Control Charts: their use and benefits

© 2017 Copyright ISC Ltd.
Control Charts: their use and
benefits
OR Society
Criminal Justice Special Interest Group
23/01/17

“WHEN A SYSTEM IS STABLE,
TELLING A WORKER ABOUT
MISTAKES IS ONLY TAMPERING”
Dr. W Edwards Deming

https://academic.oup.com/policing/article-
abstract/10/1/71/2362373/Getting-Police-
Performance-Measurement-under
https://inspguilfoyle.wordpress.com/

Week 1 52
Week 2 52
Week 3 52
Week 4 55
Week 5 51
Week 6 51
Week 7 53
Week 8 58
Week 9 52
Week 10 54
Week 11 47
Week 12 54
Week 13 52
Week 14 52
Week 15 56
Week 16 49
Week 17 52
Week 18 54
Week 19 52
Week 20 50
Week 21 53
Week 22 49
Week 23 57
Week 24 52
Week 25 51
Week 26 54
Week 27 55
Week 28 54
Week 29 48
Week 30 49
Week 31 52
Week 32 54
Week 33 55
Week 34 56
Week 35 53
Week 36 54
Week 37 55
Week 38 54
Week 39 49
Week 40 50
Week 41 52
Week 42 52
Week 43 54
Week 44 50
Week 45 49
Week 46 52
Week 47 55
Week 48 53
Week 49 52
Week 50 45
Week 51 53
Week 52 56
Data
Sample Observation
Apr-Y1 37
May 31
Jun 19
Jul 22
Aug 18
Sep 30
Oct 25
Nov 42
Dec 26
Jan 27
Feb 21
Mar 19
Apr-Y2 39
May 25
Jun 31
Jul 35
Aug 38
Sep 24
Oct 44
Nov 30
Dec 38
Jan 27
Feb 59
Mar 63
Apr-Y3 37
May 41
Jun 51
Jul 35
Aug 26
Sep 50
Oct 43
Nov 33
Dec 41
Jan 52
Feb 31
Mar 31
Apr-Y4 37
May 36
Jun 47
Jul 38
Aug 24
Sep 37
Oct 48
Nov 36
What’s
happening to
street crime?
Has the case
load increased
in the Victim
Liaison Unit?

Has the case
load increased
in the Victim
Liaison Unit?
Data
Sample Observation
Apr-Y1 37
May 31
Jun 19
Jul 22
Aug 18
Sep 30
Oct 25
Nov 42
Dec 26
Jan 27
Feb 21
Mar 19
Apr-Y2 39
May 25
Jun 31
Jul 35
Aug 38
Sep 24
Oct 44
Nov 30
Dec 38
Jan 27
Feb 59
Mar 63
Apr-Y3 37
May 41
Jun 51
Jul 35
Aug 26
Sep 50
Oct 43
Nov 33
Dec 41
Jan 52
Feb 31
Mar 31
Apr-Y4 37
May 36
Jun 47
Jul 38
Aug 24
Sep 37
Oct 48
Nov 36

The normal distribution is at the heart
of understanding control charts
2
S
D
1
S
D
3
S
D
3
S
D
2
S
D
1
S
D
This is a normal distribution curve.
If we turn this on its side, we get this

We can then think of the control chart as being
the normal distribution telling us when
variation is outside what is normal.
Upper Control
Limit
Lower Control
Limit

Not all variation is significant
 Common Cause:
 Many small sources
 Stable and relatively
predictable
 Not assignable to individual
causes
 Often over-reacted to
 Special Cause:
 One, or a few, major
sources
 Irregular and unpredictable
 Can be assigned to
individual causes and
acted upon

Upper Control
Limit
Lower Control
Limit
Control charts allow us to see if what is happening to a process is
outside what we would normally expect to see.

Mean &
Control Limits
from 1st 20
observations +/-
2 SD

This is an X-chart and is appropriate for continuous (or variables) data
where a single observation is made at each point in time.
With this type of chart the calculation of the control limits is based on the mean
moving range (MMR).
Change of
legislation

Benefits of Control Limits
 They measure variability of a process over time
 rather than variation of a static distribution
 They are not probability or confidence limits
 they provide useful warning signals when applied to
processes in the real world

Interpreting Control Charts
 Detect special causes of variation by noting:
 points outside action limits, or
 Unusual patterns of points, such as:
 7 successive points above the process mean
 7 successive points below the process mean,
 7 points rising in a line (6 successive rises in points)
 7 points falling in a line (6 successive falls in points)
 Too many, or too few points, within the middle third of
the chart (we should have two-thirds of the points
within the middle third of the chart [1 SD])

What’s going on here?

EXAMPLES
Some more

Thematic Inspection of Performance
Management in the Scottish Police
Service
http://www.gov.scot/Publications/2005/09/27134643/46499

Do extended drinking hours cause
more violence?
http://www.simoncaulkin.com/article/192/ (Observer 2005)
LB Bromley

Control Chart approach - Summary
 Determine the measurement you wish to control/track
 Collect data (i.e. a sample of measurements) over a
period of time
 Usually a sample of 15-25 measures is sufficient
 Calculate the mean and standard deviation for all the
measures taken so far
 Plot the mean on an appropriate chart
 Calculate the control limits based on plus or minus 2 or 3
standard deviations
 Continue to take samples of data
 Plot each point on the control chart
 Observe the values and trends of the individual points

Which type of Control Chart?
 Variable data: how large are the subgroups?
 If the subgroup size is one, then use an Individual measurements
chart, with or without a moving R chart.
 If the subgroup size is from two to ten (or possibly twelve), then use an
X and R chart.
 If the subgroup size is over ten (or twelve), then use an X and S chart.
 Attribute data: what type of distribution does the
data follow?
 Binomial data takes on two values, usually "good" or "bad". If the
sample size is constant, use an np-chart. If the sample size changes,
use a p-chart.
 Poisson data is a count of infrequent events, usually defects. If the
sample size is constant, use a c-chart. If the sample size changes, use
a u-chart.
http://www.nwasoft.com/services/support/technotes/which-control-charts-use

Benefits of using Control Charts
 They are simple graphical tools that enable
process performance monitoring
 They are designed to identify which type of
variation exists within a process
 They highlight areas of performance that may
require further investigation
 They are easy to construct and interpret

 ian.seath@improvement-skills.co.uk
 07850 728506
 @ianjseath
 www.improvement-skills.co.uk

Control Charts: their use and benefits

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