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Statistical Process Control
Chapter 3
Russell and Taylor
Operations and Supply Chain Management, 8th Edition
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Lecture Outline
• Basics of Statistical Process Control – Slide 4 • Control Charts – Slide 12• Control Charts for Attributes – Slide 16• Control Charts for Variables – Slide 27• Control Chart Patterns – Slide 45• SPC with Excel and OM Tools – Slide 52• Process Capability – Slide 54
3-2© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
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Learning Objectives
• Explain when and how to use statistical process control to ensure the quality of products and services
• Discuss the rationale and procedure for constructing attribute and variable control charts
• Utilize appropriate control charts to determine if a process is in-control
• Identify control chart patterns and describe appropriate data collection
• Assess the process capability of a process
3-3© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
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Statistical Process Control (SPC)
• Statistical Process Control• monitoring production process
to detect and prevent poor quality
• Sample• subset of items produced to
use for inspection
• Control Charts• process is within statistical
control limits
3-4© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
UCL
LCL
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Process Variability
• Random• inherent in a process• depends on equipment
and machinery, engineering, operator, and system of measurement
• natural occurrences
• Non-Random• special causes• identifiable and
correctable• include equipment out of
adjustment, defective materials, changes in parts or materials, broken machinery or equipment, operator fatigue or poor work methods, or errors due to lack of training
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 3-5
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SPC in Quality Management
• SPC uses• Is the process in control?• Identify problems in order to make
improvements• Contribute to the TQM goal of continuous
improvement
3-6© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
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Quality Measures:Attributes and Variables
• Attribute• A characteristic which is evaluated with a
discrete response• good/bad; yes/no; correct/incorrect
• Variable measure• A characteristic that is continuous and can be
measured• Weight, length, voltage, volume
3-7© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
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SPC Applied to Services
• Nature of defects is different in services• Service defect is a failure to meet customer
requirements• Monitor time and customer satisfaction
3-8© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
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SPC Applied to Services
• Hospitals• timeliness & quickness of care, staff responses to requests,
accuracy of lab tests, cleanliness, courtesy, accuracy of paperwork, speed of admittance & 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 & luggage handling, waiting time at
ticket counters & check-in, agent & flight attendant courtesy, accurate flight information, cabin cleanliness & maintenance
3-9© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
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SPC Applied to Services
• Fast-food restaurants• waiting time for service, customer complaints, cleanliness, food
quality, order accuracy, employee courtesy
• Catalogue-order companies• order accuracy, operator knowledge & courtesy, packaging,
delivery time, phone order waiting time
• Insurance companies• billing accuracy, timeliness of claims processing, agent
availability & response time
3-10© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
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Where to Use Control Charts
• Process • Has a tendency to go out of control
• Is particularly harmful and costly if it goes out of control
• Examples• At beginning of process because of waste to begin
production process with bad supplies• Before a costly or irreversible point, after which product is
difficult to rework or correct• Before and after assembly or painting operations that
might cover defects• Before the outgoing final product or service is delivered
3-11© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
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Control Charts
• A graph that monitors process quality• Control limits
• upper and lower bands of a control chart
• Attributes chart• p-chart• c-chart
• Variables chart• mean (x bar – chart)• range (R-chart)
3-12© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
