This document provides an introduction to quality management and statistical process control. It outlines Deming's 14 points and Juran's 10 steps for quality improvement and discusses the basic seven quality tools. The document then explains different types of statistical process control charts, including x-bar and R charts for variable data and p-charts for attribute data. It describes how to construct these charts and interpret them to determine whether a process is in or out of control. The goal is to identify special causes of variation and take steps to eliminate them.

1. 1
Introduction to Quality and
Statistical Process Control

2. 2
Chapter Goals
After completing this chapter, you should be
able to:
 Use the seven basic tools of quality
 Construct and interpret x-bar and R-charts
 Construct and interpret p-charts
 Construct and interpret c-charts

3. 3
Chapter Overview
Quality Management and
Tools for Improvement
Deming’s 14
Points
Juran’s 10
Steps to
Quality
Improvement
The Basic
7 Tools
Philosophy of
Quality
Tools for Quality
Improvement
Control
Charts
X-bar/R-charts
p-charts
c-charts

4. 4
Themes of Quality Management
 Primary focus is on process improvement
 Most variations in process are due to systems
 Teamwork is integral to quality management
 Customer satisfaction is a primary goal
 Organization transformation is necessary
 It is important to remove fear
 Higher quality costs less

5. 5
 1. Create a constancy of purpose toward
improvement
 become more competitive, stay in business, and provide jobs
 2. Adopt the new philosophy
 Better to improve now than to react to problems later
 3. Stop depending on inspection to achieve
quality -- build in quality from the start
 Inspection to find defects at the end of production is too late
 4. Stop awarding contracts on the basis of low
bids
 Better to build long-run purchaser/supplier relationships
Deming’s 14 Points

6. 6
 5. Improve the system continuously to
improve quality and thus constantly reduce
costs
 6. Institute training on the job
 Workers and managers must know the difference between common
cause and special cause variation
 7. Institute leadership
 Know the difference between leadership and supervision
 8. Drive out fear so that everyone may work
effectively.
(continued)
Deming’s 14 Points

7. 7
 10. Eliminate slogans and targets for the
workforce
 They can create adversarial relationships
 11. Eliminate quotas and management by
objectives
 12. Remove barriers to pride of workmanship
 13. Institute a vigorous program of education
and self-improvement
 14. Make the transformation everyone’s job
(continued)
Deming’s 14 Points

8. 8
Juran’s 10 Steps to Quality
Improvement
 1. Build awareness of both the need for
improvement and the opportunity for
improvement
 2. Set goals for improvement
 3. Organize to meet the goals that have been
set
 4. Provide training
 5. Implement projects aimed at solving
problems

9. 9
Juran’s 10 Steps to Quality
Improvement
 6. Report progress
 7. Give recognition
 8. Communicate the results
 9. Keep score
 10. Maintain momentum by building
improvement into the company’s regular
systems
(continued)

10. 10
The Deming Cycle
The
Deming
Cycle
The key is a
continuous
cycle of
improvement
Act
Plan
Do
Study

11. 11
The Basic 7 Tools
1. Process Flowcharts
2. Brainstorming
3. Fishbone Diagram
4. Histogram
5. Trend Charts
6. Scatter Plots
7. Statistical Process Control Charts

12. 12
The Basic 7 Tools
1. Process Flowcharts
2. Brainstorming
3. Fishbone Diagram
4. Histogram
5. Trend Charts
6. Scatter Plots
7. Statistical Process Control Charts
Map out the process to better
visualize and understand
opportunities for improvement
(continued)

13. 13
The Basic 7 Tools
1. Process Flowcharts
2. Brainstorming
3. Fishbone Diagram
4. Histogram
5. Trend Charts
6. Scatter Plots
7. Statistical Process Control Charts
Cause 4
Cause 3
Cause 2
Cause 1
Problem
Fishbone (cause-and-effect) diagram:
Sub-causes
Sub-causes
Show patterns of variation
(continued)

14. 14
The Basic 7 Tools
1. Process Flowcharts
2. Brainstorming
3. Fishbone Diagram
4. Histogram
5. Trend Charts
6. Scatter Plots
7. Statistical Process Control Charts
time
y
x
y
Identify trend
Examine relationships
(continued)

15. 15
The Basic 7 Tools
1. Process Flowcharts
2. Brainstorming
3. Fishbone Diagram
4. Histogram
5. Trend Charts
6. Scatter Plots
7. Statistical Process Control Charts
X
Examine the performance
of a process over time
time
(continued)

16. 16
Introduction to Control Charts
 Control Charts are used to monitor variation in
a measured value from a process
 Exhibits trend
 Can make correction before process is out of
control
 A process is a repeatable series of steps leading
to a specific goal
 Inherent variation refers to process variation
that exists naturally. This variation can be
reduced but not eliminated

17. 17
Process Variation
Total Process
Variation
Common Cause
Variation
Special Cause
Variation
= +
Variation is natural; inherent in the world
around us
No two products or service experiences are
exactly the same
With a fine enough gauge, all things can be
seen to differ

