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How to use Statistical Process Control (SPC) charts?
ContentsWhy do we use statistical process control (SPC) charts? PAGE 1
What is a statistical process control (SPC) chart? PAGE 2
How to choose between a line chart, run chart and control chart? PAGE 4
The different type of variation that exists within a process/system PAGE 6
What to do when seeing non-random/special cause variation PAGE 7
When do you revise the centre line and control limits? PAGE 8
Formatting recommendations when creating an SPC PAGE 9
APPENDIX 1 – Control (Shewhart) chart selection guide PAGE 10
APPENDIX 2 – Flowchart for selecting the most appropriate control (Shewhart) chart PAGE 11
APPENDIX 3 – Rules of Non-Random Variation for a Run Chart PAGE 14
APPENDIX 4 – Rules of Special Cause for a Control Chart PAGE 16
APPENDIX 5 – Chart examples PAGE 17
Why do we use statistical process control (SPC) charts?
Statistical Process Control (SPC) charts are used to study how a system or process changes over time. It allows us to understand what is ‘different’ and what is the ‘norm’. By using these charts, we can then understand where the focus of work needs to be concentrated in order to make a difference.
We can also use SPC charts to determine if an improvement is actually improving a process and also use them to ‘predict’ statistically whether a process is ‘capable’ of meeting a target.
SPC charts are therefore the best tools to determine:
• The variation that lives in the process.• Predict how the process will perform in the future.• If our improvement strategies have had the desired effect. • Determine if an improvement strategy has sustained the gains.
Page 1Contents PageProduced by Forid Alom
What is a statistical process control (SPC) chart?
Statistical Process Control (SPC) charts consist of data over time and come in two forms:1. Run charts2. Control chart (also known as a Shewhart chart).
Figure 1a and 1b illustrate the elements of both charts.
Figure 1a – Elements of a run chart. Data plotted over time with a centre line based on the median value
Figure 1b – Elements of a control chart. Data plotted over time with a centre line based on the mean value, an upper control limit and a lower control limit.
Me
asu
re
Time Time
Me
asu
rePage 2Contents Page
CL = Centreline(Mean)
Produced by Forid Alom
What is a statistical process control (SPC) chart?
Statistical Process Control (SPC) charts consist of data over time and come in two forms:1. Run charts – can take any data type i.e. count, percentage, rate, days between etc
2. Control chart (also known as a Shewhart chart) – each data type has a specific chart
There is only one type of run chart and many different types of control charts (figure 2).
SPC CHARTS
RUN CHART CONTROL CHARTS
C Chart
U Chart
U ‘ Chart
P Chart
P ‘ Chart
G Chart
T Chart
XmRChart
X bar S Chart
Figure 2 – Different type of SPC charts
Page 3Contents PageProduced by Forid Alom
How to choose between a line chart, run chart and control chart?
When constructing an SPC chart, you need to make sure you have the correct number of data points. Figure 3 explains how to choose the right chart?
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24+
Line Chart Run Chart Control chart with “trial” limits
Control chart
"Trial" UCL
CL = Centreline
"Trial" LCL
UCL
CL = Centreline
LCL
CL = Centreline
Figure 3 – Choosing the right chart depending on the number of data points. When you have less than 20 data points, you can create a control chart with “trial” limits. Once you reach 20
points, you would recalculate the limits again.
Number of data points
Page 4Contents PageProduced by Forid Alom
How to choose between a line chart, run chart and control chart?
When using a control chart, it is important you choose the right one. There are different types of control charts depending on what type of data you’re looking at. Appendix 1 and Appendix 2 provide guidance on choosing the correct chart.
Control chart with “trial” limits
Control chart
"Trial" UCL
CL = Centreline
"Trial" LCL
UCL
CL = Centreline
LCL
C Chart
U Chart
U ‘ Chart
P Chart
P ‘ Chart
G Chart
T Chart
XmRChart
X bar S Chart
Page 5Contents PageProduced by Forid Alom
The different type of variation that exists within a process/system
By ordering the data points over time, we can identify the variation that exists within process/system. Figure 4 describes how we describe these.
Random / Common cause variation Non-random / Special cause variation
Is inherent in the design of the process Is due to irregular or unnatural causes that are not inherent in the design of the process
Is due to regular, natural or ordinary causes Affect some, but not necessarily all aspects of the process
Affects all the outcomes of a process Results in an “unstable” process that is not predictable
Results in a “stable” process that is predictable Also known as non-random or assignable variation
Also known as random or unassignable variation
SPC CHARTS
RUN CHARTS CONTROL CHARTS
Random Variation
Non-Random Variation
Common Cause Variation
Special Cause Variation
Figure 4 – Different type of variation that exists within a process/system Page 6Contents PageProduced by Forid Alom
What to do when seeing non-random/special cause variation
There are specific rules that help us identify non-random variation (Appendix 3) / special cause variation (Appendix 4) within an SPC charts.
