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1SPC
STATISTICAL
PROCESS CONTROL

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STATISTICAL PROCESS CONTROL (SPC)
• Is the application of Statistical Methods to monitor and
control a process to ensure that it operates at its full potential
to produce conforming product.
OR
• Is an analytical decision making tool which allows you to see
when a process is working correctly and when it is not.
• Variation is present in any process, deciding when the
variation is natural and when it needs correction is the key to
quality control.

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HISTORY
Was Pioneered By Walter .A. Shewhart In The Early 1920s.
W. Edwards Deming Later Applied SPC Methods
In The US During World war II, Successfully Improved Quality In The
Manufacture Of Munitions And Other Strategically Important Products.
Deming introduced SPC Methods to Japanese IndustryAfter The
War Had Ended.
Resulted high quality of Japanese products.
Shewhart Created The Basis For The Control Chart And The
Concept Of A State Of Statistical Control By Carefully Designed
Experiments

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• Concluded That While Every Process Displays Variation, Some
Processes Display Controlled Variation That Is Natural To The Process
(Common Causes Of Variation), While Others Display Uncontrolled
Variation That Is Not Present In The Process Causal System At All
Times (Special Causes Of Variation).
• In 1988, The Software Engineering Institute Introduced The Notion
That SPC Can Be Usefully Applied To Non-manufacturing Processes
HISTORY

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TRADITIONAL METHODS VS STATISTICAL PROCESS
CONTROL
Traditional Method :
The quality of the finished article was traditionally achieved through
post-manufacturing inspection of the product; accepting or rejecting
each article (or samples from a production lot) based on how well it
met.
Statistical Process Control :
SPC uses Statistical tools to observe the performance of the
production process in order to predict significant deviations that may
later result in rejected product.

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TYPES OF VARIATION
Two kinds of variation occur in all manufacturing processes
1.Natural or Common Cause Variation
It consists of the variation inherent in the
process as it is designed, may include
variations in temperature, properties of
raw materials, strength of an electrical
current etc.
2.Special Cause Variation or
Assignable-cause Variation
With sufficient investigation, a specific
cause, such as abnormal raw material or
incorrect set-up parameters, can be
found for special cause variations.
Random Variability
– common causes
– inherent in a process
– can be eliminated
only through
improvements in the
system
Non-Random Variability
– special causes
– due to identifiable
factors
– can be modified
through operator or
management action

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‘In Control’and ‘Out Of Control’
Process is said to be ‘in control’ and stable
If common cause is the only type of variation that exists in the
process.
It is also predictable within set limits i.e. the probability of any
future outcome falling within the limits can be stated
approximately.
Process is said to be ‘out of control’ and unstable
Special cause variation exists within the process.

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Statistical process control -broadly broken down
into 3 sets of activities
1. Understanding the process
2. Understanding the causes of variation
3. Elimination of the sources of special cause variation.

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Understanding the process
• Process is typically mapped out and the process is monitored
using control charts.
Understanding the causes of variation
• Control charts are used to identify variation that may be due to
special causes, and to free the user from concern over variation due
to common causes.
• It is a continuous, ongoing activity.
• When a process is stable and does not trigger any of the detection
rules for a control chart, a process capability analysis may also be
performed to predict the ability of the current process to produce
conforming product in the future.
Statistical process control

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•When excessive variation is identified by the control chart detection
rules, or the process capability is found lacking, additional effort is
exerted to determine causes of that variance.
The tools used include
• Ishikawa diagrams
• Designed experiments
• Pareto charts
•Designed experiments are critical -only means of objectively
quantifying the relative importance of the many potential causes of
variation.
Statistical process control

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Elimination of the sources of special cause variation
Once the causes of variation have been quantified, effort is spent in
eliminating those causes that are both statistically and practically
significant.
Includes development of standard work, error-proofing and training.
Additional process changes may be required to reduce variation or
align the process with the desired target, especially if there is a
problem with process capability.

