is the paper production process in
control?
Copyright © 2006 McGraw-Hill Ryerson Limited
9-87
Using a c-Chart
SOLUTION
a. The average number of defects per roll is 20. Therefore
UCLc = c + z√c = 20 + 2(√20) = 28.94
LCLc = c – z√c = 20 – 2(√20) = 11.06
Copyright © 2006 McGraw-Hill Ryerson Limited
9-88
Using a c-Chart
The c-Chart from POM for Windows for Defects per Roll of Paper
b. Because the first five rolls had defects that fell within the control
limits, the process is still in control. Five defects, however, is less
than the LCL, and therefore, the process is technically “out of
control.” The control chart indicates that something good has
happened.
9-89
Copyright © 2006 McGraw-Hill Ryerson Limited
Example
At Webster Chemical, lumps in the caulking compound could cause
difficulties in dispensing a smooth bead from the tube. Even when the
process is in control, there will still be an average of 4 lumps per tube of
caulk. Testing for the presence of lumps destroys the product, so
Webster takes random samples. The following are results of the study:
Tube #
Lumps
Tube #
Lumps
Tube #
1
6
5
6
9
Lumps
5
2
5
6
4
10
0
3
0
7
1
11
9
4
4
8
6
12
2
Determine the c-chart two-sigma upper and lower control limits for
this process.
Copyright © 2006 McGraw-Hill Ryerson Limited
9-90
Example
c=
6 + 5 + 0 + 4 + 6 + 4 + 1+ 6 + 5 + 0 + 9 + 2
=4
12
σc =
4 =2
UCL c = c + zσ c = 4 + 2(2 ) = 8
LCL c = c − zσ c = 4 − 2(2 ) = 0
Copyright © 2006 McGraw-Hill Ryerson Limited
9-91
Process Capability
• Process capability refers to the ability of
th process to
the
t meett the
th design
d i
specification for the product or service
– Whether the variability of the process output
falls within acceptable range of variability
allowed by the design specifications
• Design specifications are often
expressed as a nominal value and a
tolerance
Copyright © 2006 McGraw-Hill Ryerson Limited
9-92
D. Process Capability
• (Design) Specifications
– A range of acceptable values established by
engineering design or customer requirements
• Control limits
– Statistical limits
• Process variability
– Natural or inherent variability in a process
• Process capability
– The inherent variability of process output relative
to the variation allowed by the design specification
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Copyright © 2006 McGraw-Hill Ryerson Limited
D. Capability Analysis
Lower
Specification
Upper
Specification
Process variability matches
specifications
Lower
Specification
Upper
Specification
Process variability well within
specifications
Lower
Upper
Specification Specification
Process variability exceeds
specifications
Copyright © 2006 McGraw-Hill Ryerson Limited
9-94
Out of Range: Managerial Solutions
• Redesign the process
• Reduce the variability by finding better setting of
controllable factors
• Use an alternative process that can achieve the desired
output
• Retain the current process but attempt to eliminate
unacceptable output using 100% inspection
• Examine the design specifications
– Necessary
– Flexible
– OK with customer satisfaction
9-95
Copyright © 2006 McGraw-Hill Ryerson Limited
Process Capability
Nominal
value
Process distribution
Lower
specification
20
Upper
specification
25
30
Minutes
(a) Process is capable
The Relationship Between a Process Distribution and Upper and Lower
Specifications
Copyright © 2006 McGraw-Hill Ryerson Limited
9-96
Process Capability
Nominal
value
Process distribution
Lower
specification
Upper
specification
20
25
30
Minutes
(b) Process is not capable
The Relationship Between a Process Distribution and Upper and Lower
Specifications
9-97
Copyright © 2006 McGraw-Hill Ryerson Limited
Process Capability
Nominal value
Six sigma
Four sigma
Two sigma
Lower
specification
Upper
specification
Mean
Effects of Reducing Variability on Process Capability
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9-98
Process Variability
• Usually measured as ±3 standard deviations from the
process mean.
• If a process is capable,
capable deviations are within this
acceptable range of variation (tolerance).
• Suppose ideal length of time for a service is 10 minutes,
with tolerance of ±1 minute. If the process has a
standard dev of 0.5 minutes, would it be capable?
No, because ±3 standard deviations would be ±1.5
minutes, which exceeds the specification of ±1 minute.
