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Statistical Process Control
(SPC)
By
Zaipul Anwar
Business & Advanced Technology Centre,
Universiti Teknologi Malaysia
Aims and objectives





Explain the concept of SPC
Understand variation and why it is important
Manage variation in our work using SPC
Learn how to do a control chart
Interpret the results
What is SPC?

Statistical Process Control
we deliver our work through processes
we use statistical concepts to help us understand our work
control = predictable and stable



branch of statistics developed by Walter Shewhart in
the 1920s at Bell Laboratories
based on the understanding of variation
used widely in manufacturing industries for over 80
years
What is SPC for?

A way of thinking

Measurement for improvement - a simple tool for
analysing data – easy and sustainable

Evidence based management – real data in real time – a
better way of making decision
week 26 - 27/6
week 22 - 30/5
week 18 - 02/5
week 14 - 4/4
week 10 - 07/03
week 6 - 08/02
week 2 - 11/01
week 50 - 14/12
week 46 - 16/11
week 42 - 19/10
week 38 - 21/09
week 34 - 24/08
week 30 - 27/07
week 26 - 29/06
week 22 - 01/06
week 18 - 04/05
week 14 - 06/04
week 10 - 09/03
week 6 - 09/02
week 2 - 12/01
week 50 - 15/12
week 46 - 17/11
week 42 - 20/10
week 38 - 22/09
week 34 - 25/08
week 30 - 28/07
week 26 - 30/06
week 22 - 02/06
week 18 - 05/05
week 14 - 07/04
week 10 - 10/03
What does this show?
QMS - 90%
110.0%
100.0%
90.0%
80.0%
70.0%
60.0%
50.0%
40.0%
Or this?
NOTHING!

This is inappropriate data presentation
 It tells us NOTHING
A typical SPC chart
Range
80
Upper
process
limit
70
60
Mean
50
40
Lower
process
limit
30
20
10
0
F M A M J J A S O N D J F M A M J J A S O N D
“A phenomenon will be said to be
controlled when, through the use of
past experience, we can predict, at
least within limits, how the
phenomenon may be expected to
vary in the future”
Shewart - Economic Control of Quality of
Manufactured Product, 1931
Walter A. Shewhart
While every process displays variation:

some processes display controlled variation



stable, consistent and predictable pattern of variation
constant causes / “chance”
while others display uncontrolled variation


pattern changes over time
special cause variation/“assignable”
11/28/2003
11/19/2003
11/10/2003
11/1/2003
10/23/2003
10/14/2003
10/5/2003
9/26/2003
9/17/2003
9/8/2003
8/30/2003
8/21/2003
8/12/2003
8/3/2003
7/25/2003
7/16/2003
7/7/2003
6/28/2003
6/19/2003
6/10/2003
6/1/2003
Controlled variation
Total discharges
140
120
100
80
60
40
20
0
11/28/2003
11/19/2003
11/10/2003
11/1/2003
10/23/2003
10/14/2003
10/5/2003
9/26/2003
9/17/2003
9/8/2003
8/30/2003
8/21/2003
8/12/2003
8/3/2003
7/25/2003
7/16/2003
7/7/2003
6/28/2003
6/19/2003
6/10/2003
6/1/2003
Uncontrolled variation
380
360
340
320
300
280
260
240
220
2 ways to improve a process
If uncontrolled variation - identify special causes (may be good or bad)
 process is unstable
 variation is extrinsic to process
 cause should be identified and “treated”



If controlled variation - reduce variation, improve outcome
process is stable
variation is inherent to process
therefore, process must be changed
Process Improvement
Common cause
variation reduced
Special causes
eliminated
Process improved
Special causes
present
Process under control
- predictable
Process out of control
- unpredictable
Then improve nominal
How to present data

Measures of location


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average
median
mode
Measures of dispersion/variation

