Chapter 6S

Report
6
Managing Quality
PowerPoint presentation to accompany
Heizer and Render
Operations Management, 10e
Principles of Operations Management, 8e
PowerPoint slides by Jeff Heyl
1
Outline
 Defining Quality
 Implications of Quality
 Ethics and Quality Management
 Total Quality Management




Continuous Improvement
Six Sigma
Employee Empowerment
TQM in Services
 Statistical Process Control (SPC)
 Control Charts for Variables
 Control Charts for Attributes
 Process Capability
 Process Capability Ratio (Cp)
 Process Capability Index (Cpk )
2
Learning Objectives
1. Define quality and TQM
2. Explain Six Sigma
3. Explain the use of a control chart
4. Build -charts and R-charts
5. Build p-charts
6. Explain process capability and
compute Cp and Cpk
3
Two Ways Quality
Improves Profitability
Sales Gains via
 Improved response
 Flexible pricing
Improved
Quality
 Improved reputation
Reduced Costs via
Increased
Profits
 Increased productivity
 Lower rework and scrap costs
 Lower warranty costs
Figure 6.1
4
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
Different Views
 User-based
 Manufacturing-based
 Product-based
5
Key Dimensions of Quality
 Performance
 Durability
 Features
 Serviceability
 Reliability
 Aesthetics
 Conformance
 Perceived quality
 Value
6
Ethics and Quality
Management
 Operations managers must deliver
healthy, safe, quality products and
services
 Poor quality risks injuries, lawsuits,
recalls, and regulation
 Organizations are judged by how
they respond to problems
 All stakeholders much be
considered
7
Deming’s Fourteen Points
1.
Create consistency of purpose
2.
Lead to promote change
3.
Build quality into the product; stop depending on
inspections
4.
Build long-term relationships based on performance
instead of awarding business on price
5.
Continuously improve product, quality, and service
6.
Start training
7.
Emphasize leadership
Table 6.2
8
Deming’s Fourteen Points
6.
Drive out fear
7.
Break down barriers between departments
8.
Stop haranguing workers
9.
Support, help, and improve
12. Remove barriers to pride in work
13. Institute education and self-improvement
14. Put everyone to work on the transformation
Table 6.2
9
Continuous Improvement
 Represents continual
improvement of all processes
 Involves all operations and work
centers including suppliers and
customers
 People, Equipment, Materials,
Procedures
10
Six Sigma Program 6
A highly structured program developed by Motorola

