SMU
EMIS 7364
NTU
TO-570-N
Statistical Quality Control
Dr. Jerrell T. Stracener,
SAE Fellow
Statistical Process Control
Concepts, Tools and Six Sigma
Updated: 1/14/04
1
Statistical Process Control - Definition
The application of statistical techniques
is to understand and analyze the variation in a
process.
- Joseph Juran
Quality Control Handbook
2
Statistical Process Control History
1920’s
Original techniques developed by Bell
Telephone Labs’ Dr. Walter Shewhart
- Statistical control
- Control charts
- Random (common) versus special
(assignable) causes of variation
1930’s
While Dr. W. Edwards Deming is at
Department of Agriculture, he meets
and studies with Shewhart
1940’s
Deming tapped to perform census, the
first using sampling
3
Statistical Process Control
1942
At request of Stanford University
professor, outlines proposal for teaching
statistical quality control to engineers,
inspectors, and others at companies in
wartime production
- Taught to over 31,000 people
- Led to formation of American Society
for Quality Control
1946 to
1949
Unparalleled demand for goods
No competition
4
Statistical Process Control
1946 to
1949
“Scientific Management” in full bloom
- Developed by Frederick Winslow Taylor
- Minimize complexity to maximize
efficiency (idiot proof
- Resulted in removing power from lower
levels (workers, supervisors)
- Led to top heavy, overly-powerful
management and modern corporate
structure.
5
Statistical Process Control
1946 to
1949
Quality took back seat to production - get
the numbers out
- Shifted to end-of-the-line inspection,
rework, etc.
By 1949 Deming notes: “No control
charts left, not even smoke.”
Management didn’t want workers to
apply the techniques, so they didn’t.
1947
Deming recruited by MacArthur to do
1951 Japanese census
6
Statistical Process Control
1947
Deming works and teaches eager
Japanese managers and workers
Shewhart’s methods
1951
Japanese had established Deming Prize
1980
America rediscovers quality
7
Statistical Process Control (SPC)
• SPC is a powerful collection of problem-solving
tools useful in achieving process stability and
improving capability through the reduction of
variability.
• SPC can be applied to any process
• Seven
1.
2.
3.
4.
5.
6.
7.
major tools
Histogram or stem and leaf display
Check sheet
Pareto chart
Cause and effect diagram
Defect concentration diagram
Scatter diagram
Control chart
8
Statistical Process Control Tools
• Control charts
• Histograms
• Process capability indices
• Process capability studies
• Process flow diagram
• Cause and effect diagram
• Pareto diagram
• Scatter diagram
9
Statistical Process Control
Causes of Variation
Assignable (special) - Intermittent sources
of variation that are unpredictable. Signaled
by violation of Western Electric rules
Common (natural) - Sources of variation
always present affecting all output from a
process
Only management can affect common causes of
variation
10
Statistical Process Control - Control Charts
Interpretation based on Western Electric rules
1. Analyze the chart by separating it into equal zones
above and below the centerline
A
B
C
C
B
A
UCL
Centerline
LCL
11
Statistical Process Control- Control Charts
2. A process is out of statistical control if:
(a) any point is above or below the control limits
(b) two out of three points in a row in zone A
or above
(c) four out of five points in a row in zone B
or above
(d) eight in a row in zone C or above
12
Statistical Process Control- Control Charts
• In general specification limits should not be on
control charts
• Data must be displayed in time sequence
• Management controls the natural variation between
the control limits
• Do not tweak the process
13
Statistical Process Control - Control Charts
Questions to Ask
• Is variable’s data on the product or process?
• Are the operators seeing this data?
• How long has control chart had this appearance?
• Do the operators know what to do when out-ofcontrol conditions occur?
14
Statistical Process Control - Control Charts
If out-of-control
Are there differences in the measurement accuracy
of instruments used?
Are there differences in the methods used by
different operators?
Is process affected by environment?
Is process affected by tool wear? machine calibration?
Has there been a change in raw materials used?
15
Statistical Process Control - Control Charts
If out-of-control
Did data come from different machines? shifts?
operators?
Are operators afraid to report bad news?