9-99
Copyright © 2006 McGraw-Hill Ryerson Limited
D. Process Capability Ratio, Cp
Cp =
Cp =
Specifications width
Process width
Upperspecification − Lowerspecification
Copyright © 2006 McGraw-Hill Ryerson Limited
6σ
9-100
Example 8, page 372
• Using the capability ratio, we see that for this process to
be capable, it must have a capability ratio of at least
1.00.
• This implies that 99.74 percent of the output of a process
can be expected to be within the specification limits,
hence only 0.26 percent, or 2,600 units per million, fall
outside the design specification zone.
• The greater the capability ratio,
ratio the greater the
probability that the output of a machine or process will
fall within design specifications.
Copyright © 2006 McGraw-Hill Ryerson Limited
9-101
D. Process Capability Ratio, Cpk
If a process is not centered between spec limits or no limit is
specified on one side, we use Cpk. It is found by taking the
difference between each spec limit and the mean, dividing the
difference by 3 standard deviations and identifying the smaller ratio.
C pk = smaller of
Upper Specification - Process mean
3σ
and
Process mean - Lower Specification
3σ
Copyright © 2006 McGraw-Hill Ryerson Limited
9-102
D. 3 Sigma and 6 Sigma Quality
Six Sigma: goal of achieving a process variability so
small that the design specifications half-width
represents six standard deviations of the process
Upper
Lower
specification
specification
1350 ppm
1350 ppm
1.7 ppm
1.7 ppm
Process
mean
+/- 3 Sigma
Cp = 2.00; 0.00034 %
of getting output not
within design
specifications
+/- 6 Sigma
9-103
Copyright © 2006 McGraw-Hill Ryerson Limited
Six Sigma vs. TQM
Six Sigma
TQM
Objective
Product and process
perfection
Product and process
improvement
Tools
Statistical, e.g. design of
experiments and
analysis of variance
Simple data analysis,
e.g. Pareto chart, causeand-effect diagram
Methodology
Define, measure,
Plan, do, study, act
analyze, improve, control (PDSA)
(DMAIC)
Team leader
Black belt
Champion
Training
Long/formal
Short/informal
Culture change
Usually enforced
Sometimes enforced
Project time frame
Months/years
Days/weeks
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9-104
Managerial Considerations
• At what point(s) in the process to use
control charts
• What type of control chart to use
• Any others?
Summary of Formulas
Formulas, page 377
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9-105
Problem 8
• The Administrator of a small town received a certain
number of complaints during the last two weeks.
– Construct a control chart with three sigma limits for
the number of complaints each day using the
following data. Is the process in control?
– If 16 complaints are received today, using the control
chart of part a, is there a change in average number
of complaints?
Copyright © 2006 McGraw-Hill Ryerson Limited
9-106
Problem 17
• A process screens a certain type of potash
grains
i resulting
lti iin a mean di
diameter
t off 0
0.03
03
cm and a standard deviation of 0.003 cm.
The allowable variation in grain diameter is
from 0.02 to 0.04 cm.
– Calculate the capacity
p
y ratio Cp
p for the
process.
– Is the process capable?
Copyright © 2006 McGraw-Hill Ryerson Limited
9-107
Problem 18
• Given the list of machines, output, and
specs half-width,
h lf idth use Cp to
t determine
d t
i
which machines are capable of performing
the given jobs. (see page 385 for data)
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9-108
Problem 19
• Suppose your manager presents you with the following information
about machines that could be used for a job, and wants your
recommendation on which one to choose. The design specification
width is 0.48 mm. Calculate the Cp index for each machine, and
explain what additional information you need to make a choice.
Machine
Cost per unit ($)
Standard
Deviation (mm)
a
20
0.079
b
12
0.080
c
11
0.084
d
10
0.081
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9-109
Problem 20
• Each of the processes listed (see page
385) iis non-centered
t d with
ith respectt to
t the
th
design specification. Calculate Cpk index
for each, and decide if the process is
capable.
Copyright © 2006 McGraw-Hill Ryerson Limited
9-110
Business Case Analysis
•
•
•
•
Introduction
Key Issues
Problem Statement
Alternatives
– Advantages/disadvantages
• Recommendation
• Risk Mitigation
• Conclusion
Copyright © 2006 McGraw-Hill Ryerson Limited
9-111
Case Project
• Introduction (background information about the company)
• Production and Operations
p
Management
g
Situation/Question or
Problem to Solve at Hand
• Profile of Personnel of Interest (Top Management, Employees,
Public, Etc.)
• Internal Policies
• External Conditions: PESTEL
• 3 questions to calculate
• 3 discussion questions / questions to think about
Copyright © 2006 McGraw-Hill Ryerson Limited
9-112