Transcript 15.2 Single - Factor (One - Way) Analysis of Variance : Independent

Chapter 6
Quality
Management
Types of Quality to
Consider
• User based quality
– Eyes of the customer, sometimes not
measurable
• Product based quality
– Measurable Quality characteristics
• Manufacturing based Quality
– Conforms to standards / designs
Dimensions of Quality (Garvin)
1. Performance
Basic operating characteristics
2. Features
“Extra” items added to basic features
3. Reliability
Probability product will operate over time
Dimensions of Quality (Garvin)
4. Conformance
Meeting pre-established standards
5. Durability
Life span before replacement
6. Serviceability
Ease of getting repairs, speed &
competence of repairs
Dimensions of Quality (Garvin)
7. Aesthetics
Look, feel, sound, smell or taste
8. Safety
Freedom from injury or harm
9. Other perceptions
Subjective perceptions based on
brand name, advertising, etc
Total Quality Management
1.
2.
3.
4.
5.
6.
7.
8.
Customer defined quality
Top management leadership
Quality as a strategic issue
All employees responsible for quality
Continuous improvement / Kaizen
Shared problem solving
Statistical quality control
Training & education for all employees
Cost of Quality
Cost of achieving good quality
Prevention
Planning, Product design, Process,
Training, Information
Appraisal
Inspection and testing,
Test equipment,
Operator
Cost of Quality
Cost of poor quality
Internal failure costs
Scrap, Rework, Process failure,
Process downtime, Pricedowngrading
External failure costs
Customer complaints,
Product return,
Warranty, Product
liability, Lost sales
Quality–Cost Relationship
Increased prevention costs lead to
decreased failure costs
Improved quality leads to increased
sales and market share
Quality improvement at the design
stage
Higher quality products can
command higher prices
Statistical Process Control
The objective of a process control
system is to provide a statistical
signal when assignable causes of
variation are present
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Statistical Process Control
(SPC)
►
Variability is inherent
in every process
►
Natural or common
causes
►
Special or assignable
causes
►
Provides a statistical signal when assignable
causes are present
►
Detect and eliminate assignable causes of
variation
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Natural Variations
►
Also called common causes
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Affect virtually all production processes
►
Expected amount of variation
►
Output measures follow a probability
distribution
►
For any distribution there is a measure of
central tendency and dispersion
►
If the distribution of outputs falls within
acceptable limits, the process is said to be
“in control”
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Assignable Variations
►
Also called special causes of variation
►
Generally this is some change in the process
►
Variations that can be traced to a specific
reason
►
The objective is to discover when assignable
causes are present
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Eliminate the bad causes
►
Incorporate the good causes
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Samples
To measure the process, we take samples and
analyze the sample statistics following these
steps
Each of these
represents one
sample of five
boxes of cereal
(a) Samples of the product,
say five boxes of cereal
taken off the filling machine
line, vary from each other
in weight
Frequency
# #
# # #
# # # #
# # # # # # #
#
Figure S6.1
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# # # # # # # # #
Weight
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Samples
To measure the process, we take samples and
analyze the sample statistics following these
steps
Frequency
(b) After enough samples
are taken from a stable
process, they form a
pattern called a
distribution
The solid line
represents the
distribution
Weight
Figure S6.1
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Samples
To measure the process, we take samples and
analyze the sample statistics following these
steps
(c) There are many types of distributions, including the normal (bellshaped) distribution, but distributions do differ in terms of central
tendency (mean), standard deviation or variance, and shape
Frequency
Figure S6.1
Central tendency
Weight
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Variation
Weight
Shape
Weight
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Samples
To measure the process, we take samples and
analyze the sample statistics following these
steps
Prediction
Frequency
(d) If only natural causes of
variation are present,
the output of a process
forms a distribution that
is stable over time and
is predictable
Weight
Figure S6.1
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Samples
To measure the process, we take samples and
analyze the sample statistics following these
steps
Prediction
Frequency
(e) If assignable causes are
present, the process output
is not stable over time and
is not predicable
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Weight
Figure S6.1
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Control Charts
Constructed from historical data, the
purpose of control charts is to help
distinguish between natural variations
and variations due to assignable causes
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Process Control
Frequency
Lower control limit
(a) In statistical
control and capable
of producing within
control limits
Upper control limit
(b) In statistical control
but not capable of
producing within
control limits
(c) Out of control
Size
(weight, length, speed, etc.)
