Statistical Process Control.pdf

Statistical Process Control Continued
With
Common & Special Cause Variations
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Introduction
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 The questions we need to answer are:
 Is the observed variation more or less than we would normally expect?
 Are there genuine outliers?
 Are there exceptionally good performers?
 What reasons might there be for excess variation?
 Alternative methods based on understanding variation may be more appropriate.
 Statistical process control is one such method and helps to answer these questions through the
use of control charts.

Why use control charts?
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Control charts are used to monitor, control, and improve
system or process performance over time by studying variation and it’s source.
What do control charts do?
• Focus attention on detecting and monitoring process variation over time
• Distinguishes special from common causes of variation, as a guide to local or management
action.
• Serves as a tool for ongoing control of a process
• Helps improve a process to perform consistently and predictably
Introduction to Control Charts

Types of Variation
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1. Common-cause or process variation is variation that is completely random; special-cause or extra-
process variation is non-random i.e. is the result of an event or action.
2. Special cause variation can be exhibited within or outwith control limits i.e trends, step functions,
drift etc.
3. In any system variation is to be expected. Using statistical techniques we define the limits of
variation (control limits and zones). Interpretation of the data relative to these limits or zones
identifies points that are worthy of investigation.

Definitions
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 A process is said to be ‘in control’ if it exhibits
only “common cause” variation.
 This process is completely stable and predictable.
 A process is said to be ‘out of control’ if it exhibits
“special cause” variation.
 This process is unstable.

Basic control chart layout
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0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
Apr-
08
May-
08
Jun-
08
Jul-
08
Aug-
08
Sep-
08
Oct-
08
Nov-
08
Dec-
08
Jan-
09
Feb-
09
Mar-
09
Apr-
09
May-
09
Jun-
09
Jul-
09
Aug-
09
Sep-
09
Oct-
09
Nov-
09
Dec-
09
Jan-
10
Feb-
10
Mar-
10
Date
Under
Run
Hours
as
a
%
of
Allocated
Hours
Centre line
(usually mean
or median)
Zone A
Zone B
Zone C
Zone A
Zone B
Zone C
Upper control
limit
Lower control limit
Warning zones

Types of control charts
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 Control charts are plots of the data with lines indicating the target value (mean, median) and
control limits superimposed.
 The common types are based on statistical distributions:
 Poisson distribution for counts, rates and ratios; e.g number of violent crimes, number of
serious accidents
 Binomial distribution for proportions; e.g where the response is a category such as success,
failure, response, non-response
 Normal distribution for continuous data e.g measures such as height, weight, blood
pressure

Types of control charts
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1. Conventional control charts (run charts)
 The indicator of interest is plotted on the y-axis, against time or the unit of analysis on
the x-axis.
 Control charts can be plotted with small numbers of data points although their power
is increased with more data.
2. Funnel plots
 A type of chart where the indicator of interest is plotted against the denominator or
sample size.
 This gives it the characteristic funnel shape

Using control charts and SPC methods
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 Control charts can help us to present and interpret our information more intelligently.
 They can be used
 To detect unusual or outlying patterns, e.g. poor performance, outbreaks or unusual
patterns of disease
 In health profiling and assessing levels of performance
 To decide whether or not targets are being met
 In assessing health inequalities

Examples – Run Charts & Control Charts
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Run Charts:
 Display of data points plotted in chronological order
 Ideally 25 data points are required
 Centre line (mean or median) is included to identify types of variation
Control Charts:
 A Run chart plus control limits and warning limits (optional)
 Control limits are set at 3 standard deviations above and below the mean
Warning limits are set at 2 standard deviations above and below the mean
 These limits provide an additional tool for detecting special cause variation

Run chart – Time to work
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08:24
08:38
08:52
09:07
09:21
09:36
Mon
Tues
Wed
Thurs
Fri
Mon
Tues
Wed
Thurs
Fri
Mon
Tues
Wed
Thurs
Fri
Mon
Tues
Wed
Thurs
Fri
Mon
Tues
Wed
Thurs
Fri
Time
arrived
at
work

Run Chart – Out of control
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08:24
08:38
08:52
09:07
09:21
09:36
09:50
10:04
10:19
10:33
10:48
Mon
Tues
Wed
Thurs
Fri
Mon
Tues
Wed
Thurs
Fri
Mon
Tues
Wed
Thurs
Fri
Mon
Tues
Wed
Thurs
Fri
Mon
Tues
Wed
Thurs
Fri
Time
arrived
at
work

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Special Cause Rule Number 1: Shifts
For detecting shifts in the middle value, look for eight or more consecutive points
either above of below the center line. Values on the center line are ignored, they
do not break a run, and are not counted as points in the run.
0.2
0.7
1.2
1.7
2.2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Blood Samples
Micrograms/ML
SERUM GENTAMICIN LEVELS - TROUGH