18. 18
Sources of Variation
Total Process
Variation
Common Cause
Variation
Special Cause
Variation
= +
People
Machines
Materials
Methods
Measurement
Environment
Variation is often due to differences in:

19. 19
Common Cause Variation
Total Process
Variation
Common Cause
Variation
Special Cause
Variation
= +
Common cause variation
naturally occurring and expected
the result of normal variation in materials,
tools, machines, operators, and the
environment

20. 20
Special Cause Variation
Total Process
Variation
Common Cause
Variation
Special Cause
Variation
= +
Special cause variation
abnormal or unexpected variation
has an assignable cause
variation beyond what is considered
inherent to the process

21. 21
Statistical Process Control Charts
 Show when changes in data are due to:
 Special or assignable causes
 Fluctuations not inherent to a process
 Represents problems to be corrected
 Data outside control limits or trend
 Common causes or chance
 Inherent random variations
 Consist of numerous small causes of random variability

22. 22
Process Average
Control Chart Basics
UCL = Process Average + 3 Standard Deviations
LCL = Process Average – 3 Standard Deviations
UCL
LCL
+3σ
-3σ
Common Cause
Variation: range of
expected variability
Special Cause Variation:
Range of unexpected variability
time

23. 23
Process Average
Process Variability
UCL = Process Average + 3 Standard Deviations
LCL = Process Average – 3 Standard Deviations
UCL
LCL
±3σ → 99.7% of
process values
should be in this
range
time
Special Cause of Variation:
A measurement this far from the process average
is very unlikely if only expected variation is present

24. 24
Statistical Process Control Charts
Statistical
Process Control
Charts
X-bar charts
and R-charts
c-charts
Used for
measured
numeric data
Used for
proportions
(attribute data)
Used for
number of
attributes per
sampling unit
p-charts

25. 25
x-bar chart and R-chart
 Used for measured numeric data from a
process
 Start with at least 20 subgroups of observed
values
 Subgroups usually contain 3 to 6 observations
each

26. 26
Steps to create an x-chart
and an R-chart
 Calculate subgroup means and ranges
 Compute the average of the subgroup means
and the average range value
 Prepare graphs of the subgroup means and
ranges as a line chart

27. 27
Steps to create an x-chart
and an R-chart
 Compute the upper and lower control limits
for the x-bar chart
 Compute the upper and lower control limits
for the R-chart
 Use lines to show the control limits on the x-
bar and R-charts
(continued)

28. 28
Example: x-chart
 Process measurements:
Subgroup measures
Subgroup
number
Individual measurements Mean, x Range, R
1
2
3
…
15
12
17
…
17
16
21
…
15
9
18
…
11
15
20
…
14.5
13.0
19.0
…
6
7
4
…
Average
subgroup mean
= x
Average
subgroup range
= R

29. 29
Average of Subgroup
Means and Ranges
k
x
x i


k
R
R i


Average of
subgroup means:
where:
xi = ith subgroup average
k = number of subgroups
Average of
subgroup ranges:
where:
Ri = ith subgroup range
k = number of subgroups

30. 30
Computing Control Limits
 The upper and lower control limits for an x-
chart are generally defined as
 or
UCL = Process Average + 3 Standard Deviations
LCL = Process Average – 3 Standard Deviations






3
3
x
LCL
x
UCL

31. 31
Computing Control Limits
 Since control charts were developed before it
was easy to calculate σ, the interval was
formed using R instead
 The value A2R is used to estimate 3σ , where
A2 is from Appendix Q
 The upper and lower control limits are
)
R
(
A
x
LCL
)
R
(
A
x
UCL
2
2




(continued)
where A2 = Shewhart
factor for subgroup size
n from appendix Q

32. 32
Example: R-chart
The upper and lower control limits for an
R-chart are
)
R
(
D
LCL
)
R
(
D
UCL
3
4


where:
D4 and D3 are taken from the Shewhart table
(appendix Q) for subgroup size = n

33. 33
x-chart and R-chart
UCL
LCL
time
x
UCL
LCL
time
R
R-chart
x-chart

34. 34
Using Control Charts
 Control Charts are used to check for process
control
H0: The process is in control
i.e., variation is only due to common causes
HA: The process is out of control
i.e., special cause variation exists
 If the process is found to be out of control,
steps should be taken to find and eliminate the
special causes of variation

35. 35
Process In Control
 Process in control: points are randomly
distributed around the center line and all
points are within the control limits
UCL
LCL
x
x
time

36. 36
Process Not in Control
Out of control conditions:
 One or more points outside control limits
 Nine or more points in a row on one side of
the center line
 Six or more points moving in the same
direction
 14 or more points alternating above and below
the center line

37. 37
Process Not in Control
 One or more points outside control limits
UCL
LCL
x
Nine or more points in a row on one
side of the center line
UCL
LCL
x
Six or more points moving in the
same direction
UCL
LCL
x
14 or more points alternating above
and below the center line
UCL
LCL
x

