Student’s Solutions Manual and Study Guide: Chapter 18 Page 1
Chapter 18
Statistical Quality Control
LEARNING OBJECTIVES
Chapter 18 presents basic concepts in quality control, with a particular emphasis on statistical quality control techniques, thereby enabling you to:
1. Explain the meaning of quality in business, compare the approaches to quality improvement by various quality gurus and movements, and compare different approaches to controlling the quality of a product, including benchmarking, just-in-time inventory systems, Six Sigma, lean manufacturing, reengineering, failure mode and effects analysis, poka-yoke, and quality circles.
2. Compare various tools that identify, categorize, and solve problems in the quality improvement process, including flowcharts, Pareto analysis, cause-and-effect diagrams, control charts, check sheets, histograms, and scatter charts.
3. Measure variation among manufactured items using various control charts, including ̄x charts, R charts, p charts, and c charts.
CHAPTER OUTLINE
18.1 Introduction to Quality Control
What is Quality Control?
Total Quality Management
Quality Gurus
Six Sigma
Design for Six Sigma
Lean Manufacturing
Some Important Quality Concepts
Benchmarking
Just-in-Time Inventory Systems
Reengineering
Failure Mode and Effects Analysis (FMEA)
Poka-Yoke
Quality Circles and Six Sigma Teams
18.2 Process Analysis
Flowcharts
Pareto Analysis
Cause-and-Effect (Fishbone) Diagrams
Control Charts
Check Sheets or checklists
Histogram
Scatter Chart or Scatter Diagram
18.3 Control Charts
Variation
Types of Control Charts
Chart
R Charts
p Charts
c Charts
Interpreting Control Charts
KEY TERMS
After-Process Quality Control Pareto Analysis
Benchmarking Pareto Chart
c Chart Poka-Yoke
Cause-and-Effect Diagram Process
Centerline Product Quality
Check Sheet Quality
Control Chart Quality Circle
Design for Six Sigma (DFSS) Quality Control
Failure Mode and Effects Analysis (FMEA) R Chart
Fishbone Diagram Reengineering
Flowchart Scatter Chart
Histogram Six Sigma
In-Process Quality Control Team Building
Ishikawa Diagram Total Quality Management (TQM)
Just-in-Time (JIT) Inventory Systems Transcendent Quality
Lean Manufacturing Upper Control Limit (UCL)
Lower Control Limit (LCL) User Quality
Manufacturing-based Quality Value Quality
p Chart Chart
STUDY QUESTIONS
1. The collection of strategies, techniques, and actions taken by an organization to assure themselves that they are producing a quality product is ______.
2. Measuring product attributes at various intervals throughout the manufacturing process in an effort to pinpoint problem areas is referred to as ______quality control.
3. Inspecting the attributes of a finished product to determine whether the product is acceptable, is in need of rework, or is to be rejected and scrapped is ______quality control.
4. An inventory system in which no extra raw materials or parts are stored for production is called a ______system.
5. When a group of employees are organized as an entity to undertake management tasks and perform other functions such as organizing, developing, and overseeing projects, it is referred to as ______.
6. A ______is a small group of workers, usually from the same department or work area, and their supervisor, who meet regularly to consider quality issues.
7. The complete redesigning of a company's core business process is called ______. This usually involves innovation and is often a complete departure from the company's normal way of doing business.
8. A systematic way for identifying the effects of potential product or process failure
including methodology for eliminating or reducing the chance of a failure occurring is
______.
9. A quality concept that means “mistake proofing” and uses devices, methods, or
inspections in order to avoid machine error or simple human error is ______.
10. A total quality management approach that measures the capability of a process to
perform defect-free work is called ______.
11. A methodology in which a company attempts to develop and establish total quality management from product to process by examining and emulating the best practices and techniques used in their industry is called ______.
12. A quality scheme that places an emphasis on designing the product or process right the first time is ______.
13. A quality management philosophy that focuses on the reduction of wastes and the
elimination of unnecessary steps in an operation or process is ______.
14. A graphical method for evaluating whether a process is or is not in a state of statistical control is called a ______.
15. A diagram that is shaped like a fish and displays potential causes of one problem is called a ______or ______diagram.
16. A bar chart that displays a quantitative tallying of the numbers and types of defects that occur with a product is called a ______.
17. Two types of control charts for measurements are the ______chart and the
______chart. Two types of control charts for attribute compliance are the
______chart and the ______chart.
18. An x bar chart is constructed by graphing the ______of a given
measurement computed for a series of small samples on a product over a period of
time.