When we see any of these rules within a chart, we need to take the following steps:
Investigate what caused it? Was it due to internal (i.e. change in process) or external factors (i.e. cyber attack)?
Determine if any action is needed
Revise centreline and control limits (if appropriate)
1
3
2
Page 7Contents PageProduced by Forid Alom
When you change the operational definition.
When the control chart remains unstable for 20 or more subgroups and approaches to
identify and remove the special causes have been exhausted.
When do you revise the centre line and control limits?
Below are five reasons that warrant recalculating of limits.
When “trial” limits have been calculated with fewer than 20 subgroups.
When the initial control chart has special causes and there is a desire to use the
calculated limits for analysis of data to be collected in the future
When improvements have be made to the process and the improvements result in
special causes on the control chart.
1
5 2
34
Page 8Contents PageProduced by Forid Alom
Formatting recommendations when creating an SPC
When creating SPC charts at ELFT, please note the following recommendations regarding formatting.
X-axis and Y-axis clearly
labelled
Title of chart explains what you’re measuring and the type of chart you’re using
Don’t use bright colours for data points. As a standard,
ELFT uses Blue
Don’t use bright colours for centreline. As a standard,
ELFT uses Black
Centreline clearly labelled and value added. Rounded to
3 decimal places
Limits clearly labelled
25.039%
25.039%
UCL
LCL
0%
10%
20%
30%
40%
50%
60%
05
-Fe
b-1
8
12
-Fe
b-1
8
19
-Fe
b-1
8
26
-Fe
b-1
8
05
-Mar
-18
12
-Mar
-18
19
-Mar
-18
26
-Mar
-18
02
-Ap
r-1
8
09
-Ap
r-1
8
16
-Ap
r-1
8
23
-Ap
r-1
8
30
-Ap
r-1
8
07
-May
-18
14
-May
-18
21
-May
-18
28
-May
-18
04
-Ju
n-1
8
11
-Ju
n-1
8
18
-Ju
n-1
8
25
-Ju
n-1
8
02
-Ju
l-1
8
09
-Ju
l-1
8
16
-Ju
l-1
8
23
-Ju
l-1
8
30
-Ju
l-1
8
06
-Au
g-1
8
13
-Au
g-1
8
20
-Au
g-1
8
27
-Au
g-1
8
Did
No
t A
tte
nd
/ %
Week
Number of people who did not attend their appointment - P Chart
Annotations added to chart to explain special cause
Limit recalculation based on the five reasons explains in
previous slide
PDSA 1
Page 9Contents PageProduced by Forid Alom
APPENDIX 1 – Control (Shewhart) chart selection guide
Type of data Continuous (variables data)
- Data in the form of a measurement- Requires some type of scale- Time, money, physical measure (i.e. length, height, weight, temperature) and throughput (volume of workload, productivity)
Count or Classification (Attributes data)
- Numbers of items that passed or failed- Data must be whole number when originally collected (can’t be fraction or scaled data)- This data is counted, not measured
Count- 1,2, 3, 4 etc. (errors, falls, incidents)- Numerator (incidences) can be greater than denominator (opportunities)
Classification- Either/or, pass/fail, yes/no- Percentage or proportion- Numerator cannot be greater than denominator
Equal area of opportunity
Unequal area of opportunityEqual or unequal
subgroup size
C chart P chart
Each dot on the chart consists of a single observation (i.e. cost per episode of care, waiting time for each patient)
Subgroup size of 1 (n=1)
Each dot on the chart consists of multiple data values
- The X-bar chart is the average of multiple data points (i.e., average cost per case for all cases this week, average waiting time for a specific no. of ER patients [e.g. 5])- S plots the standard deviation of the data values
Equal or unequal subgroup size (n>1)
XmR chart X and S chart
Subgroup size <5000
Subgroup size > 5000
Subgroup size < 5000
Subgroup size > 5000
P’ chartU chart U’ chart
Other types of control charts for count/classification data:• T Chart [time between rare events]• G Chart [case between rare events]
Other types of control charts for continuous data:• X-bar and Range Chart• Median and Range Chart Page 10Contents Page
Produced by Forid Alom
APPENDIX 2 – Flowchart for selecting the most appropriate control (Shewhart) chart
*A run chart may be used with any type of
data. It is often the starting point for viewing data over time when little data are yet available.
