1. Quality Control Tools for Improving Processes
DAVIS
AQUILANO
CHASE
PowerPoint Presentation by
Charlie
Cook
F O U R T H E D I T I O N
supplement 6
Quality Control Tools for Improving Processes
© The McGraw-Hill Companies, Inc., 2003

2. 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

3. 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

4. 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
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5. Checksheet for Recording Complaints
Exhibit S6.1
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6. Checksheet for Group Sizes in a Restaurant
Exhibit S6.2
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7. Bar Chart of Daily Units Produced
Exhibit S6.3
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8. Histogram of Hole Diameters
Exhibit S6.4
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9. Pareto Chart of Factors in an Emergency Room
Exhibit S6.5
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10. Scatterplot of Customer Satisfaction and Waiting Time in an Upscale Restaurant
Exhibit S6.6
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11. Run Chart of the Number of Daily Errors
Exhibit S6.7
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12. Cause-and-Effect Diagram for Customer Complaints in a Restaurant
Exhibit S6.8
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13. Statistical Analysis of Processes
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.
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14. 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.
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15. Statistical Quality Control Methods
Exhibit S6.9
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16. Sampling Errors Type I (α Error or Producer’s Risk)
Occurs when a sample says parts 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.
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17. Types of Sampling Errors
Exhibit S6.10
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18. 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

19. Attribute Sampling Defining an Attribute Sampling Plan LTPD
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.
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20. Excerpt from a Sampling Plan Table for α = 0.05, β = 0.10
Exhibit S6.11
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21. Operating Characteristic Curves
Operating Characteristic (OC) Curves
Curves that illustrate graphically the probability of accepting lots that contain different percent defectives.
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22. Operating Characteristic Curve for AQL=. 020, α = 0. 05, LTPD= 0
Exhibit S6.12
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23. 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)
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24. Establishing Control Limits for Acceptance Sampling Using Variables
Exhibit S6.13
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25. Determining the Probability of Committing a Type II error (β error)
Exhibit S6.14
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26. 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
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27. Areas Under the Normal Distribution Curve Corresponding to Different Numbers of Standard Deviation from the Mean
Exhibit S6.15
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28. 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.
Exhibit S6.16a
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29. 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.
Exhibit S6.16b
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30. SPC Using Attribute Measurements
Calculating Control Limits
The centerline for an attribute chart is the long-run average for the attribute in question.
p-chart: percent defective chart
Centerline = p
= Long-run average
Standard deviation of sample =
Upper control limit = UCL=
Lower control limit = LCL=
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31. 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
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32. Constructing X-bar Charts
A chart that tracks the changes in the means of the samples by plotting the means that were taken from a process.
Total number of items in the sample
Item number
Mean of the sample = n i X
Total number of samples
Sample number
The average of the means of the samples = m j X
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33. 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 lowest and highest values in that sample.
Total number of samples
Difference between the highest and lowest values in sample j
Average of the measurement differences R for all samples = m Rj R
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34. Exhibit S6.17 Fundamentals of Operations Management 4e
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..
Exhibit S6.17
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35. Exhibit S6.18
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36. Chart R
and X
Exhibit S6.19
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37. A Framework for Applying Different Quality Control Tools
Exhibit S6.20
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38. - Six Sigma Process Capability Cp =
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 -
Lower tolerance limit 6s
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39. 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).
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40. 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.
Exhibit S6.21a
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41. 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.
Exhibit S6.21b
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42. The Goal of Six Sigma Exhibit S6.22
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43. Impact of 1.5 Shift on 3 Process
Exhibit S6.23a
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44. Impact of 1.5 Shift on 6 Process
Exhibit S6.23b
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45. Defect Rates for Different Levels of Sigma () Assuming a 1
Defect Rates for Different Levels of Sigma () Assuming a 1.5 Shift in Actual Mean from Design Mean
Exhibit S6.24
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46. 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.
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47. A Traditional View of the Cost of Variability
Exhibit S6.25
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48. Taguchi’s View of the Cost of Variability
Exhibit S6.26
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49. Why Customers Has to Wait
Exhibit CS6.1
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50. Cause and Effect Diagram
Exhibit CS6.2
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51. Causes of Callers’ Waits
Checklist—Designed to identify the problems
Exhibit CS6.3A
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52. Causes of Callers’ Waits (cont’d)
Reasons Why Callers Had to Wait
Exhibit CS6.3B
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53. Causes of Callers’ Waits (cont’d)
Reasons Why Callers Had to Wait (Pareto Diagram)
Exhibit CS6.3C
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54. Effects of QC Effects of QC (Comparison Before and After QC)
Total number
Daily average
Reasons why callers had to wait
Before
After A
One operator (partner out of the office)
172 15
14.3
1.2 B
Receiving party not present 73 17
6.1
1.4 C
No one present in the section receiving the call 61 20
5.1
1.7 D
Section and name of receiving party not given 19 4
1.6
0.3 E
Inquiry about branch office Locations 16 3
1.3
0.2 F
Others 10
0.8
Total
351 59
29.2
4.8
Period: 12 days from Aug. 17 to 30.
Problems are classified according to cause and presented in order of the amount of time consumed. The are illustrated in a bar graph. 100% indicates the total number of time-consuming calls.
Exhibit CS6.4A
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55. Effects of QC (cont’d) Exhibit CS6.4b
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