19. An R chart plots the sample ______. The centerline of an R chart is
equal to the value of ______.
20. A p chart graphs the proportion of sample items in ______
for multiple samples. The centerline of a p chart is equal to ______.
21. A c chart displays the number of ______per item or unit.
22. Normally, an x bar chart is constructed from 20 to 30 samples. However, assume
that an x bar chart can be constructed using the four samples of five items shown
below:
Sample 1 Sample 2 Sample 3 Sample 4
23 21 19 22
22 18 20 24
21 22 20 18
23 19 21 16
22 19 20 17
The value of A2 for this control chart is ______.
The centerline value is ______.
The value of is ______.
The value of UCL is ______.
The value of LCL is ______.
The following samples have means that fall outside the outer control limits
______. In constructing an R chart from these data, the
value of the centerline is ______. The value of D3 is
______and the value of D4 is ______. The UCL of the R
chart is ______and the value of LCL is ______.
The following samples have ranges that fall outside the outer control limits
______.
23. p charts should be constructed from data gathered from 20 to 30 samples. Suppose,
however, that a p chart could be constructed from the data shown below:
Sample n Number out of Compliance
1 70 3
2 70 5
3 70 0
4 70 4
5 70 3
6 70 6
The value of the centerline is ______.
The UCL for this p chart is ______.
The LCL for this p chart is ______.
The samples with sample proportions falling outside the outer control limits are
______.
24. c charts should be constructed using at least 25 items or units. Suppose, however,
that a c chart could be constructed from the data shown below:
Item Number of
Number Nonconformities
1 3
2 2
3 2
4 4
5 0
6 3
7 1
The value of the centerline for this c chart is ______.
The value of UCL is ______and the value of
LCL is ______.
25. A process is considered to be out of control if ______or more consecutive
points occur on one side of the centerline of the control chart.
26. Four possible causes of control chart abnormalities are (at least eight are mentioned
in the text) ______, ______, ______, and
______.
ANSWERS TO STUDY QUESTIONS
1. Quality Control 16. Pareto Chart
2. In-Process 17. , R, p, c
3. After-Process 18. Means
4. Just-in-Time 19. Ranges,
5. Team Building 20. Noncompliance, p (average
proportion)
6. Quality Circle
21. Nonconformances
7. Reengineering
22. 0.577, 20.35, 4.0, 22.658, 18.042,
8. FMEA None, 4.0, 0, 2.115, 8.46, 0.00, None
9. Poka-Yoke 23. .05, .128, .000, None
10. Six Sigma 24. 2.143, 6.535, 0.00
11. Benchmarking 25. 8
12. Design for Six Sigma 26. Changes in the Physical Environment,
Worker Fatigue, Worn Tools, Changes
13. Lean Manufacturing in Operators or Machines,
Maintenance, Changes in Worker
14. Control Chart Skills, Changes in Materials, Process
Modification
15. Fishbone, Ishikawa
SOLUTIONS TO PROBLEMS IN CHAPTER 18
18.5 = 4.55, = 4.10, = 4.80, = 4.70,
= 4.30, = 4.73, = 4.38
R1 = 1.3, R2 = 1.0, R3 = 1.3, R4 = 0.2, R5 = 1.1, R6 = 0.8, R7 = 0.6
= 4.51 = 0.90
For Chart: Since n = 4, A2 = 0.729
Centerline: = 4.51
UCL: + A2 = 4.51 + (0.729)(0.90) = 5.16
LCL: - A2 = 4.51 – (0.729)(0.90) = 3.85
For R Chart: Since n = 4, D3 = 0 D4 = 2.282
Centerline: = 0.90
UCL: D4 = (2.282)(0.90) = 2.05
LCL: D3 = 0
Chart:
R Chart:
18.7 = .025, = .000, = .025, = .075,
= .050, = .125, = .050
= .050
Centerline: = .050
UCL: .05 + 3 = .05 + .1034 = .1534
LCL: .05 - 3 = .05 - .1034 ~ .000
p Chart:
The proportion for sample 2 is very close to the lower quality control limit.
18.9 = = 1.344
Centerline: = 1.344
UCL: = 1.344 + 3 =
1.344 + 3.478 = 4.822
LCL: = 1.344 - 3 =
1.344 - 3.478 ~ 0.000
c Chart:
None of the points are beyond the control limits. However, some
points are close to LCL.