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ADVANTAGES OF SPC
• Reduces waste.
• Lead to a reduction in the time required to produce the product or
service from end to end due to a diminished likelihood that the final
product will have to be reworked, identify bottlenecks, wait times, and
other sources of delays within the process.
• A distinct advantage over other quality methods, such as inspection
- its emphasis on early detection and prevention of problems.
• Cost reduction.
• Customer satisfaction.

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Applying SPC to Service
Nature of defect is different in services
Service defect is a failure to meet customer requirements
Monitor times, customer satisfaction
Hospitals
timeliness and quickness of care, staff responses to requests, accuracy of
lab tests, cleanliness, courtesy, accuracy of paperwork, speed of
admittance and checkouts
Grocery Stores
waiting time to check out, frequency of out-of-stock items, quality of
food items, cleanliness, customer complaints, checkout register errors.

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Airlines
flight delays, lost luggage and luggage handling, waiting time at ticket
counters and check-in, agent and flight attendant courtesy, accurate
flight information, passenger cabin cleanliness and maintenance
Fast-Food Restaurants
waiting time for service, customer complaints, cleanliness, food quality,
order accuracy, employee courtesy
Catalogue-Order Companies
order accuracy, operator knowledge and courtesy, packaging, delivery
time, phone order waiting time
Insurance Companies
billing accuracy, timeliness of claims processing, agent availability and
response time

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Where to Use Control Charts
Process has a tendency to go out of control
Process is particularly harmful and costly if it goes out of control
Examples
– at the beginning of a process because it is a waste of time and money
to begin production process with bad supplies
– before a costly or irreversible point, after which product is difficult to
rework or correct
– before and after assembly or painting operations that might cover
defects
– before the outgoing final product or service is delivered.

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SPC CHARTS
• One method of identifying the type of variation present.
• Statistical Process Control (SPC) Charts are essentially:
Simple graphical tools that enable process performance
monitoring.
Designed to identify which type of variation exists within the
process.
Designed to highlight areas that may require further investigation.
Easy to construct and interpret.
Most popular SPC tools
Run Chart
Control Chart

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SPC charts can be applied to both dynamic processes and static
processes.
Dynamic Processes
A process that is observed across time is known as a dynamic process.
An SPC chart for a dynamic process - „time-series‟ or a „longitudinal‟
SPC chart.
Static Processes
A process that is observed at a particular point in time is known as a
static process.
An SPC chart for a static process is often referred to as a „cross
sectional‟ SPC chart.
SPC CHARTS

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Control Charts
A graph that establishes control limits of a process
Control limits
– upper and lower bands of a control chart.
Variables : a product
characteristic that is continuous
and can be measured –
weight - length
range (R-chart)
mean (x bar – chart)
Variable charts require smaller
samples
2 to 10 parts in a sample
Attributes : a product
characteristic that can be evaluated
with a discrete response.
Good – bad; yes – no
p-chart
c-chart
Attribute charts require larger
sample sizes
50 to 100 parts in a sample)
Types of charts

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Control charts
Show the variation in a measurement during the time period that the
process is observed.
Monitor processes to show how the process is performing and how
the process and capabilities are affected by changes to the process.
This information is then used to make quality improvements.
A time ordered sequence of data, with a centre line calculated by the
mean.
Used to determine the capability of the process.
Help to identify special or assignable causes for factors that impede
peak performance.

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Control charts have four key features:
1) Data Points:
Either averages of subgroup measurements or individual measurements
plotted on the x/y axis and joined by a line. Time is always on the x-axis.
2) The Average or Center Line
The average or mean of the data points and is drawn across the middle
section of the graph, usually as a heavy or solid line.
3) The Upper Control Limit (UCL)
Drawn above the centerline and annotated as "UCL". This is often called the
“+ 3 sigma” line.
4) The Lower Control Limit (LCL)
Drawn below the centerline and annotated as "LCL". This is called the “- 3
sigma” line.