16
Statistical Process Control - Control Charts
x
UCL
x
x
x
x
x
x
x
x
x
x
CL
x
x
x
LCL
•
•
•
•
Helps reduce variability
Monitors performance over time
Allows process corrections to prevent rejections
Trends and out-of-control conditions are
immediately detected
17
Statistical Process Control - Histograms
Histograms
• Used to display data to discover distribution
• Used with variables data
• Data are grouped into cells for display
• Reveals amount of variation in measurements
(product/process)
• Reveals centering of measurements
• Include specification limits to check for capability
• Include process (production) limits
18
Statistical Process Control - Histograms
Histograms - Questions to ask
• What is the shape of distribution?
• What would you expect shape to be?
• If computer generated, is data really normal?
• Is variation acceptable?
• Is the centering acceptable?
• Did you generate a histogram with and without
outlier points?
• Did you include specification limits and process
limits on the histogram?
19
Statistical Process Control - Histograms
LSL
USL
• The shape shows the nature of the distribution
of the data
• The central tendency (average) and variability
are easily seen
• Specification limits can be used to display the
capability of the process
20
Statistical Process Control - Histograms
Possible answers for a Cliff-like histogram
• Hiding data that should be outside the specification
• Supplier is screening the product before shipment
• Lower specification is a physical limit like zero
thickness, but this is not normally the case
lower spec
upper spec
21
Statistical Process Control - Histograms
Possible answers for a Bimodal histogram
• Two primary sources of process variation
• The process is stable, but it has experienced
a large shift during the time the data were collected
lower spec
upper spec
22
Statistical Process Control - Histograms
Possible answers for a Comb-like histogram
• Insufficient data collected
• Too many classes displayed
• Process is unstable
• Process is stable but is multimodal
lower spec
upper spec
23
Statistical Process Control - Histograms
Possible answers for a Skewed histogram
• May be the natural result of the process
• For a machined part, the equipment may be losing
tolerance or tools may be wearing out
• The process is shifting slowly to the side with the
long tail
lower spec
upper spec
24
Statistical Process Control - Histograms
By including specification limits on a histogram, the
amount of data that falls outside of the specification
limits can be easily seen
specification
frequency
lower spec
upper spec
25
Process Capability Measures or Indices
Process capability indices are used to measure the
process variability due to common causes present
in the process
• The Cp index
Inherent or potential measure of capability
Cp = specification spread
process spread
• The CpK index
Realized or actual measure of capability
• Other indices
CpM, CpMK
26
Statistical Process Control
ppm = parts per million
Interpretation
CpK < 1
= process not capable
1  CpK < 1.5
= process capable, monitor
frequently
CpK  1.5
= process capable, monitor
infrequently
Pareto CpK’s to attack worst problems
Can only convert CpK, Cp to ppm if distribution normal
27
Statistical Process Control
Use Z-scores and standard normal table for this
calculation
Must be based on ‘first pass’ data collected over
normal operating cycle of process
28
Statistical Process Control
Questions to ask
• Was this data collected over a short or long period
of time?
• Was the collection of data structured?
• Did you construct a histogram?
• Is your data normal?
• If repeating the calculation, did your CpK improve?
• What is Cp compared to CpK?
29
Statistical Process Control
Process capability studies
• Determines the centering of the process
• Determines the variation of the process
• Puts stake in the ground to measure future
improvement
• Short term study provides snapshot of capability
• It is not the true process capability
• Long term study (over normal operating cycle of
the process) provides true process capability CpK
30
Statistical Process Control
Impact of special causes on process capability
process
stable
process
unstable
time
time
31
Statistical Process Control
Difference between process capability and process
control
process
control
time
out of control
size
32
Statistical Process Control
Difference between process capability and process
control
process
capability
time
in control
but not capable
size
33
Statistical Process Control
Process Capability Studies - Questions to ask
• Were adequate records maintained?
• Is this data a result of a short or long study?
• What is the centering of the process?
• How does it relate to the center of the spec?
• What is the variation of the process?
• How does the process spread compare to the spec?
• What actions have been taken as a result of this
study?
• When will another study by conducted to verify that
improvements have been made?
34
Statistical Process Flow Diagram
Process Flow Diagram
• Used to detail the actual steps of a process
• Allows understanding of points where problems arise
• Ensures feedback mechanisms in place
• Shows relationship between process steps
• Must be designed by those involved in process, not
by outsiders
35
Statistical Process Flow Diagram
Questions to ask
• Is this the correct level of detail?
• Do we agree on all blocks?
• Is process unnecessarily complicated?
• Do all loops have an exit?
• Have we captured every step?