Do you have
Continuous data?
Do you have
Attribute data?
DATA*
A B
Get in touch with QI team
Yes
Yes
No
No
Attribute data can only take particular values. There may potentially be an infinite number of those values, but each is distinct and there’s no grey area in between. The data can be numeric – for example number of falls – but it can also be categorical – such as pass or fail, male or female, good or bad.
Important points about attribute data:
•It is counted, not measured.•Data must be whole numbers when collected (can’t be fraction or scaled data)•There is two sub-types:
-Count data-Classification data
Typical examples:
•Number of falls•Number of violent incidents•% of missed doses•% of service users scoring “effective” or “very effective” for patient care
Continuous data is not restricted to defined separate values, but can have almost any numeric value and can be subdivided into finer and finer increments, depending upon the precision of the measurement system. Between any two continuous data values, there may be an infinite number of others – for example time waited for 1st appointment.
Important points about continuous data:
•Data is in the form of a measurement. -Time-Money-Physical measure (length, height, weight, temperature)-Throughput (volume of workload, productivity)
•It requires some type of scale
Typical examples
•Waiting times for 1st appointment•Service user length of stay•Service user weight
No
Page 11Contents PageProduced by Forid Alom
APPENDIX 2 – Flowchart for selecting the most appropriate control (Shewhart) chart
Count
- 1, 2, 3, 4 etc. (errors, occurrences, defects,
complications)
- Numerator can be greater than denominator
Typical examples:
- Number of falls
- Number of incidents of physical violence
- Complaints per 1,000 visits
Classification
- Either/or, pass/fail, yes/ no
- Percentage or proportion
- Numerator cannot be greater than the
denominator
- Can have an equal or unequal subgroup size
Typical examples:
- Did Not Attend (DNA) rate
- % of service user participation
- % of safety huddles completed every
week
A Do you have
Count data?
YesDo you have
Classification
data?
No
Get in touch
with QI team
PChart
Yes
E.g. Number of Falls causing
harm as a % of all falls
reported
NoYes
TChart
E.g. Days between
number of Falls
Do you have an equal area of
opportunity?
Typical examples:
- Number of incidents per week
- Number of uses per month
NoYesCChart
UChart
E.g. Number of Falls per
1,000 occupied bed days
E.g. Number of Falls
Is it a rare
event?
Are you
measuring in
days?
Yes
No
GChart
E.g. Cases
between infection
No
Page 12Contents PageProduced by Forid Alom
APPENDIX 2 – Flowchart for selecting the most appropriate control (Shewhart) chart
B
Does each data point on the
chart consist of a single
observation?
Typical examples:
- Cost per episode of care
- Waiting time for each patient
- Average decibel reading for noise level
Typical examples:
- Average waiting time for 1st appointment
across multiple teams
- Average cost per case for all cases this week
- Average weight gain for all service users this
month
YesX Bar S
Chart
X Bar S chart characteristics:
- Two charts are created:
o An average chart known as the X bar chart
▪ Upper and lower control limit vary with sample size
▪ Y-axis usually the average of a measurement
o A standard deviation chart known as the S chart
▪ Y-axis is the standard deviation of all data points making up each point on the X bar chart
E.g. Cost per episode of Falls E.g. Average cost per episode of
falls across all inpatient wards
XmRChart
No
Page 13Contents PageProduced by Forid Alom
APPENDIX 3 – Rules of Non-Random Variation for a Run Chart
There are four rules for a run chart that help you identify non-random variation.
CL = MEDIAN
20
30
40
50
60
70
80
90 RULE 1 - SHIFT
CL = MEDIAN
15
20
25
30
35
40
45RULE 2 - TREND
CL = MEDIAN
10
15
20
25RULE 3 - TOO MANY OR TOO FEW
CL = MEDIAN
35
55
75
95
115RULE 4 - ASTRONOMICAL POINT
Rule 1 – Shift
Six or more consecutive points either all above or all below the centreline (CL). Values that fall on
the CL do not add to nor break a shift. Skip values that fall on the median and continue counting
Rule 2 – Trend
Five or more consecutive points all going up or all going down. If the value of two or more
successive points is the same (repeats), ignore the like points when counting.
Rule 3 – Too Many or Too FewIf there are too many or too few runs, this is a sign of non-random variation. To see what an appropriate number of runs for a given number of data sets, refer to the table on the next page. An easy way to count the number of runs is to count the number of times the line connecting all the data points crosses the median and add one. If the number of runs you have are:- Within the range outlined in the table, then you have a random pattern.- Outside the range outline in the table, then you have a non-random pattern or signal of change.
