Transcript PowerPoint Chapter 6 Supplement

DAVIS
F O U R T H
E D I T I O N
AQUILANO
CHASE
supplement 6
Quality Control Tools for
Improving Processes
© The McGraw-Hill Companies, Inc., 2003
PowerPoint
Presentation
by
Charlie
Cook
Supplement Objectives
• Introduce the different quality control tools that are
used in analyzing and improving the quality of
processes.
• Describe in detail the two major approaches (that is,
acceptance sampling and statistical process control)
in which statistical analysis can be used to improve
process quality.
• Define the two different types of errors that can occur
when statistical sampling is used.
• Distinguish between attributes and variables with
respect to the statistical analysis of processes.
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–2
Supplement Objectives (cont’d)
• Discuss Taguchi methods and how they are different
from traditional statistical quality control methods.
• Describe the quantitative methodology behind six
sigma.
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–3
The Basic Quality Control Tools
• Seven Basic Quality Control (QC) Tools
–Process flowcharts (or diagrams)
–Bar charts and histograms
–Pareto charts
–Scatterplots (or diagrams)
–Run (or trend) charts
–Cause-and-effect (or fishbone) charts
–Statistical process control
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–4
Checksheet for Recording Complaints
Exhibit S6.1
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–5
Checksheet for Group Sizes in a Restaurant
Exhibit S6.2
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–6
Bar Chart of Daily Units Produced
Exhibit S6.3
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–7
Histogram of Hole Diameters
Exhibit S6.4
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–8
Pareto Chart of Factors in an Emergency Room
Exhibit S6.5
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–9
Scatterplot of Customer Satisfaction and
Waiting Time in an Upscale Restaurant
Exhibit S6.6
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–10
Run Chart of the Number of Daily Errors
Exhibit S6.7
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–11
Cause-and-Effect Diagram for
Customer Complaints in a Restaurant
Exhibit S6.8
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–12
Statistical Analysis of Processes
• Statistical Analysis
–Requires less labor (reduces costs)
–Useful when testing destroys products
• Categories of Statistical Tools
–Acceptance sampling
• Assesses the quality of parts or products after they
have been produced.
–Statistical process control
• Assesses whether or not an ongoing process is
performing within established limits.
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–13
Attributes and Variables
• Types of Data
–Attribute data
• Data that count items, such as the number of defective
items in a sample.
–Variable data
• Data that measure of a particular product characteristic
such as length or width.
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–14
Statistical Quality Control Methods
Exhibit S6.9
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–15
Sampling Errors
• Type I (α Error or Producer’s Risk)
–Occurs when a sample says part are bad or the
process is out of control when the opposite is
true.
–The probability of rejecting good parts as scrap.
• Type II (β error or Consumer’s Risk)
–Occurs when a sample says parts are good or
the process is in control when the reverse is
true.
–The probability of a customer getting a bad lot
represented as good.
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–16
Types of Sampling Errors
Exhibit S6.10
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–17
Acceptance Sampling
• Designing a Sampling Plan for Attributes
–Costs to justify inspection
• Costs of not inspecting must exceed costs of
inspecting.
–Purposes of sampling plan
• Find quality or ensure quality is what it is supposed to
be.
–Acceptable quality level (AQL)
• Maximum percentage of defects that a company is
willing to accept.
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–18
Attribute Sampling
• Defining an Attribute Sampling Plan
–N: number of units in the lot
–n: number of units in the sample
–c: the acceptance number (the maximum
number of defectives allowed in the sample
before the whole lot is rejected.
• LTPD
–Lot tolerance percentage defective: the
percentage of defective units that can be in a
single lot.
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–19
Excerpt from a Sampling Plan Table
for α = 0.05, β = 0.10
Exhibit S6.11
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–20
Operating Characteristic Curves
• Operating Characteristic (OC) Curves
–Curves that illustrate graphically the probability
of accepting lots that contain different percent
defectives.
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–21
Operating Characteristic Curve for AQL=.020,
α = 0.05, LTPD= 0.80, β = 0.10
Exhibit S6.12
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–22
Developing a Sampling Plan for Variables
• Control Limits
–Points on an acceptance sampling chart that
distinguish the accept and reject region(s).
–Also, the points on a process control chart that
distinguish between a process being in or out of
control.
• Factors to Consider in Designing a Plan
–The probability of rejecting a good lot (α error)
–The probability of accepting bad lot (β error)
–The size of the sample (n)
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–23
Establishing Control Limits for Acceptance
Sampling Using Variables
Exhibit S6.13
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–24
Determining the Probability of Committing a
Type II error (β error)
Exhibit S6.14
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–25
Statistical Process Control
• Statistical Process Control (SPC)
–A quantitative method for determining whether a
particular process is in or out of control.
• Central Limit Theorem
–Sample means will be normally distributed no
matter what the shape of the distribution.
• Variation
–Random variation
–Nonrandom (assignable) variation
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–26
Areas Under the Normal Distribution Curve
Corresponding to Different Numbers of
Standard Deviation from the Mean
Exhibit S6.15
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–27
Control Chart Evidence for Investigation
Source: Bertrand L. Hansen, Quality Control: Theory and Applications, © 1963, p.
65. Reprinted by permission of Prentice Hall, Inc., Englewood Cliffs, NJ.
Fundamentals of Operations Management 4e
Exhibit S6.16a
© The McGraw-Hill Companies, Inc., 2003
S6–28
Control Chart Evidence for Investigation
(cont’d)
Source: Bertrand L. Hansen, Quality Control: Theory and Applications, © 1963, p.
65. Reprinted by permission of Prentice Hall, Inc., Englewood Cliffs, NJ.
Fundamentals of Operations Management 4e
Exhibit S6.16b
© The McGraw-Hill Companies, Inc., 2003
S6–29
SPC Using Attribute Measurements
• Calculating Control Limits
–The centerline for an attribute chart is the longrun average for the attribute in question.
• p-chart: percent defective chart
Centerline =
p = Long-run average
Standard deviation of sample =
sp 
Upper control limit = UCL=
p  3s p
Lower control limit = UCL=
p  3s p
Fundamentals of Operations Management 4e
p1  p 
n
© The McGraw-Hill Companies, Inc., 2003
S6–30
Variable Measurements Using
X-bar and R Charts
• Variable Data
–Data that are measured, such as length or
weight.
• Main Issues
–Size of Samples
–Number of Samples
–Frequency of Samples
–Control limits
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–31
Constructing X-bar Charts
• X-bar Chart
–A chart that tracks the changes in the means of
the samples by plotting the means that were
taken from a process.
n