38. 38
Out-of-control Processes
 When the control chart indicates an out-of-
control condition (a point outside the control
limits or exhibiting trend, for example)
 Contains both common causes of variation and
assignable causes of variation
 The assignable causes of variation must be
identified
 If detrimental to the quality, assignable causes of
variation must be removed
 If increases quality, assignable causes must be
incorporated into the process design

39. 39
p-Chart
 Control chart for proportions
 Is an attribute chart
 Shows proportion of nonconforming items
 Example -- Computer chips: Count the number of
defective chips and divide by total chips inspected
 Chip is either defective or not defective
 Finding a defective chip can be classified a “success”

40. 40
p-Chart
 Used with equal or unequal sample sizes
(subgroups) over time
 Unequal sizes should not differ by more than
±25% from average sample sizes
 Easier to develop with equal sample sizes
 Should have np > 5 and n(1-p) > 5
(continued)

41. 41
Creating a p-Chart
 Calculate subgroup proportions
 Compute the average of the subgroup
proportions
 Prepare graphs of the subgroup proportions as
a line chart
 Compute the upper and lower control limits
 Use lines to show the control limits on the p-
chart

42. 42
p-Chart Example
Subgroup
number
Sample
size
Number of
successes
Proportion, p
1
2
3
…
150
150
150
15
12
17
…
10.00
8.00
11.33
…
Average subgroup
proportion = p

43. 43
Average of Subgroup Proportions
The average of subgroup proportions = p
where:
pi = sample proportion for subgroup i
k = number of subgroups of size n
where:
ni = number of items in sample i
ni = total number of items
sampled in k samples
If equal sample sizes: If unequal sample sizes:
k
p
p i





i
i
i
n
p
n
p

44. 44
Computing Control Limits
 The upper and lower control limits for an p-
chart are
 or
UCL = Average Proportion + 3 Standard Deviations
LCL = Average Proportion – 3 Standard Deviations






3
3
p
LCL
p
UCL

45. 45
Standard Deviation of
Subgroup Proportions
The estimate of the standard deviation for
the subgroup proportions is
n
)
p
)(1
p
(
sp


If equal sample sizes: If unequal sample sizes:
where:
= mean subgroup proportion
n = common sample size
p
Generally, is
computed separately
for each different
sample size
p
s

46. 46
Computing Control Limits
 The upper and lower control limits for the p-
chart are
(continued)
n
)
p
)(1
p
(
p
LCL
n
)
p
)(1
p
(
p
UCL






3
3
)
s
(
p
LCL
)
s
(
p
UCL
p
p
3
3




If sample sizes are
equal, this becomes
Proportions are
never negative, so
if the calculated
lower control limit
is negative, set
LCL = 0

47. 47
p-Chart Examples
 For equal sample sizes For unequal
sample sizes
UCL
LCL
UCL
LCL
p p
p
s is constant since
n is the same for
all subgroups
p
s varies for each
subgroup since
ni varies

48. 48
c-Chart
 Control chart for number of nonconformities
(occurrences) per sampling unit (an area of
opportunity)
 Also a type of attribute chart
 Shows total number of nonconforming items
per unit
 examples: number of flaws per pane of glass
number of errors per page of code
 Assume that the size of each sampling unit
remains constant

49. 49
Mean and Standard Deviation
for a c-Chart
 The mean for a c-chart is
k
x
c i


The standard deviation
for a c-chart is
c
s 
where:
xi = number of successes per sampling unit
k = number of sampling units

50. 50
c-Chart Control Limits
c
c
LCL
c
c
UCL
3
3




The control limits for a c-chart are

51. 51
Process Control
Determine process control for p-chars and c-
charts using the same rules as for x-bar and R-
charts
Out of control conditions:
 One or more points outside control limits
 Nine or more points in a row on one side of the center line
 Six or more points moving in the same direction
 14 or more points alternating above and below the center line

52. 52
c-Chart Example
 A weaving machine makes cloth in a standard
width. Random samples of 10 meters of cloth
are examined for flaws. Is the process in
control?
Sample number 1 2 3 4 5 6 7
Flaws found 2 1 3 0 5 1 0

53. 53
Constructing the c-Chart
 The mean and standard deviation are:
1.714
7
0
1
5
0
3
1
2
k
x
c i










1.309
1.7143
c
s 


2.2
3(1.309
1.7143
c
3
c
LCL
5.64
3(1.309
1.7143
c
3
c
UCL











The control limits are:
Note: LCL < 0 so set LCL = 0

54. 54
The completed c-Chart
The process is in control. Individual points are distributed around the center
line without any pattern. Any improvement in the process must come
from reduction in common-cause variation
UCL = 5.642
LCL = 0
Sample number
1 2 3 4 5 6 7
c = 1.714
6
5
4
3
2
1
0