A discipline – DMAIC
Also,

Statistical definition of a process that is 99.9997%
capable, 3.4 defects per million opportunities (DPMO)
Lower limits
Upper limits
2,700 defects/million
3.4 defects/million
Mean
±3
±6
Figure 6.4
11
Six Sigma
1. Define critical outputs
and identify gaps for
improvement
DMAIC Approach
2. Measure the work and
collect process data
3. Analyze the data
4. Improve the process
5. Control the new process to
make sure new performance
is maintained
12
Employee Empowerment
 Getting employees involved in product
and process improvements
 85% of quality problems are due
to process and material
 Techniques
 Build communication networks
that include employees
 Develop open, supportive supervisors
 Move responsibility to employees
 Build a high-morale organization
 Create formal team structures
13
TQM In Services
 Service quality is more difficult to
measure than the quality of goods
 Service quality perceptions depend
on
 Intangible differences between
products
 Intangible expectations customers
have of those products
14
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
15
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”
16
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
17
Types of Data
Variables
 Characteristics that
can take any real
value
 May be in whole or
in fractional
numbers
 Continuous random
variables
Attributes
 Defect-related
characteristics
 Classify products
as either good or
bad or count
defects
 Categorical or
discrete random
variables
18
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
19
Setting Chart Limits
For x-Charts when we know 
Upper control limit (UCL) = x + zx
Lower control limit (LCL) = x - zx
where
x = mean of the sample means or a target
value set for the process
z = number of normal standard deviations
x = standard deviation of the sample means
= / n
 = population standard deviation
n = sample size
20
Setting Control Limits
Hour 1
Sample
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
=
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 + zx = 16 + 3(1/3) = 17 ozs
LCLx = x - zx = 16 - 3(1/3) = 15 ozs
21
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
22
Setting Chart Limits
For x-Charts when we don’t know 
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
23
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
24
Setting Control Limits
Process average x = 12 ounces
Average range R = .25
Sample size n = 5
25
Setting Control Limits
Process average x = 12 ounces
Average range R = .25
Sample size n = 5
UCLx
= x + A2R
= 12 + (.577)(.25)
= 12 + .144
= 12.144 ounces
From
Table S6.1
26
Setting Control Limits
Process average x = 12 ounces
Average range R = .25
Sample size n = 5
UCLx
LCLx
= x + A2R
= 12 + (.577)(.25)
= 12 + .144
= 12.144 ounces
UCL = 12.144
= x - A2R
= 12 - .144
= 11.857 ounces
LCL = 11.857
Mean = 12
27
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 –
|
|
|
|
|
|
|
|
|
1
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
|
|
|
|
|
|
|
|
3
5
7
9
11
13
15
17
LCL = 0
28
R – Chart
 Type of variables control chart
 Shows sample ranges over time
 Difference between smallest and
largest values in sample
 Monitors process variability
 Independent from process mean
29
Setting Chart Limits
For R-Charts
Upper control limit (UCLR) = D4R
Lower control limit (LCLR) = D3R
where
R = average range of the samples
D3 and D4 = control chart factors from Table S6.1
30
Setting Control Limits
Average range R = 5.3 pounds
Sample size n = 5
From Table S6.1 D4 = 2.115, D3 = 0
UCLR = D4R
= (2.115)(5.3)
= 11.2 pounds
UCL = 11.2
LCLR
LCL = 0
= D3R
= (0)(5.3)
= 0 pounds
Mean = 5.3
31
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
LCL
Figure S6.5
32
Mean and Range Charts
(b)
These
sampling
distributions
result in the
charts below
(Sampling mean
is constant but
dispersion is
increasing)
UCL
(x-chart does not
detect the increase
in dispersion)
x-chart
LCL
UCL
(R-chart detects
increase in
dispersion)
R-chart
LCL
Figure S6.5
33
Control Charts for Attributes
 For variables that are categorical
 Good/bad, yes/no,
acceptable/unacceptable
 Measurement is typically counting
defectives
 Charts may measure
 Percent defective (p-chart)
 Number of defects (c-chart)
34
Control Limits for p-Charts
Population will be a binomial distribution,
but applying the Central Limit Theorem
allows us to assume a normal distribution
for the sample statistics
UCLp = p + zp^
p =
^
LCLp = p - zp^
where
p
z
p^
n
=
=
=
=
p(1 - p)
n
mean fraction defective in the sample
number of standard deviations
standard deviation of the sampling distribution
sample size
35
p-Chart for Data Entry
Sample
Number
1
2
3
4
5
6
7
8
9
10
Number
of Errors
Fraction
Defective
6
5
0
1
4
2
5
3
3
2
.06
.05
.00
.01
.04
.02
.05
.03
.03
.02
80
p = (100)(20) = .04
Sample
Number
Number
of Errors
11
6
12
1
13
8
14
7
15
5
16
4
17
11
18
3
19
0
20
4
Total = 80
p^ =
Fraction
Defective
.06
.01
.08
.07
.05
.04
.11
.03
.00
.04
(.04)(1 - .04)
= .02
100
36
p-Chart for Data Entry
UCLp = p + zp^ = .04 + 3(.02) = .10
Fraction defective
LCLp = p - zp^ = .04 - 3(.02) = 0
.11
.10
.09
.08
.07
.06
.05
.04
.03
.02
.01
.00
–
–
–
–
–
–
–
–
–
–
–
–
UCLp = 0.10
p = 0.04
|
|
|
|
|
|
|
|
|
|
2
4
6
8
10
12
14
16
18
20
LCLp = 0.00
Sample number
37
p-Chart for Data Entry
UCLp = p + zp^ = .04 + 3(.02) = .10