X Mean of the sample
Xi

i  Item number
X  i 1

n
Total number of items in the sample
X  The average of the means of the samples
j  Sample number
m  Total number of samples
Fundamentals of Operations Management 4e
n
m
Xj
X
j 1
m
© The McGraw-Hill Companies, Inc., 2003
S6–32
Constructing R Charts
• R Chart
–A chart that tracks the change in the variability
by plotting the range within each sample. The
range is the difference between the lowers and
highest values in that sample.
R  Average of the measurement
differences R for all samples
Rj Difference between the highest
and lowest values in sample j
m  Total number of samples
Fundamentals of Operations Management 4e
m
 Rj
R
j 1
m
© The McGraw-Hill Companies, Inc., 2003
S6–33
Note: All factors based on the normal distribution.
Source: E. L. Grant, Statistical Quality Control, 6th ed. (New York:
McGraw-Hill, 1988). Reprinted by permission of McGraw-Hill, Inc..
Fundamentals of Operations Management 4e
Exhibit S6.17
© The McGraw-Hill Companies, Inc., 2003
S6–34
Exhibit S6.18
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–35
X Chart and
R Chart
Exhibit S6.19
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–36
A Framework for Applying Different
Quality Control Tools
Exhibit S6.20
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–37
Six Sigma
• Process Capability
–A comparison of control chart limits to design
specification limits to determine if the process
itself is (or is not) capable of making products
within design specification (or tolerance) limits.
–Process capability ratio
Cp =
Upper tolerance
limit
Fundamentals of Operations Management 4e
-
Lower tolerance
limit
6s
© The McGraw-Hill Companies, Inc., 2003
S6–38
Six Sigma
• Capability Index
–A calculation to determine how well the process
is performing relative to the target dimensions:
is the process closer to the upper specification
limit (USL) or the lower specification limit (LSL).
–Capability Index
 X  LSL USL  X 
C pk  min 
,

3s 
 3s
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–39
Reducing Process Variance So that All Parts
Are within Specification (Tolerance)*
*Tolerance: The range within which all individual measurements of units produced is desired to fall.
Source: Robert W. Hall, Attaining Manufacturing Excellence: Just-in-Time Manufacturing, Total Quality, Total People
Involvement (Homewood, IL: Dow Jones-Irwin, 1987), p. 66. By permission of The McGraw-Hill Companies.
Fundamentals of Operations Management 4e
Exhibit S6.21a
© The McGraw-Hill Companies, Inc., 2003
S6–40
Reducing Process Variance So that All Parts
Are within Specification (Tolerance)* (cont’d)
*Tolerance: The range within which all individual measurements of units produced is desired to fall.
Source: Robert W. Hall, Attaining Manufacturing Excellence: Just-in-Time Manufacturing, Total Quality, Total People
Involvement (Homewood, IL: Dow Jones-Irwin, 1987), p. 66. By permission of The McGraw-Hill Companies.
Fundamentals of Operations Management 4e
Exhibit S6.21b
© The McGraw-Hill Companies, Inc., 2003
S6–41
The Goal of Six Sigma
Exhibit S6.22
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–42
Impact of 1.5 Shift on 3 Process
Exhibit S6.23a
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–43
Impact of 1.5 Shift on 6 Process
Exhibit S6.23b
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–44
Defect Rates for Different Levels of
Sigma () Assuming a 1.5 Shift in
Actual Mean from Design Mean
Exhibit S6.24
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–45
Taguchi Methods
• Taguchi Methods
–Used for identifying the cause(s) of process
variation that reduces the number of tests that
are necessary.
–Use to conduct experiments to determine the
best combinations of product and process
variables to make a product at the lowest cost
with the highest uniformity.
–Quality loss function
• Relates the cost of quality directly to variation in a
process.
• Any deviation from target quality is a loss to society.
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–46
A Traditional View of the Cost of Variability
Exhibit S6.25
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–47
Taguchi’s View of the Cost of Variability
Exhibit S6.26
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–48
Exhibit CS6.1
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–49
Exhibit CS6.2
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–50
Exhibit CS6.3a
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–51
Exhibit CS6.3b
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–52
Exhibit CS6.3c
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–53
Exhibit CS6.4b
Fundamentals of Operations Management 4e
© The McGraw-Hill Companies, Inc., 2003
S6–54