10-1 Quality Control
William J. Stevenson
Operations Management
8th edition
10-2 Quality Control
CHAPTER
10
Quality Control
McGraw-Hill/IrwinOperations Management, Eighth Edition, by William J. Stevenson
Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved.
10-3 Quality Control
Phases of Quality Assurance
Acceptance
sampling
Process
control
Continuous
improvement
Inspection
before/afterproduction
Inspection and
corrective
action duringproduction
Quality built
into theprocess
The least
progressive
The most
progressive
Figure 10.1
10-4 Quality Control
Inspection
• How Much/How Often
• Where/When
• Centralized vs. On-site
Inputs Transformation Outputs
Acceptancesampling
Process
control
Acceptancesampling
Figure 10.2
10-5 Quality Control
Co
st
OptimalAmount of Inspection
Inspection Costs
Cost of inspection
Cost of
passingdefectives
Total Cost
Figure 10.3
10-6 Quality Control
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
10-7 Quality Control
Examples of Inspection Points
Type of
business
Inspection
points
Characteristics
Fast Food Cashier
Counter areaEating area
Building
Kitchen
Accuracy
Appearance, productivityCleanliness
Appearance
Health regulations
Hotel/motel Parking lot
AccountingBuilding
Main desk
Safe, well lighted
Accuracy, timelinessAppearance, safety
Waiting times
Supermarket Cashiers
Deliveries
Accuracy, courtesy
Quality, quantity
Table 10.1
10-8 Quality Control
• Statistical Process Control: Statistical evaluation of the output of a process during production
• Quality of Conformance:A product or service conforms to specifications
10-9 Quality Control
Control Chart
• Control Chart
• Purpose: to monitor process output to see if
it is random
• A time ordered plot representative sample
statistics obtained from an on going process
(e.g. sample means)
• Upper and lower control limits define the
range of acceptable variation
10-10 Quality Control
Control Chart
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
UCL
LCL
Sample number
Mean
Out ofcontrol
Normal variationdue to chance
Abnormal variation
due to assignable sources
Abnormal variationdue to assignable sources
Figure 10.4
10-11 Quality Control
Statistical Process Control
• The essence of statistical process control is
to assure that the output of a process is
random so that future output will be random.
10-12 Quality Control
Statistical Process Control
• The Control Process
• Define
• Measure
• Compare
• Evaluate
• Correct
• Monitor results
10-13 Quality Control
Statistical Process Control
• Variations and Control
• Random variation: Natural variations in the
output of a process, created by countless
minor factors
• Assignable variation: A variation whose
source can be identified
10-14 Quality Control
Sampling Distribution
Sampling
distribution
Processdistribution
Mean
Figure 10.5
10-15 Quality Control
Normal Distribution
Mean−3σ−3σ−3σ−3σ −2σ−2σ−2σ−2σ +2σ+2σ+2σ+2σ +3σ+3σ+3σ+3σ
95.44%
99.74%
σ = σ = σ = σ = Standard deviation
Figure 10.6
10-16 Quality Control
Control Limits
Samplingdistribution
Process
distribution
Mean
Lowercontrol
limit
Uppercontrol
limit
Figure 10.7
10-17 Quality Control
SPC Errors
• Type I error
• Concluding a process is not in control when
it actually is.
• Type II error
• Concluding a process is in control when it
is not.
10-18 Quality Control
Type I Error
Mean
LCL UCL
αααα/2 αααα/2
α = α = α = α = Probabilityof Type I error
Figure 10.8
10-19 Quality Control
Observations from Sample Distribution
Sample number
UCL
LCL
1 2 3 4
Figure 10.9
10-20 Quality Control
Control Charts for Variables
• Mean control charts
• Used to monitor the central tendency of a
process.
• X bar charts
• Range control charts
• Used to monitor the process dispersion
• R charts
Variables generate data that are measured.
10-21 Quality Control
Mean and Range Charts
UCL
LCL
UCL
LCL
R-chart
x-Chart Detects shift
Does notdetect shift
Figure 10.10A
(process mean is
shifting upward)Sampling
Distribution
10-22 Quality Control
x-Chart
UCL
Does notreveal increase
Mean and Range Charts
UCL
LCL
LCL
R-chart Reveals increase
Figure 10.10B
(process variability is increasing)Sampling
Distribution
10-23 Quality Control
Control Chart for Attributes
• p-Chart - Control chart used to monitor the
proportion of defectives in a process
• c-Chart - Control chart used to monitor the
number of defects per unit
Attributes generate data that are counted.
10-24 Quality Control
Use of p-Charts
• When observations can be placed into two
categories.
• Good or bad
• Pass or fail
• Operate or don’t operate
• When the data consists of multiple samples
of several observations each
Table 10.3
10-25 Quality Control
Use of c-Charts
• Use only when the number of occurrences per
unit of measure can be counted; non-
occurrences cannot be counted.
