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Chapter 3
Statistical Process Control
Operations Management - 6th Edition
Roberta Russell & Bernard W. Taylor, III
Copyright 2009 John Wiley & Sons, Inc.
Beni Asllani
University of Tennessee at Chattanooga
Lecture Outline






Basics of Statistical Process Control
Control Charts
Control Charts for Attributes
Control Charts for Variables
Control Chart Patterns
Process Capability
Copyright 2009 John Wiley & Sons, Inc.
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Product
launch
activities:
Revise
periodically
Customer Requirements
Product Specifications
Process Specifications
Statistical Process Control:
Measure & monitor quality
Ongoing
Activities
Meets
Specifications?
Yes
Conformance Quality
No
Fix process
or inputs
Basics of Statistical
Process Control
 Statistical Process Control
(SPC)

monitoring production process
to detect, correct, and prevent
poor quality
UCL
 Sample

subset of items produced to
use for inspection
LCL
 Control Chart

Is the process within statistical
control limits?
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Variation in a
Transformation Process
Inputs
• Facilities
• Equipment
• Materials
• Energy
• Employees
Transformation
Process
Outputs
Goods &
Services
•Variation in inputs create variation in outputs
•Variations in the transformation process create
variation in outputs
Basics of Statistical Process Control
Types of Variation (1)
1. Random variation





Also called common cause variation
This type of variation is inherent in a process.
Caused by usual variations in equipment, tooling,
employee actions, facility environment, materials,
measurement system, etc.
If random variation is excessive, the goods or
services will not meet quality standards.
To reduce random variation, we must reduce
variation in the inputs and the process
Copyright 2009 John Wiley & Sons, Inc.
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Basics of Statistical Process Control
Types of Variation (2)
2. Non-random variation




Also called special cause variation or assignable
cause variation
Caused by equipment out of adjustment, worn
tooling, operator errors, poor training, defective
materials, measurement errors, etc.
The process is not behaving as it usually does.
The cause can and should be identified and
corrected.
Copyright 2009 John Wiley & Sons, Inc.
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Statistical Process Control (SPC)
When is a process in control?
 A process is in control if it has no special cause
variation.
 The process is consistent or predictable.
 SPC distinguishes between common cause and
special cause variation
 Measure characteristics of goods or services that are
important to customers
 Make a control chart for each characteristic
 The chart is used to determine whether the
process is in control
Specification Limits
 The target is the ideal value
 Example: if the amount of beverage in a bottle should be 16
ounces, the target is 16 ounces
 Specification limits are the acceptable range of values for a
variable
 Example: the amount of beverage in a bottle must be at least
15.98 ounces and no more than 16.02 ounces.



Range is 15.98 – 16.02 ounces.
Lower specification limit = 15.98 ounces or LSPEC = 15.98 ounces
Upper specification limit = 16.02 ounces or USPEC = 16.02 ounces
Specifications and Conformance Quality
 A product which meets its specification has
conformance quality.
 Capable process: a process which
consistently produces products that have
conformance quality.
 Must be in control and meet specifications
Quality Measures
Attributes and Variables
 Discrete measures



Discrete means separate or distinct
Good/bad, yes/no (p charts) - Does the product meet
standards?
Count of defects (c charts) – the count is a whole number
 Variables – continuous numerical measures

Length, diameter, weight, height, time, speed,
temperature, pressure - does not have to be a whole
number

Controlled with x-bar and R charts
SPC Applied to Services (1)
 A service defect is a failure to meet customer
requirements.
 Different customers have different requirements.
 Examples of attribute measures used in services
 Customer satisfaction surveys – provides customer
perceptions
 Reports from mystery shoppers, based on
standards
 Employee or supervisor inspects cleanliness, etc.,
according to standards
Copyright 2009 John Wiley & Sons, Inc.
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SPC Applied to Services (2)
 Examples of variable measures used in
services






Waiting time and service time
On-time service delivery
Accuracy
Number of stockouts (retail and distribution)
Percentage of lost luggage (airlines)
Web site availability (online retailing or technical
support)
Copyright 2009 John Wiley & Sons, Inc.
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SPC Applied to Services (3)
 Hospitals

timeliness and quickness of care, staff responses to requests,
accuracy of lab tests, cleanliness, courtesy, accuracy of
paperwork, speed of admittance and checkouts
 Grocery stores

waiting time to check out, frequency of out-of-stock items,
quality of food items, cleanliness, customer complaints,
checkout register errors
 Airlines

flight delays, lost luggage and luggage handling, waiting time
at ticket counters and check-in, agent and flight attendant
courtesy, accurate flight information, passenger cabin
cleanliness and maintenance
Copyright 2009 John Wiley & Sons, Inc.
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SPC Applied to Services (4)
 Fast-food restaurants

waiting time for service, customer complaints,
cleanliness, food quality, order accuracy, employee
courtesy
 Catalogue-order companies

order accuracy, operator knowledge and courtesy,
packaging, delivery time, phone order waiting time
 Insurance companies

billing accuracy, timeliness of claims processing,
agent availability and response time
Copyright 2009 John Wiley & Sons, Inc.
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Process Control Chart
Out of control
Upper
control
limit
Process
average
Lower
control
limit
1
2
3
4
5
6
7
8
9
10
Sample number
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Control Charts for
Variables
 Range chart ( R-Chart )
 uses amount of dispersion in a
sample
 Mean chart ( x -Chart )
 uses process average of a
sample
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Control Charts for Variables
 Mean chart: sample means are plotted.
 Range chart: sample ranges are plotted.
 Two cases:


The standard deviation is known
The standard deviation is unknown.
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SPC for Variables
The Normal Distribution
 = the population mean
 = the standard deviation
for the population
99.74% of the area under the
normal curve is between
 - 3 and  + 3
SPC for Variables
The Central Limit Theorem
 Samples are taken from a distribution with
mean  and standard deviation .
k = the number of samples
n = the number of units in each sample
 The sample means are normally distributed

with mean  and standard deviation  x 
n
when k is large.
x-bar Chart:
Standard Deviation Known
UCL = x= + zx
LCL = =x - zx
x1 + x2 + ... xn
n
x= =
where
=
x = average of sample means
Copyright 2009 John Wiley & Sons, Inc.
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x-bar Chart Example:
Standard Deviation Known (cont.)
Given: The standard deviation is 0.08
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x-bar Chart Example:
Standard Deviation Known (cont.)
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x-bar Chart Example:
Standard Deviation Unknown
UCL = x= + A2R
LCL = x= - A2R
A2 is a factor that depends on n,
the number of units in each sample
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Control
Limits
In this problem,
n=5
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x-bar Chart Example:
Standard Deviation Unknown
OBSERVATIONS (SLIP- RING DIAMETER, CM)
SAMPLE k
1
2
3
4
5
x
R
1
2
3
4
5
6
7
8
9
10
5.02
5.01
4.99
5.03
4.95
4.97
5.05
5.09
5.14
5.01
5.01
5.03
5.00
4.91
4.92
5.06
5.01
5.10
5.10
4.98
4.94
5.07
4.93
5.01
5.03
5.06
5.10
5.00
4.99
5.08
4.99
4.95
4.92
4.98
5.05
4.96
4.96
4.99
5.08
5.07
4.96
4.96
4.99
4.89
5.01
5.03
4.99
5.08
5.09
4.99
4.98
5.00
4.97
4.96
4.99
5.01
5.02
5.05
5.08
5.03
0.08
0.12
0.08
0.14
0.13
0.10
0.14
0.11
0.15
0.10
50.09
1.15
Example 15.4
Copyright 2009 John Wiley & Sons, Inc.
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x-bar Chart Example:
Standard Deviation Unknown (cont.)
R=
∑R
k
=
1.15
10
= 0.115
50.09
= x
x=
=
= 5.01 cm
k
10
UCL = x= + A2R = 5.01 + (0.58)(0.115) = 5.08
LCL = x= - A2R = 5.01 - (0.58)(0.115) = 4.94
Retrieve Factor Value A2
Copyright 2009 John Wiley & Sons, Inc.
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5.10 –
5.08 –
UCL = 5.08
5.06 –
Mean
5.04 –
x- bar
Chart
Example
(cont.)
5.02 –
x= = 5.01
5.00 –
4.98 –
4.96 –
LCL = 4.94
4.94 –
4.92 –
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Sample number
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A Process Is in
Control If …
1. There are no sample points outside limits &
2. Most points are near the process average &
3. The number of points above and below the
center line is about equal &
4. The points appear to be randomly distributed
This is only a rough guide. Quality analysts
use more precise rules.
Copyright 2009 John Wiley & Sons, Inc.
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R- Chart
UCL = D4R
LCL = D3R
R
R= k
where
R = range of each sample
k = number of samples
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R-Chart Example
OBSERVATIONS (SLIP-RING DIAMETER, CM)
SAMPLE k
1
2
3
4
5
x
R
1
2
3
4
5
6
7
8
9
10
5.02
5.01
4.99
5.03
4.95
4.97
5.05
5.09
5.14
5.01
5.01
5.03
5.00
4.91
4.92
5.06
5.01
5.10
5.10
4.98
4.94
5.07
4.93
5.01
5.03
5.06
5.10
5.00
4.99
5.08
4.99
4.95
4.92
4.98
5.05
4.96
4.96
4.99
5.08
5.07
4.96
4.96
4.99
4.89
5.01
5.03
4.99
5.08
5.09
4.99
4.98
5.00
4.97
4.96
4.99
5.01
5.02
5.05
5.08
5.03
0.08
0.12
0.08
0.14
0.13
0.10
0.14
0.11
0.15
0.10
50.09
1.15
Example 15.3
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R-Chart Example (cont.)
UCL = D4R = 2.11(0.115) = 0.243
LCL = D3R = 0(0.115) = 0
Retrieve Factor Values D3 and D4
Example 15.3
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R-Chart Example (cont.)
0.28 –
0.24 –
Range
0.20 –
0.16 –
UCL = 0.243
R = 0.115
0.12 –
0.08 –
0.04 –
0–
LCL = 0
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Sample number
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Using x- bar and R-Charts
Together
 Process average and process variability must be
in control
 It is possible for samples to have very narrow
ranges, but their averages might be beyond
control limits
 It is possible for sample averages to be in
control, but ranges might be very large
 It is possible for an R-chart to exhibit a distinct
downward trend, suggesting some nonrandom
cause is reducing variation
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Non-random Patterns in Control Charts
Change in Mean
UCL
UCL
LCL
Sample observations
consistently below the
center line
LCL
Sample observations
consistently above the
center line
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Non-random Patterns in Control Charts
Trend
UCL
UCL
LCL
Sample observations
consistently increasing
LCL
Sample observations
consistently decreasing
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Process Capability
 Tolerances

design specifications reflecting product
requirements
 Process capability

range of natural variability in a process—
what we measure with control charts
 A capable process consistently produces
products that conform to specifications
Copyright 2009 John Wiley & Sons, Inc.
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Copyright 2009 John Wiley & Sons, Inc.
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use of the information herein.
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