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ADVERSE DRUG REACTIONS
Special Cause Rule Number 2: Trends
For Detecting trends, look for six lines between seven consecutive points all going
up or all going down. If the value of two or more consecutive points is the same,
ignore the lines connecting those values when counting. Like values do not make or
break a trend.
0
1
2
3
4
5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Week Number
Number
of
Adverse
Drug
Reactions

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75
80
85
90
95
100
105
110
115
120
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
INDIVIDUAL PATIENT READINGS
MEASUREMENT
DIASTOLIC BLOOD PRESSURE
Special Cause Rule Number 3: Zig-Zag Patterns
Any non-random pattern may be an indication of a special cause variation. A
general rule is to investigate where 14 consecutive points go up and down
alternately.

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Special Cause Rule Number 4: Cyclical Patterns
A non-random cyclical pattern may be an indication of a special cause variation.
For example, a seasonal pattern occurring across months or quarters of the year.
0
1
2
3
4
5
6
7
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Time
Observations

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Special Cause Rule Number 5: Points Outside Limits
A point or points outside control limits is/ are evidence of special cause. Control
limits are calculated based on data from the process.
0
10
20
30
40
50
60
70
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
COLPOSCOPYPATIENTS
TIME
IN
DAYS
Mean = 35
ABNORMAL PAP TEST FOLLOW-UP PROCESS
UCL

Determining if the process is out of
control – Control Rules
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 One or more points fall outside of the control limits
 8 or more consecutive points on same side of centre line
 7 successive points all going up or down
 14 consecutive points going up and down alternately
 2 out of 3 consecutive points in zone A or beyond
 4 out of 5 consecutive points in zone B or beyond
 15 consecutive points in zone C (above and below)

8+ points on same side of centre line
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16 points going up and down
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4 out of 5 points in zone B or beyond
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0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
A
p
r
-
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M
a
y
-
0
8
J
u
n
-
0
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J
u
l
-
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A
u
g
-
0
8
S
e
p
-
0
8
O
c
t
-
0
8
N
o
v
-
0
8
D
e
c
-
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8
J
a
n
-
0
9
F
e
b
-
0
9
M
a
r
-
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A
p
r
-
0
9
M
a
y
-
0
9
J
u
n
-
0
9
J
u
l
-
0
9
A
u
g
-
0
9
S
e
p
-
0
9
O
c
t
-
0
9
N
o
v
-
0
9
D
e
c
-
0
9
J
a
n
-
1
0
F
e
b
-
1
0
M
a
r
-
1
0
Date
Under
Run
Hours
as
a
%
of
Allocated
Hours

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Acting on Variation
Special or common cause variation?
Common
Special
Is the process capable?
Yes No
Search for and
eliminate
differences in causes
between data points Do
nothing
Search for and eliminate
causes common to all
data points

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Management of Variation
Special Cause Variation Common Cause Variation
•Identify and study the special
cause.
•React to special cause
- If it is a negative impact,
prevent it or minimise impact.
-If it is a positive impact, build
into process.
•Recognise that the capability will not
change unless the process is changed.
•Work to reduce variation due to
common causes
•Do not react to individual occurrences
or differences between high and low
numbers.
•Change the system to react to
special causes
•Treat every occurrence as a special
cause
Inappropriate
Action
Appropriate
Action

Summary
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 Understanding the causes of variation has reformed industry
 Application to healthcare has provided important insight to
inform improvement
 Effectively highlights areas meriting further investigation
through simple data presentation

Example 1: rate of mortality at 120 days
following admission to a surgical specialty
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 In this example each data point is a hospital (all hospitals in NHS Board X are shaded
blue).
 The number of people admitted to a surgical specialty is represented on the horizontal
axis, which essentially means that smaller hospitals appear towards the left hand side of
the graph and larger hospitals towards the right.
 The proportion of people who died within 120 days of admission to hospital is
represented on the vertical axis – the higher up the data point, the higher the rate of
mortality would appear to be.
 The funnel formed by the control limits (and from which the graph gets its name) is
wider towards the left hand side.This is simply so the level of activity (in this case, the
number of admissions) is taken into account when identifying‘outliers’ (i.e. the larger
the denominator, the most stable the data points are).

.00
.50
1.00
1.50
2.00
2.50
3.00
0 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000
Number of Patients
Mortality
rate(%)
at
120
days
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Elective admissions to any surgical
specialty: overall mortality at 120 days

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.00
2.00
4.00
6.00
8.00
10.00
12.00
0 50 100 150 200 250 300 350
Number of Patients
Mortality
(%)
at
120
days

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