• Scratches, chips, dents, or errors per item
• Cracks or faults per unit of distance
• Breaks or Tears per unit of area
• Bacteria or pollutants per unit of volume
• Calls, complaints, failures per unit of time
Table 10.3
10-26 Quality Control
Use of Control Charts
• At what point in the process to use control
charts
• What size samples to take
• What type of control chart to use
• Variables
• Attributes
10-27 Quality Control
Run Tests
• Run test – a test for randomness
• Any sort of pattern in the data would suggest
a non-random process
• All points are within the control limits - the
process may not be random
10-28 Quality Control
Nonrandom Patterns in Control charts
• Trend
• Cycles
• Bias
• Mean shift
• Too much dispersion
Figure 10.11
10-29 Quality Control
Counting Above/Below Median Runs (7 runs)
Counting Up/Down Runs (8 runs)
U U D U D U D U U D
B A A B A B B B A A B
Figure 10.12
Figure 10.13
Counting Runs
10-30 Quality Control
• Tolerances or specifications
• Range of acceptable values established by
engineering design or customer requirements
• Process variability
• Natural variability in a process
• Process capability
• Process variability relative to specification
Process Capability
10-31 Quality Control
Process Capability
LowerSpecification
UpperSpecification
A. Process variability matches specifications
LowerSpecification
UpperSpecification
B. Process variabilitywell within specifications
LowerSpecification
UpperSpecification
C. Process variability exceeds specifications
Figure 10.15
10-32 Quality Control
Process Capability Ratio
Process capability ratio, Cp =specification width
process width
Upper specification – lower specification
6σCp =
10-33 Quality Control
Process
mean
Lower
specification
Upper
specification
1350 ppm 1350 ppm
1.7 ppm 1.7 ppm
+/- 3 Sigma
+/- 6 Sigma
3 Sigma and 6 Sigma Quality
10-34 Quality Control
Improving Process Capability
• Simplify
• Standardize
• Mistake-proof
• Upgrade equipment
• Automate
10-35 Quality Control
Taguchi Loss Function
Cost
TargetLower
specUpper
spec
Traditional
cost function
Taguchi
cost function
Figure 10.17
10-36 Quality Control
Limitations of Capability Indexes
1. Process may not be stable
2. Process output may not be normally
distributed
3. Process not centered but Cp is used
10-37 Quality Control
Additional PowerPoint slides contributed by
Geoff Willis, University of Central Oklahoma.
CHAPTER
10
10-38 Quality Control
Statistical Process Control (SPC)
• Invented by Walter Shewhart at Western
Electric
• Distinguishes between
• common cause variability (random)
• special cause variability (assignable)
• Based on repeated samples from a process
10-39 Quality Control
Empirical Rule
-3� �-1�-2� +1� +2� +3�
68%
95%
99.7%
10-40 Quality Control
Control Charts in General
• Are named according to the statistics being
plotted, i.e., X bar, R, p, and c
• Have a center line that is the overall average
• Have limits above and below the center line
at ± 3 standard deviations (usually)
Center line
Lower Control Limit (LCL)
Upper Control Limit (UCL)
10-41 Quality Control
Variables Data Charts
• Process Centering
• X bar chart
• X bar is a sample mean
• Process Dispersion (consistency)
• R chart
• R is a sample range
n
X
X
n
i
i∑=
=1
)min()max( ii XXR −=
10-42 Quality Control
X bar charts
• Center line is the grand mean (X double bar)
• Points are X bars
xzXUCL σ+=
nx
/σσ =
xzXLCL σ−=
m
X
X
m
j
j∑=
=1
RAXUCL 2+= RAXLCL 2−=
-OR-
10-43 Quality Control
R Charts
• Center line is the grand mean (R bar)
• Points are R
• D3 and D4 values are tabled according to n
(sample size)
RDUCL 4= RDLCL 3=
10-44 Quality Control
Use of X bar & R charts
• Charts are always used in tandem
• Data are collected (20-25 samples)
• Sample statistics are computed
• All data are plotted on the 2 charts
• Charts are examined for randomness
• If random, then limits are used “forever”
10-45 Quality Control
Attribute Charts
• c charts – used to count defects in a constant
sample size
centerlinem
c
c
n
i==
∑=1
czcUCL +=
czcLCL −=
10-46 Quality Control
Attribute Charts
• p charts – used to track a
proportion (fraction)
defective
centerlinenm
x
m
p
p ij
m
j===
∑∑=1
n
ppzpUCL
)1( −+=
n
ppzpLCL
)1( −−=
n
x
p
n
i
i
i
∑=
=1
10-47 Quality Control
Process Capability
The ratio of process variability to design specifications
Upper
Spec
Lower
Spec
Natural data
spread
The natural spread
of the data is 6σ-1σ +2σ-2σ +1σ +3σ-3σ µ