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Process Control Chart
3-13© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
1 2 3 4 5 6 7 8 9 10Sample number
Uppercontrol
limit
Processaverage
Lowercontrol
limit
Out of control
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Normal Distribution
• Probabilities for Z= 2.00 and Z = 3.00
3-14© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
=0 1 2 3-1-2-3
95%
99.74%
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A Process Is in Control If …
3-15© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
1. … no sample points outside limits
2. … most points near process average
3. … about equal number of points above and below centerline
4. … points appear randomly distributed
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Control Charts for Attributes
• p-chart• uses portion defective in a sample
• c-chart• uses number of defects (non-conformities) in a
sample
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p-Chart
3-17© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
UCL = p + zp
LCL = p - zp
z = number of standard deviations from process average
p = sample proportion defective; estimates process mean
p = standard deviation of sample proportionp =
p(1 - p)
n
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Construction of p-Chart
3-18© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
20 samples of 100 pairs of jeans
NUMBER OF PROPORTIONSAMPLE # DEFECTIVES DEFECTIVE
1 6 .06
2 0 .00
3 4 .04
: : :
: : :
20 18 .18
200
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Construction of p-Chart
3-19© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
UCL = p + z =p(1 - p)
n
UCL =
LCL =
LCL = p - z =p(1 - p)
n
=total defectives
total sample observationsp =
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Construction of p-Chart
3-20© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
UCL = p + z = 0.10 + 3p(1 - p)
n
0.10(1 - 0.10)
100
UCL = 0.190
LCL = 0.010
LCL = p - z = 0.10 - 3p(1 - p)
n
0.10(1 - 0.10)
100
= 200 / 20(100) = 0.10total defectives
total sample observationsp =
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Construction of p-Chart
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p-Chart in Excel
3-22© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
Click on “Insert” then “Charts”
to construct control chart
I4 + 3*SQRT(I4*(1-I4)/100)
I4 - 3*SQRT(I4*(1-I4)/100)
Column values copiedfrom I5 and I6
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c-Chart
3-23© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
UCL = c + zc
LCL = c - zc
where
c = number of defects per sample
c = c
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c-Chart
3-24© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
Number of defects in 15 sample rooms
1 122 83 16
: :: :15 15 190
SAMPLE
c =
NUMBER OF
DEFECTS
UCL = c + zc
LCL = c - zc
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c-Chart
3-25© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
Number of defects in 15 sample rooms
1 122 83 16
: :: :15 15 190
SAMPLE
c = = 12.6719015
UCL = c + zc
= 12.67 + 3 12.67= 23.35
LCL = c - zc
= 12.67 - 3 12.67= 1.99
NUMBER OF
DEFECTS
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c-Chart
3-26© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
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Control Charts for Variables
3-27© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
Range chart ( R-Chart ) Plot sample range (variability)
Mean chart ( x -Chart ) Plot sample averages
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-
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 3-28
x-bar Chart: Known
UCL = x + z x LCL = x - z x
-==
Where
s = process standard deviations
x = standard deviation of sample means =/k = number of samples (subgroups)n = sample size (number of observations)
x1 + x2 + ... + xk
kX = =
- - -
n
-
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Observations(Slip-Ring Diameter, cm) n
Sample k 1 2 3 4 5 -
x-bar Chart Example: Known
3-29© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
x
We know σ = .08
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x-bar Chart Example: Known
3-30© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
LCL = x - z x = -UCL = x + z x
= -
x1 + x2 + ... + xk
kX = =
- - -
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x-bar Chart Example: Known
3-31© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
= 5.01 - 3(.08 / )10
= 4.93
_____10
50.09 = 5.01X =
=
LCL = x - z x = -UCL = x + z x
= -= 5.01 + 3(.08 / )10
= 5.09
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x-bar Chart Example: Unknown
3-32© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
_UCL = x + A2R LCL = x - A2R
= =_
where
x = average of the sample means
R = average range value