Fraction defective
Possible
LCLp = p - zp^ = .04 - 3(.02) =
0
assignable
causes present
.11
.10
.09
.08
.07
.06
.05
.04
.03
.02
.01
.00
–
–
–
–
–
–
–
–
–
–
–
–
UCLp = 0.10
p = 0.04
|
|
|
|
|
|
|
|
|
|
2
4
6
8
10
12
14
16
18
20
LCLp = 0.00
Sample number
38
Which Control Chart to Use
Variables Data
Using an x-Chart and R-Chart
1. Observations are variables
2. Collect 20 - 25 samples of n = 4, or n = 5, or
more, each from a stable process and compute
the mean for the x-chart and range for the Rchart
3. Track samples of n observations each.
Table S6.3
39
Which Control Chart to Use
Attribute Data
Using the p-Chart
1. Observations are attributes that can be
categorized as good or bad (or pass–fail, or
functional–broken), that is, in two states.
2. We deal with fraction, proportion, or percent
defectives.
3. There are several samples, with many
observations in each. For example, 20 samples
of n = 100 observations in each.
Table S6.3
40
Patterns in Control Charts
UCL
Target
LCL
Normal behavior. Process
is “in control.”
UCL
UCL
Target
LCL
One plot out above (or
below). Process is “out of
control.”
UCL
UCL
Target
LCL
Trends in either direction, 5
plots. Progressive change.
UCL
Target
Target
Target
LCL
LCL
LCL
Two plots very near lower
(or upper) control.
Run of 5 above (or below)
central line.
Erratic behavior.
41
Process Capability
 The natural variation of a process
should be small enough to produce
products that meet the standards
required
 A process in statistical control does not
necessarily meet the design
specifications
 Process capability is a measure of the
relationship between the natural
variation of the process and the design
specifications
42
Process Capability Ratio
Upper Specification - Lower Specification
Cp =
6
 A capable process must have a Cp of at
least 1.0
 Does not look at how well the process
is centered in the specification range
 Often a target value of Cp = 1.33 is used
to allow for off-center processes
 Six Sigma quality requires a Cp = 2.0
43
Process Capability Ratio
Insurance claims process
Process mean x = 210.0 minutes
Process standard deviation  = .516 minutes
Design specification = 210 ± 3 minutes
Upper Specification - Lower Specification
Cp =
6
44
Process Capability Ratio
Insurance claims process
Process mean x = 210.0 minutes
Process standard deviation  = .516 minutes
Design specification = 210 ± 3 minutes
Upper Specification - Lower Specification
Cp =
6
213 - 207
=
= 1.938
6(.516)
45
Process Capability Ratio
Insurance claims process
Process mean x = 210.0 minutes
Process standard deviation  = .516 minutes
Design specification = 210 ± 3 minutes
Upper Specification - Lower Specification
Cp =
6
213 - 207
=
= 1.938
6(.516)
Process is
capable
46
Process Capability Index
Upper
Lower
Cpk = minimum of Specification - x , x - Specification
Limit
Limit
3
3
 A capable process must have a Cpk of at
least 1.0
 A capable process is not necessarily in the
center of the specification, but it falls within
the specification limit at both extremes
47
Process Capability Index
New Cutting Machine
New process mean x = .250 inches
Process standard deviation  = .0005 inches
Upper Specification Limit = .251 inches
Lower Specification Limit = .249 inches
48
Process Capability Index
New Cutting Machine
New process mean x = .250 inches
Process standard deviation  = .0005 inches
Upper Specification Limit = .251 inches
Lower Specification Limit = .249 inches
(.251) - .250
Cpk = minimum of
,
(3).0005
49
Process Capability Index
New Cutting Machine
New process mean x = .250 inches
Process standard deviation  = .0005 inches
Upper Specification Limit = .251 inches
Lower Specification Limit = .249 inches
(.251) - .250
.250 - (.249)
Cpk = minimum of
,
(3).0005
(3).0005
Both calculations result in
.001
Cpk =
= 0.67
.0015
New machine is
NOT capable
50
Interpreting Cpk
Cpk = negative number
Cpk = zero
Cpk = between 0 and 1
Cpk = 1
Cpk > 1
Figure S6.8
51
SPC and Process Variability
Lower
specification
limit
Upper
specification
limit
(a) Acceptance
sampling (Some
bad units accepted)
(b) Statistical process
control (Keep the
process in control)
(c) Cpk >1 (Design
a process that
is in control)
Process mean, m
Figure S6.10
52
In-Class Problems from the
Lecture Guide Practice Problems
Problem 1:
Twenty-five engine mounts are sampled each day and found to have
an average width of 2 inches, with a standard deviation of 0.1 inches.
What are the control limits that include 99.73% of the sample means
 .
53
In-Class Problems from the
Lecture Guide Practice Problems
Problem 2:
Several samples of size have been taken from today’s production of
fence posts. The average post was 3 yards in length and the average
sample range was 0.015 yard. Find the 99.73% upper and lower
control limits.
54
In-Class Problems from the
Lecture Guide Practice Problems
Problem 3:
The average range of a process is 10 lbs. The sample size is 10. Use
Table S6.1 to develop upper and lower control limits on the range.
55
In-Class Problems from the
Lecture Guide Practice Problems
Problem 4:
Based on samples of 20 IRS auditors, each handling 100 files, we
find that the total number of mistakes in handling files is 220. Find the
95.45% upper and lower control limits.
56

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