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

http://www.simoncaulkin.com/article/192/

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



[email protected]

07850 728506

@ianjseath

www.improvement-skills.co.uk

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Control Charts: their use and benefits

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