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Control charts
1 2 3 4 5 6 7 8 9 10
Sample number
Upper
control
limit
Process
average
Lower
control
limit
Out of control

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Control Charts for Variables
Mean chart ( x -Chart )
uses average of a sample
x-bar Chart
x =
x1 + x2 + ... xk
k
=
UCL = x + A2R LCL = x - A2R
= =
where
x = average of sample means
=
Retrieve Factor
Value A2

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x-bar Chart Example
OBSERVATIONS (SLIP- RING DIAMETER, CM)
SAMPLE 1 2 3 4 5 x R
1 5.02 5.01 4.94 4.99 4.96 4.98 0.08
2 5.01 5.03 5.07 4.95 4.96 5.00 0.12
3 4.99 5.00 4.93 4.92 4.99 4.97 0.08
4 5.03 4.91 5.01 4.98 4.89 4.96 0.14
5 4.95 4.92 5.03 5.05 5.01 4.99 0.13
6 4.97 5.06 5.06 4.96 5.03 5.01 0.10
7 5.05 5.01 5.10 4.96 4.99 5.02 0.14
8 5.09 5.10 5.00 4.99 5.08 5.05 0.11
9 5.14 5.10 4.99 5.08 5.09 5.08 0.15
10 5.01 4.98 5.08 5.07 4.99 5.03 0.10
50.09 1.15

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x- bar Chart Example (cont.)
x = = = 5.01
= x
k
50.09
10
UCL = x + A2R = 5.01 + (0.58)(0.115) = 5.08
LCL = x - A2R = 5.01 - (0.58)(0.115) = 4.94
=
=
UCL = 5.08
LCL = 4.94
Mean
Sample number
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1
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2
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3
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4
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5
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6
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7
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8
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10
5.10 –
5.08 –
5.06 –
5.04 –
5.02 –
5.00 –
4.98 –
4.96 –
4.94 –
4.92 –
x = 5.01
|
7
x- bar
Chart –
Example
Retrieve Factor
Value A2

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Range chart ( R-Chart )
uses amount of dispersion in a sample
Control Charts for Variables
R- Chart
UCL = D4R LCL = D3R
R =
R
k
where
R = range of each sample
k = number of samples
Retrieve Factor
Values D3 and D4

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R - Chart Example
OBSERVATIONS (SLIP- RING DIAMETER, CM)
SAMPLE 1 2 3 4 5 x R
1 5.02 5.01 4.94 4.99 4.96 4.98 0.08
2 5.01 5.03 5.07 4.95 4.96 5.00 0.12
3 4.99 5.00 4.93 4.92 4.99 4.97 0.08
4 5.03 4.91 5.01 4.98 4.89 4.96 0.14
5 4.95 4.92 5.03 5.05 5.01 4.99 0.13
6 4.97 5.06 5.06 4.96 5.03 5.01 0.10
7 5.05 5.01 5.10 4.96 4.99 5.02 0.14
8 5.09 5.10 5.00 4.99 5.08 5.05 0.11
9 5.14 5.10 4.99 5.08 5.09 5.08 0.15
10 5.01 4.98 5.08 5.07 4.99 5.03 0.10
50.09 1.15

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R-Chart Example (cont.)
R = = = 0.115
R
k
1.15
10
UCL = D4R = 2.11(0.115) = 0.243
LCL = D3R = 0(0.115) = 0
Retrieve Factor Values D3 and D4
UCL = 0.243
LCL = 0.0
Mean
Sample number
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2
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10
R =0.115
0.30 –
0.28 –
0.24 –
0.20 –
0.16 –
0.12 –
0.08 –
0.04 –
0 –

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Appendix:
Determining Control Limits for x-bar and R-Charts
SAMPLE SIZE FACTOR FOR x-CHART FACTORS FOR R-CHART
2 1.88 0.00 3.27
3 1.02 0.00 2.57
4 0.73 0.00 2.28
5 0.58 0.00 2.11
6 0.48 0.00 2.00
7 0.42 0.08 1.92
8 0.37 0.14 1.86
9 0.44 0.18 1.82
10 0.11 0.22 1.78
11 0.99 0.26 1.74
12 0.77 0.28 1.72
13 0.55 0.31 1.69
14 0.44 0.33 1.67
15 0.22 0.35 1.65
16 0.11 0.36 1.64
17 0.00 0.38 1.62
18 0.99 0.39 1.61
19 0.99 0.40 1.61
20 0.88 0.41 1.59
n A2 D3 D4

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Using x- bar and R-Charts Together
Process average and process variability must be in control.
It is possible for samples to have very narrow ranges, but their
averages is beyond control limits.
It is possible for sample averages to be in control, but ranges might be
very large.