=_
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© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 3-33
Control Chart Factors
n A2 D3 D42 1.880 0.000 3.2673 1.023 0.000 2.5754 0.729 0.000 2.2825 0.577 0.000 2.1146 0.483 0.000 2.0047 0.419 0.076 1.9248 0.373 0.136 1.8649 0.337 0.184 1.81610 0.308 0.223 1.77711 0.285 0.256 1.74412 0.266 0.283 1.71713 0.249 0.307 1.69314 0.235 0.328 1.67215 0.223 0.347 1.65316 0.212 0.363 1.63717 0.203 0.378 1.62218 0.194 0.391 1.60919 0.187 0.404 1.59620 0.180 0.415 1.58521 0.173 0.425 1.57522 0.167 0.435 1.56523 0.162 0.443 1.55724 0.157 0.452 1.54825 0.153 0.459 1.541
Factors for R-chartSample
Size Factor for X-chart
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x-bar Chart Example: Unknown
3-34© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
OBSERVATIONS (SLIP- RING DIAMETER, CM)
SAMPLE k 1 2 3 4 5 x R
1 5.02 5.01 4.94 4.99 4.96 4.98 0.082 5.01 5.03 5.07 4.95 4.96 5.00 0.123 4.99 5.00 4.93 4.92 4.99 4.97 0.084 5.03 4.91 5.01 4.98 4.89 4.96 0.145 4.95 4.92 5.03 5.05 5.01 4.99 0.136 4.97 5.06 5.06 4.96 5.03 5.01 0.107 5.05 5.01 5.10 4.96 4.99 5.02 0.148 5.09 5.10 5.00 4.99 5.08 5.05 0.119 5.14 5.10 4.99 5.08 5.09 5.08 0.15
10 5.01 4.98 5.08 5.07 4.99 5.03 0.10
50.09 1.15Totals
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x-bar Chart Example: Unknown
3-35© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
_R = ____∑ R
k
_UCL = x + A2R
=
=x =åx
k___
_LCL = x - A2R
=
_
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x-bar Chart Example: Unknown
3-36© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
∑ Rk
1.1510R = = = 0.115
_ ____ ____
_UCL = x + A2R
=
= 50.0910
_____x = = = 5.01 cmåx
k___
= 5.01 + (0.58)(0.115) = 5.08
_LCL = x - A2R
== 5.01 - (0.58)(0.115) = 4.94
_
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x- bar Chart
Example
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R- Chart
3-38© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
UCL = D4R LCL = D3R
R = åRk
WhereR = range of each samplek = number of samples (sub groups)
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R-Chart Example
3-39© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
OBSERVATIONS (SLIP- RING DIAMETER, CM)
SAMPLE k 1 2 3 4 5 x R
1 5.02 5.01 4.94 4.99 4.96 4.98 0.082 5.01 5.03 5.07 4.95 4.96 5.00 0.123 4.99 5.00 4.93 4.92 4.99 4.97 0.084 5.03 4.91 5.01 4.98 4.89 4.96 0.145 4.95 4.92 5.03 5.05 5.01 4.99 0.136 4.97 5.06 5.06 4.96 5.03 5.01 0.107 5.05 5.01 5.10 4.96 4.99 5.02 0.148 5.09 5.10 5.00 4.99 5.08 5.05 0.119 5.14 5.10 4.99 5.08 5.09 5.08 0.15
10 5.01 4.98 5.08 5.07 4.99 5.03 0.10
50.09 1.15Totals
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R-Chart Example
3-40© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
Retrieve chart factors D3 and D4
UCL = D4R =
LCL = D3R = _
_
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R-Chart Example
3-41© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
Retrieve chart factors D3 and D4
UCL = D4R = 2.11(0.115) = 0.243
LCL = D3R = 0(0.115) = 0_
_
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R-Chart Example
3-42© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
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X-bar and R charts – Excel & OM Tools
3-43© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
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Using x- bar and R-Charts Together
• Process average and process variability must be in control
• Samples can have very narrow ranges, but sample averages might be beyond control limits
• Or, sample averages may be in control, but ranges might be out of control
• An R-chart might show a distinct downward trend, suggesting some nonrandom cause is reducing variation
3-44© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
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Control Chart Patterns
• Run• sequence of sample values that display same
characteristic
• Pattern test• determines if observations within limits of a control
chart display a nonrandom pattern
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Control Chart Patterns
• To identify a pattern look for:• 8 consecutive points on one side of the center line• 8 consecutive points up or down• 14 points alternating up or down• 2 out of 3 consecutive points in zone A (on one side of
center line)• 4 out of 5 consecutive points in zone A or B (on one
side of center line)
3-46© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
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Control Chart Patterns
3-47© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
UCL
LCL
Sample observationsconsistently above thecenter line
LCL
UCL
Sample observationsconsistently below thecenter line
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Control Chart Patterns