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
range
root mean square deviation
standard deviation
PRACTICAL INTERPRETATION OF THE STANDARD
DEVIATION
Mean - 3s
Mean
Mean + 3s
Standard Deviation
• A measure of the range of variation from an average of a group of measurements. 68% of all
measurements fall within one standard deviation of the average. 95% of all measurements fall within
two standard deviations of the average
• The standard deviation is a statistic that tells you how tightly all the various examples are clustered
around the mean in a set of data. When the examples are pretty tightly bunched together and the
bell-shaped curve is steep, the standard deviation is small. When the examples are spread apart and
the bell curve is relatively flat, that tells you have a relatively large standard deviation. If you looked at
normally distributed data on a graph, it would look something like this:
3s and the Control Chart
UCL
3s
3s
6s
Mean
LCL
2 dangers to beware of

Reacting to special cause variation by changing
the process

Ignoring special cause variation by assuming “it’s
part of the process”
Task


Think of your normal routine for coming to
work every day. This is a process!
Discuss briefly on your tables:
How long does it take on average?
 What factors might cause you to take longer (or
shorter) than usual?

Richard’s trip to work
120
100
Upper process limit
Mean
80
Lower process limit
Min. 60
40
20
0
Consecutive trips
What Can It Do For Me?

to identify if a process is sustainable


to identify when an implemented change has
improved a process



are your improvements sustained over time
and it has not just occurred by chance
to understand that variation is normal and to help
reduce it
to understand processes - this helps make better
predictions and improves decision making
Using Charts

Run chart records data points in time order
median used as centre line

Control chart adds in estimates of predictability
process in control
mean used as the centre line
upper and lower process limits (3 sigma)
Using SPC in practice



Constructing an I chart
Learning the rules
Examples of measurement for improvement
in practice
Constructing the I
(XmR) chart
Don’t run here comes the maths!!!
The I (XmR) chart



I stands for Individual
XmR stands for X moving Range
the ‘I or X’ represents the data from the process we
are monitoring and corresponds to a single
observation or individual value


e.g. number of cancelled operations each day
the moving Range describes the way in which we
measure the variation in the process

Use individual values to calculate the Mean

Difference between 2 consecutive readings, always positive
Moving Range, mR

Calculate the Mean mR

One Sigma/standard deviation = (Mean mR)/d2 *

=
s or σ

Upper Process Limit (UPL) = Mean + 3 s

Lower Process limit (LPL) = Mean - 3 s
* The bias correction factor, d2 is a constant for given subgroups of size n (n =
2, d2 = 1.128)
H.L. Harter, “Tables of Range and Studentized Range”, Annals of Mathematical Statistics, 1960.
How to construct the chart
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
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Plot the individual values
Calculate the mean and plot it
Calculate a measure of the variation (sigma)
Derive upper and lower limits from this measure
of variation (control limits)
1. Plot the individual values
Average wait in days
120
100
80
60
40
20
0
Jan
Mar
May
Jul
Sep
Nov
Jan
Mar
May
Jul
Sep
Nov
2. Calculate the mean and plot it
Average wait in days
120
100
80
60
40
20
0
Jan
Mar
May
Jul
Sep
Nov
Jan
Mar
May
Jul
Sep
Nov
3. Calculate a measure of variation:
the average moving range

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
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Find out the difference between successive values
(ignore the plus or minus signs!)
Find the average (mean) of these differences (17.96)
Convert to 1 sigma
(17.96 / 1.128 = 15.92)
Value Difference
Use 3 sigma to
85
calculate the limits:
76
9
83
7
Mean +/- 3 x 15.92
58

NB (Take Note): 1.128 is a standard bias correction factor (d2) used to calculate sigma value
25
4. Derive the limits and plot them
Average wait in days
120
100
80
60
40
20
0
Jan
Mar
May
Jul
Sep
Nov
Jan
Mar
May
Jul
Sep
Nov
Things to remember
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



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You only need 20 data points to set up a control chart
if one of initial 20 data points is out of process limits
consider excluding that point from calculations
Sigma is not the same as the standard deviation of a
normal distribution
d2 constant means a sample size of 2 and refers to the
sample size for moving range (which is nearly always 2)
20 data points produces 19 moving ranges
Data must be in time ordered sequence
Benefits of process limits?