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Control Chart Patterns
UCL
LCL
5 consecutive points
consistently above the
center line.
Investigate for cause.
Process is “out of control.”
LCL
UCL
consistently below the
center line
1

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Control Chart Patterns (cont.)
LCL
UCL
consistently increasing
UCL
LCL
consistently decreasing.
2

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LCL
UCL
5 points are either in one
direction.
2 points very near to lower or
upper control limits.
LCL
UCL
3 4

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LCL
UCL
One point above or below
the control limits.
3 consecutive points above
and below the center line
Cyclic behavior.
LCL
UCL
5 6

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Zones for Pattern Tests
UCL
LCL
Zone A
Zone B
Zone C
Zone C
Zone B
Zone A
Process
average
3 sigma = x + A2R
=
3 sigma = x - A2R
=
2 sigma = x + (A2R)
= 2
3
2 sigma = x - (A2R)
= 2
3
1 sigma = x + (A2R)
= 1
3
1 sigma = x - (A2R)
= 1
3
x
=
Sample number
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1
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2
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3
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4
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5
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6
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7
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8
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13

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Control limits define the zone where the observed data for a stable
and consistent process occurs virtually all of the time (99.7%).
Any fluctuations within these limits come from common causes
inherent to the system, such as choice of equipment, scheduled
maintenance or the precision of the operation that results from the
design.
An outcome beyond the control limits results from a special cause.
The automatic control limits have been set at 3-sigma limits.
Control charts

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The area between each control limit and the centerline is divided
into thirds.
1. Zone A - "1-sigma zone“
2. Zone B - "2-sigma zone“
3. Zone C - " 3-sigma zone “
=0 1 2 3-1-2-3
Normal Distribution
1-sigma zone“ – 93.3%
2-sigma zone“ – 95%
3-sigma zone “ – 99.74%

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PROCESS CAPABILITYANALYSIS
Examines
whether the process is capable of producing products which conforms to
specifications
range of natural variability in a process what we measure with control charts
Process capability studies distinguish between conformance to control limits
and conformance to specification limits (also called tolerance limits)
if the process mean is in control, then virtually all points will remain within
control limits
staying within control limits does not necessarily mean that specification
limits are satisfied
specification limits are usually dictated by customers.

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Process
Design Specifications
Process
Process Capability analysis cont.
(a) Natural variation exceeds design
Specifications, process is not
capable of meeting specifications
all the time
(b) Design specifications and
natural variation the same; process
is capable of meeting specifications
most of the time.

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Process
Process
Process Capability (cont.)
(c) Design specifications greater than
natural variation; process is
capable of always conforming to
specifications.
(d) Specifications greater than
natural variation, but process off
center; capable but some output
will not meet upper specification.

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Process Capability Measures
Process Capability Ratio
Cp =
=
tolerance range
process range
upper specification limit -
lower specification limit
6
Net weight specification = 9.0 0.5
Process mean = 8.80
Process standard deviation = 0.12
Cp =
upper specification limit - lower specification limit
6
9.5 - 8.5
6(0.12)
Cp = = 1.39
Example :

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Process Capability Measures
Process Capability Index
Cpk = minimum
x - lower specification limit
3
=
upper specification limit - x
3
=
Example :
Net weight specification = 9.0 0.5
Process mean = 8.80
Process standard deviation = 0.12
Cpk = minimum
x - lower specification limit
3
=
upper specification limit - x
3
=
8.80 - 8.50
3(0.12)
9.50 - 8.80
3(0.12)
,
,
,Cpk = minimum = 0.83

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Cpk = negative number
Cpk = zero
Cpk = between 0 and 1
Cpk = 1
Cpk > 1
Interpreting Cpk

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Any
Questions,
???
Thanks.

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