18.11 While there are no points outside the limits, the first chart exhibits some
problems. The chart ends with 9 consecutive points below the centerline.
Of these 9 consecutive points, there are at least 4 out of 5 in the outer 2/3 of the lower region. The second control chart contains no points outside the control limits. However, near the end, there are 8 consecutive points above the centerline. The p chart contains no points outside the upper control limit. Three times, the chart contains two out of three points in the outer third. However, this occurs in the lower third where the proportion of noncompliance items approaches zero and is probably not a problem to be concerned about. Overall, this seems to display a process that is in control. One concern might be the wide swings in the proportions at samples 15, 16 and 22 and 23.
18.13
Problem / Frequency / % of Total / Cumulative %1 / 673 / 27.0 / 27.0
6 / 564 / 22.6 / 49.6
8 / 402 / 16.1 / 65.7
4 / 379 / 15.2 / 80.9
10 / 202 / 8.1 / 89.0
3 / 108 / 4.3 / 93.3
5 / 73 / 2.9 / 96.2
9 / 54 / 2.2 / 98.4
2 / 29 / 1.2 / 99.6
7 / 12 / 0.5 / 100
Total / 2,496 / 100
18.15 = .06, = .22, = .14, = .04, = .10,
= .16, = .00, = .18, = .02, = .12
= .104
Centerline: = .104
UCL: .104 + 3 = .104 + .130 = .234
LCL: .104 - 3 = .104 - .130 ~ .000
p Chart:
18.17 = = 2.139
Centerline: = 2.139
The centreline is the average of the numbers of nonconformances for all
sheets.
UCL: = 2.139 + 3 = 2.139 + 4.388 = 6.527
LCL: = 2.139 - 3 = 2.139 – 4.388 ~ .00000
c Chart:
18.19 = 14.993, = 15.000, = 14.978, = 14.990,
= 15.013, = 15.000, = 15.017, = 14.997,
R1 = .03, R2 = .07, R3 = .05, R4 = .05,
R5 = .04, R6 = .05, R7 = .05, R8 = .06
= 14.999 = 0.05
For Chart: Since n = 6, A2 = .483
Centerline: = 14.999
UCL: + A2 = 14.999 + .483(.05) =
14.999 + .024 = 15.023
LCL: - A2 = 14.999 - .483(.05) =
14.999 - .024 = 14.975
For R Chart: Since n = 6, D3 = 0 D4 = 2.004
Centerline: = .05
UCL: D4 = 2.004(.05) = .100
LCL: D3 = 0(.05) = .000
Two out of three consecutive points on the chart are in the outer one
third.
18.21 = = 0.640
Centerline: = 0.640
UCL: = 0.640 + 3 = 0.640 + 2.400 = 3.040
LCL: = 0.640 - 3 = 0.640 – 2.400 ~ .000
c Chart:
None of the points are beyond the control limits, but three consecutive points
(bottle number = 14, 15, 16) are close to LCL.
18.23 = .050, = .000, = .150, = .075,
= .025, = .025, = .125, = .000,
= .100, = .075, = .050, = .050,
= .150, = .025, = .000
= .06
Centerline: = .060
UCL: .060 + 3 = .060 + .113= .173
LCL: .060 - 3 = .060 - .113 ~ .000
p Chart:
Twice two out of three consecutive values fall in the outer one third.
18.25 The following list provides summary of the control chart abnormalities that should be of concern to a statistical process controller:
· Range of the sample 25 is above UCL.
· Near the beginning of the chart there are nine consecutive sample ranges below the centerline.
· Near the end of the chart there are nine consecutive sample ranges above the centerline.
The controller might want to determine if there is some systematic reason why there is a string of ranges below the centerline and, perhaps more importantly, why there are a string of ranges above the centerline.
18.27 The centerline of the c chart indicates that the process is averaging 0.7400 nonconformances per part. Twenty-five of the fifty sampled items have zero nonconformances. None of the samples exceed the upper control limit for nonconformances. However, the upper control limit is 3.321 nonconformances which, in and of itself, may be too many. Indeed, three of the fifty (6%) samples actually had three nonconformances. An additional six samples (12%) had two nonconformances. One matter of concern may be that there is a run of ten samples in which nine of the samples exceed the centerline (samples 12 through 21). The question raised by this phenomenon is whether or not there is a systematic flaw in the process that produces strings of nonconforming items.