Measure variability of process over time

NOT probability or confidence limits

Work well even if measurements not normally
distributed
How to interpret the
charts and results
Rules, Patterns and Signals
The Empirical Rule
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99-100% will be within 3 sigmas either side of mean

90-98% will be within 2 sigmas either side of mean

60-75% of data within 1 sigma either side of the mean
In real life, only the first of these is of any real benefit
Rules for special causes

Rule 1 - Any point outside the control limits

Rule 2 - Run of 7 points or more all above or all below
the mean, or all increasing or all decreasing

Rule 3 - An unusual pattern or trend within the control
limits

Rule 4 - Number of points within the middle third of
the region between the control limits differs
markedly from two-thirds of the total number
of points
Special causes - Rule 1
Point above UCL
X
UCL
X
X
X
UCL
X
X
X
X
X
X
MEAN
X
X
X
X
X
X
MEAN
X
X
X
LCL
X
Point below LCL
LCL
Special causes - Rule 2
Seven points above
centre line
UCL
X
X
X
X
X
X
X
X
UCL
X
X
X
MEAN
X
X
X
X
X
MEAN
X
X
X
X
X
LCL
LCL
Seven points below
centre line
Special causes - Rule 2
Seven points in a
downward direction
UCL
UCL
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
MEAN
X
MEAN
X
LCL
LCL
Seven points in an
upward direction
Special causes - Rule 3
Cyclic pattern
Trend pattern
UCL
X
X
X
X
X
X
X X
X
X
X
X
X
X
X
X
X
X X
X
UCL
X X
X
X
X
X
X
LCL
X X
X
X
X
X
X
X
X
X
X X
LCL
Special causes - Rule 4
Considerably less than 2/3 of all
the points fall in this zone
X
X
Considerably more than 2/3 of all
the points fall in this zone
UCL
UCL
X
X
X
XX
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
LCL
LCL
USING SPC TO SHOW IMPROVEMENT
What is Statistical Process Control (SPC)?
Control limits define the estimated variation inherent
within the process (common variation or common
cause) and are calculated using the difference between
each successive value in time order (shown by the red
lines). They are centred on the mean value for the data
set (shown by the green line)
- branch of statistics founded on understanding variation
- used for over 80 years in manufacturing industries
- plots real data in real time
Upper control limits
Seven or more values steadily increasing
or decreasing indicates a change in the
process – this usually requires
recalculation of the mean and the control
limits as it indicates a new process – this
is called a step change
650
600
number of patients
550
500
450
Run of seven or
more on same
side of centreline
picks up a small
but consistent
change in the
process
400
350
300
Period
Special cause –a single point falling outside a control
limit – a rare event with a probability of occurring by
chance of 3 in a thousand
26/10/2003
05/10/2003
14/09/2003
24/08/2003
03/08/2003
13/07/2003
22/06/2003
01/06/2003
11/05/2003
20/04/2003
30/03/2003
09/03/2003
16/02/2003
26/01/2003
05/01/2003
15/12/2002
24/11/2002
03/11/2002
13/10/2002
22/09/2002
01/09/2002
11/08/2002
21/07/2002
30/06/2002
09/06/2002
19/05/2002
28/04/2002
Lower control limits
07/04/2002
250
Summary




What is SPC and why it is a useful tool
Understanding variation
Presenting data as control charts
Understanding the results
Useful SPC references



Walter A Shewhart. Economic control of quality of
manufactured product. New York: D Van Nostrand 1931.
Donald Wheeler. Understanding Variation. Knoxville: SPC
Press Inc, 1995
Raymond G Carey. Improving healthcare with control charts.
ASQ Quality Press, 2003

Mal Owen. SPC and continuous improvement: IFS Publications

WE Deming. Out of the crisis. Massachusetts: MIT 1986


Donald M Berwick. Controlling variation in health care: a
consultation from Walter Shewhart. Med Care 1991; 29: 121225.
www.steyn.org