ISEN 220
Introduction to Production and
Manufacturing Systems
Dr. Gary Gaukler
Quality and Profit
 Profit = Revenue – Cost
 Quality impacts on the revenue
side:
 Quality impacts on the cost side:
6–2
Defining Quality
The totality of features and
characteristics of a product or
service that bears on its ability to
satisfy stated or implied needs
American Society for Quality
3
6–3
Costs of Quality
 Prevention costs - reducing the
potential for defects
 Appraisal costs - evaluating
products, parts, and services
 Internal failure - producing defective
parts or service before delivery
 External costs - defects discovered
after delivery
4
6–4
Costs of Quality
 There is a tradeoff between the
costs of improving quality, and the
costs of poor quality
 Philip Crosby (1979):
“Quality is free”
5
6–5
Inspection
 Involves examining items to see if
an item is good or defective
 Detect a defective product
 Does not correct deficiencies in
process or product
 It is expensive
 Issues
 When to inspect
 Where in process to inspect
6
6–6
Inspection
 Many problems
 Worker fatigue
 Measurement error
 Process variability
 Cannot inspect quality into a
product
 Robust design, empowered
employees, and sound processes
are better solutions
7
6–7
Statistical Process Control
(SPC)
 Uses statistics and control charts to
tell when to take corrective action
 Drives process improvement
 Four key steps
 Measure the process
 When a change is indicated, find the
assignable cause
 Eliminate or incorporate the cause
 Restart the revised process
8
6–8
An SPC Chart
Plots the percent of free throws missed
20%
Upper control limit
10%
Coach’s target value
0%
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1
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2
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3
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4
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5
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6
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7
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8
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9
Lower control limit
Game number
Figure 6.7
9
6–9
Control Charts
Constructed from historical data, the
purpose of control charts is to help
distinguish between natural variations
and variations due to assignable
causes
10
6 – 10
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
11
6 – 11
Natural Variations
 Also called common causes
 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”
12
6 – 12
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
 Eliminate the bad causes
 Incorporate the good causes
13
6 – 13
Samples
To measure the process, we take samples
and analyze the sample statistics following
these steps
Figure S6.1
Frequency
(a) Samples of the
product, say five
boxes of cereal
taken off the filling
machine line, vary
from each other in
weight
Each of these
represents one
sample of five
boxes of cereal
# #
# # #
# # # #
# # # # # # #
#
# # # # # # # # #
Weight
14
6 – 14
Samples
To measure the process, we take samples
and analyze the sample statistics following
these steps
Figure S6.1
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
15
6 – 15
Samples
To measure the process, we take samples
and analyze the sample statistics following
these steps
Frequency
(c) There are many types of distributions, including
the normal (bell-shaped) distribution, but
distributions do differ in terms of central
tendency (mean), standard deviation or
variance, and shape
Figure S6.1
Central tendency
Weight
Variation
Weight
Shape
Weight
16
6 – 16
Samples
(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
Frequency
To measure the process, we take samples
and analyze the sample statistics following
these steps
Prediction
Weight
Figure S6.1
17
6 – 17
Samples
To measure the process, we take samples
and analyze the sample statistics following
these steps
Frequency
(e) If assignable
causes are
present, the
process output is
not stable over
time and is not
predicable
?
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Prediction
Weight
Figure S6.1
18
6 – 18
Central Limit Theorem
Regardless of the distribution of the
population, the distribution of sample means
drawn from the population will tend to follow
a normal curve
1. The mean of the sampling
distribution (x) will be the same
as the population mean m
2. The standard deviation of the
sampling distribution (sx) will
equal the population standard
deviation (s) divided by the
square root of the sample size, n
x=m
sx =
s
n
19
6 – 19
Population and Sampling
Distributions
Three population
distributions
Distribution of
sample means
Mean of sample means = x
Beta
Standard
deviation of
s
the sample = sx = n
means
Normal
Uniform
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-3sx
-2sx
-1sx
x
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+1sx +2sx +3sx
95.45% fall within ± 2sx
99.73% of all x
fall within ± 3sx
Figure S6.3
20
6 – 20
Control Charts for Variables
 For variables that have continuous
dimensions
 Weight, speed, length, strength, etc.
 x-charts are to control the central
tendency of the process
 R-charts are to control the dispersion of
the process
 These two charts must be used together
21
6 – 21
Setting Chart Limits
For x-Charts when we know s
Upper control limit (UCL) = x + zsx
Lower control limit (LCL) = x - zsx
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 standard deviation
n = sample size
22
6 – 22
Setting Control Limits
Hour 1
Box
Weight of
Number
Oat Flakes
1
17
2
13
3
16
4
18
n=9
5
17
6
16
7
15
8
17
9
16
Mean 16.1
s=
1
Hour
1
2
3
4
5
6
Mean
16.1
16.8
15.5
16.5
16.5
16.4
Hour
7
8
9
10
11
12
Mean
15.2
16.4
16.3
14.8
14.2
17.3
For 99.73% control limits, z = 3
UCLx = x + zsx = 16 + 3(1/3) = 17 ozs
LCLx = x - zsx = 16 - 3(1/3) = 15 ozs
23
6 – 23
Setting Control Limits
Control Chart
for sample of
9 boxes
Variation due
to assignable
causes
Out of
control
17 = UCL
Variation due to
natural causes
16 = Mean
15 = LCL
| | | | | | | | | | | |
1 2 3 4 5 6 7 8 9 10 11 12
Sample number
Out of
control
Variation due
to assignable
causes
24
6 – 24
Setting Chart Limits
For x-Charts when we don’t know s
Upper control limit (UCL) = x + A2R
Lower control limit (LCL) = x - A2R
where
R = average range of the samples
A2 = control chart factor found in Table S6.1
x = mean of the sample means
25
6 – 25
Control Chart Factors
Sample Size
n
Mean Factor
A2
Upper Range
D4
Lower Range
D3
2
3
4
5
6
7
8
9
10
12
1.880
1.023
.729
.577
.483
.419
.373
.337
.308
.266
3.268
2.574
2.282
2.115
2.004
1.924
1.864
1.816
1.777
1.716
0
0
0
0
0
0.076
0.136
0.184
0.223
0.284
Table S6.1
26
6 – 26
Setting Control Limits
Process average x = 16.01 ounces
Average range R = .25
Sample size n = 5
27
6 – 27
Setting Control Limits
Process average x = 16.01 ounces
Average range R = .25
Sample size n = 5
UCLx
LCLx
= x + A2R
= 16.01 + (.577)(.25)
= 16.01 + .144
= 16.154 ounces
UCL = 16.154
= x - A2R
= 16.01 - .144
= 15.866 ounces
LCL = 15.866
Mean = 16.01
28
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