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Figure S6.2
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Control Charts for Variables
►
Characteristics that can take any real value
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May be in whole or in fractional numbers
►
Continuous random variables
x-chart tracks changes in the central
tendency
R-chart indicates a gain or loss of
dispersion
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Setting Chart Limits
For x-Charts when we know s
Lower control limit (UCL) = x= - zs x
Upper control limit (UCL) = x= + zs x
Where
x= = mean of the sample means or a target value set for the
process
z = number of normal standard deviations
sx = standard deviation of the sample means = s / n
s = population (process) standard deviation
n = sample size
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Setting Control Limits
▶ Randomly select and weigh nine (n = 9) boxes
each hour
Average weight in 17 +13 +16 +18 +17 +16 +15 +17 +16
=
= 16.1 ounces
the first sample
9
WEIGHT OF SAMPLE
HOUR
(AVG. OF 9
BOXES)
1
WEIGHT OF SAMPLE
WEIGHT OF SAMPLE
HOUR
(AVG. OF 9
BOXES)
HOUR
(AVG. OF 9
BOXES)
16.1
5
16.5
9
16.3
2
16.8
6
16.4
10
14.8
3
15.5
7
15.2
11
14.2
4
16.5
8
16.4
12
17.3
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Setting Control Limits
12
é
Avg of 9 boxes
ê
å
Average mean ê = i=1
= x=
of 12 samples
ê
12
ê
ë
(
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)
ù
ú
ú
ú
ú
û
x= = 16 ounces
n=9
z=3
s = 1 ounce
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Setting Control Limits
12
é
Avg of 9 boxes
ê
å
Average mean ê = i=1
= x=
of 12 samples
ê
12
ê
ë
(
)
ù
ú
ú
ú
ú
û
x= = 16 ounces
n=9
z=3
s = 1 ounce
æ 1 ö
æ 1ö
UCL x = x + zs x = 16 + 3 ç
÷ = 16 + 3 ç ÷ = 17 ounces
è3ø
è 9ø
=
æ 1 ö
æ 1ö
LCL x = x - zs x = 16 - 3 ç
÷ = 16 - 3 ç ÷ = 15 ounces
è3ø
è 9ø
=
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Setting Control Limits
Control Chart
for samples
of 9 boxes
Variation due
to assignable
causes
Out of
control
17 = UCL
Variation due to
natural causes
16 = Mean
15 = LCL
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1 2 3 4 5 6 7 8 9 10 11 12
Sample number
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Out of
control
Variation due
to assignable
causes
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Restaurant Control Limits
Sample Mean
For salmon filets at Darden Restaurants
x Bar Chart
11.5 –
UCL = 11.524
11.0 –
=
x = – 10.959
10.5 –
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3
5
7
9
11
13
15
17
LCL = – 10.394
Sample Range
Range Chart
0.8 –
UCL = 0.6943
0.4 –
–
R = 0.2125
0.0 – |
1
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3
5
7
9
11
13
15
17
LCL = 0
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Mean and Range Charts
(a)
(Sampling mean is
shifting upward, but
range is consistent)
These
sampling
distributions
result in the
charts below
UCL
(x-chart detects
shift in central
tendency)
x-chart
LCL
UCL
(R-chart does not
detect change in
mean)
R-chart
Figure S6.5
LCL
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Mean and Range Charts
(b)
These
sampling
distributions
result in the
charts below
(Sampling mean
is constant, but
dispersion is
increasing)
UCL
(x-chart indicates
no change in
central tendency)
x-chart
LCL
UCL
(R-chart detects
increase in
dispersion)
R-chart
Figure S6.5
LCL
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Control Charts for Attributes
►
For variables that are categorical
►
Defective/nondefective, good/bad,
yes/no, acceptable/unacceptable
►
Measurement is typically counting
defectives
►
Charts may measure
1. Percent defective (p-chart)
2. Number of defects (c-chart)
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Six Sigma
• Developed by Motorola, a disciplined
approach calling for at most 3
defects for every million units of
production / customers served
• Seven Tools will not be covered in
depth
Benchmarking
• Comparing product / service
against best-in-class
• In computing
– Standard test cases
• Auto safety
– Crash tests
• In a large company, internal benchmarking:
– Compare different divisions or
departments
• In General: Who does it the best and how do
we compare?
What is JIT ?
Producing only what is needed, when
it is needed
A philosophy
An integrated management system
JIT’s mandate:
Eliminate all waste
“Poka-yokes” used to eliminate errors
and wasteful repetition
Kaizen
Continuous improvement
Requires total employee involvement
Essence of JIT is willingness of workers
to:
Spot quality problems
Halt production when necessary
Generate ideas for improvement
Analyze problems
Perform different functions
Visual Control
Visual Control
Visual Control