3-48© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
LCL
UCL
Sample observationsconsistently increasing
UCL
LCL
Sample observationsconsistently decreasing
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Zones for Pattern Tests
3-49© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
UCL
LCL
Zone A
Zone B
Zone C
Zone C
Zone B
Zone A
Process average
3 sigma = x + A2R=
3 sigma = x - A2R=
2 sigma = x + (A2R)= 23
2 sigma = x - (A2R)= 23
1 sigma = x + (A2R)= 13
1 sigma = x - (A2R)= 13
x=
Sample number
|1
|2
|3
|4
|5
|6
|7
|8
|9
|10
|11
|12
|13
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Performing a Pattern Test
3-50© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
1 4.98 B — B
2 5.00 B U C
3 4.95 B D A
4 4.96 B D A
5 4.99 B U C
6 5.01 — U C
7 5.02 A U C
8 5.05 A U B
9 5.08 A U A
10 5.03 A D B
SAMPLE x ABOVE/BELOW UP/DOWN ZONE
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Sample Size Determination
• Attribute charts require larger sample sizes• 50 to 100 parts in a sample
• Variable charts require smaller samples• 2 to 10 parts in a sample
3-51© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
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SPC with Excel
3-52© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
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SPC with OM Tools
3-53© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
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Process Capability
• Compare natural variability to design variability • Natural variability
• What we measure with control charts• Process mean = 8.80 oz, Std dev. = 0.12 oz
• Tolerances• Design specifications reflecting product
requirements• Net weight = 9.0 oz 0.5 oz • Tolerances are 0.5 oz
3-54© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
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Process Capability
3-55© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
(b) Design specifications and natural variation the same; process is capable of meeting specifications most of the time.
Design Specifications
Process
(a) Natural variation exceeds design specifications; process is not capable of meeting specifications all the time.
Design Specifications
Process
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Process Capability
3-56© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
(c) Design specifications greater than natural variation; process is capable of always conforming to specifications.
Design Specifications
Process
(d) Specifications greater than natural variation, but process off center; capable but some output will not meet upper specification.
Design Specifications
Process
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Process Capability Ratio
3-57© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
Cp =tolerance range
process range
upper spec limit - lower spec limit
6=
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Computing Cp
3-58© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
Net weight specification = 9.0 oz 0.5 ozProcess mean = 8.80 ozProcess standard deviation = 0.12 oz
Cp =
upper specification limit - lower specification limit
6
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Computing Cp
3-59© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
Net weight specification = 9.0 oz 0.5 ozProcess mean = 8.80 ozProcess standard deviation = 0.12 oz
Cp =
= = 1.39
upper specification limit - lower specification limit
6
9.5 - 8.5
6(0.12)
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Process Capability Index
3-60© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
Cpk = minimum
x - lower specification limit
3
=
upper specification limit - x
3
=
,
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Computing Cpk
3-61© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
Net weight specification = 9.0 oz 0.5 ozProcess mean = 8.80 ozProcess standard deviation = 0.12 oz
Cpk = minimum
x - lower specification limit
3
=
upper specification limit - x
3
=
,
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Computing Cpk
3-62© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
Net weight specification = 9.0 oz 0.5 ozProcess mean = 8.80 ozProcess standard deviation = 0.12 oz
Cpk = minimum
= minimum , = 0.83
x - lower specification limit
3
=
upper specification limit - x
3
=
,
8.80 - 8.50
3(0.12)
9.50 - 8.80
3(0.12)
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Process Capability With Excel
3-63© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
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Process Capability With OM Tools
3-64© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
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3-65© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e
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