36
Statistical Process Flow Diagram
• Expresses detailed knowledge of the process
• Identifies process flow and interaction among
the process steps
• Identifies potential control points
37
Statistical Process Control - Cause & Effect Diagram
Cause and effect diagram
• Used to identify and explore all possible causes for
a problem
• Also called fishbone or Ishikawa diagram
• Should be generated by team
• Use as many categories as needed for causes
• Once generated must discover which ‘cause’ impacts
the effect
• Combine with process flow diagram to form cause
and effect flow diagram
• Best used early in problem solving success
38
Statistical Process Control Cause & Effect (Fishbone) Diagram
Materials
Machines
Measurements
Causes
Effect
Man
Methods
Other Factors
• All contributing factors and their relationship are
displayed
• Identifies problem area where data can be
collected and analyzed
39
Statistical Process Control
Questions to ask
• Have you at least covered the 6 M’s
materials
manpower
machines
measurements
methodology
mother nature
• Has ever one who impacts the process had input?
• How did you prioritize causes to begin to attack?
• What have you done to mistake proof the process?
40
Statistical Process Control - Pareto Diagram
Used to display relative importance of problems
• Pareto principle: 80% of costs are associated with
20% of defects
• Prioritize problems to direct resources
• Attack tall bars first
• Use check sheets or collected data to build
• Provide to those involved in the process
• Do before and after snapshots to check for
improvement
• Generally used for attribute data
• Can use time rollups to see trends
41
Statistical Process Control - Pareto Diagram
Questions to ask
• Has the data been sanitized
• Have people who do the work see the information?
• What action has been taken to prevent tall bar
recurrence?
• Are the operators collecting this data?
42
16
80
12
60
8
40
4
20
0
Cumulative percent
Number of occurrences
Statistical Process Control - Pareto Diagram
20
100
0
• Identifies the most significant problems to be
worked first
• Historically 80% of the problems are due to
20% of the factors
43
• Shows the vital few
Statistical Process Control - Scatter Plot
Scatter Plot
• Used to display relationship between two variables
• Tests for cause and effect
• Doesn’t prove that one variable causes the other
• Does provide for existence and strength of
relationship
• Horizontal = cause
• Vertical = effect
• Interpretation based on picture if relationship is
linear
44
Statistical Process Control - Scatter Plot
Questions to ask
• Are you sure the relationship is linear?
• Have you chose the most relevant data?
• Did you gather enough data?
• Was relationship negative or positive? How strong?
45
Statistical Process Control - Scatter Plot
x
x
Temp.
x
x
x
x
x
x
x
x
x
x
x
x
Pressure
• Identifies the relationship between two variables
• A positive, negative, or no relationship can be
easily detected
46
Correlation
Possible Relationship Between X and Y as Indicated by
Scatter Diagrams
47
Statistical Process Control
How to implement
• Must have a model to work from
• Must have discipline to follow model
• Cannot only be ‘quality’ championed
• Needs to be team driven
• Must not chase charts for charts sake
• Management must understand, believe, and expect
results
• Start small
• Focus on process
• Get operators involved in the process
• Must provide right training to right people at right
time
• Do not need fancy computers
48
• Don’t take capability for granted
Statistical Process Control
Recommendations
• Establish steering team to implement SPC
• Establish SPC methodology
• Choose pilot processes to study
• Train practitioners with detailed understanding of
SPC
• Put stake in ground on chosen processes
• Follow and document your chosen SPC plan
• Understand the process!
49
Background of Six Sigma
• Six Sigma is a business initiative first espoused by
Motorola in the early 1990’s.
• Six Sigma strategy involves the use of statistical
tools within a structured methodology for gaining
the knowledge needed to achieve better, faster,
and less expensive products and services than the
competition.
• A Six Sigma initiative in a company is designed
to change the culture through breakthrough
improvement by focusing on out-of-the-box
thinking in order to achieve aggressive, stretch
goals
50
Motorola’s Six Sigma Ten Steps
1.
2.
3.
4.
5.
6.
7.
Prioritize opportunities for improvement
Select the appropriate team
Describe the total process
Perform measurement system analysis
Identify and describe the potential critical process
Isolate and verify the critical processes
Perform process and measurement system
capability studies
8. Implement optimum operating conditions and
control methodology
9. Monitor processes over time/continuous
improvement
10. Reduce common cause variation toward
achieving six sigma
51