Rule 4 – Astronomical point
This is a data point that is clearly different from all others. This is a judgement call. Different
people looking at the same graph would be expected to recognise the same data point as
astronomical.
Data line crosses the centreline (CL) once.
10 data points = runs should be between 3 and 9
Total runs = 2 so too few runs
Page 14Contents PageProduced by Forid Alom
APPENDIX 3 – Rules of Non-Random Variation for a Run Chart
Page 15Contents PageProduced by Forid Alom
Table 1 - Runs Rule Guidance – Table for checking too many or too few runs on a Run chart
Total no. of data points on run chart
not falling on
Lower limit for no. of runs (< than
this is “too few”)
Upper limit for no. of runs
(>than this is “too many”)
Total no. of data points on run chart
not falling on
Lower limit for no. of runs (< than
this is “too few”)
Upper limit for no. of runs (>than
this is “too many”)
10 3 9 37 13 25
11 3 10 38 14 26
12 3 11 39 14 26
13 4 11 40 15 27
14 4 12 41 15 27
15 5 12 42 16 28
16 5 13 43 16 28
17 5 13 44 17 29
18 6 14 45 17 30
19 6 15 46 17 31
20 6 16 47 18 31
21 7 16 48 18 32
22 7 17 49 19 32
23 7 17 50 19 33
24 8 18 51 20 33
25 8 18 52 20 34
26 9 19 53 21 34
27 10 19 54 21 35
28 10 20 55 22 35
29 10 20 56 22 36
30 11 21 57 23 36
31 11 22 58 23 37
32 11 23 59 24 38
33 12 23 60 24 38
34 12 24
35 12 24
36 13 25
APPENDIX 4 – Rules of Special Cause for a Control Chart
There are five rules for a control chart that help you identify special cause variation.
UCL
CL = MEAN
LCL25
30
35
40
45
50
55
60
65
70 RULE 1 - SHIFT UCL
CL = MEAN
LCL21
26
31
36
41
46
51
56
61RULE 2 - TREND
UCL
CL = MEAN
LCL21
26
31
36
41
46
51
56
61
RULE 4 - TWO OUT OF THREE
UCL
CL = MEAN
LCL21
26
31
36
41
46
51
56
61
66 RULE 3 - THREE SIGMA VIOLATION
UCL
CL = MEAN
LCL21
26
31
36
41
46
51
56
61
RULE 5 - 15 OR MORE POINTS HUGGING THE MEAN
Rule 1 – Shift
Eight or more consecutive
points either all above or all
below the centreline (CL).
Values that fall on the CL do
not add to nor break a shift.
Skip values that fall on the
mean and continue counting
Rule 2 – Trend
Six or more consecutive
points all going up or all
going down. If the value
of two or more successive
points is the same
(repeats), ignore the like
points when counting.
Rule 3 – Three Sigma
Violation
When you have a data
point that exceeds the
UCL/LCL.
Rule 4 – Two out of
three
When you get two out
of three consecutive
points in the outer
one-third of chart.
Rule 5 – 15 or more data points hugging the mean
15 or more data points hugging the centreline (inner one-third of the chart).
In a normal distribution, you should have around 68% of the data near the
mean of the distribution (+/- 1 standard deviation). When you get a pattern
like this, you’re exceeding the 68%.
Page 16Contents PageProduced by Forid Alom
APPENDIX 5 – Chart Example 1 (Count Data)
Page 17Contents Page
Date No. of Incidents
6-Jan-2014 8220-Jan-2014 693-Feb-2014 72
17-Feb-2014 533-Mar-2014 82
17-Mar-2014 9331-Mar-2014 7114-Apr-2014 6328-Apr-2014 5812-May-2014 4226-May-2014 68
9-Jun-2014 6323-Jun-2014 877-Jul-2014 62
21-Jul-2014 544-Aug-2014 65
18-Aug-2014 611-Sep-2014 73
15-Sep-2014 5829-Sep-2014 65
30
40
50
60
70
80
90
100
6-J
an-1
4
20-
Jan
-14
3-F
eb-1
4
17-
Feb
-14
3-M
ar-1
4
17-
Mar
-14
31-
Mar
-14
14-
Ap
r-14
28-
Ap
r-14
No
. of
Inci
den
ts /
Co
un
t
Number of incidents - Line chart
70.000
30
40
50
60
70
80
90
100
6-J
an-1
4
20-
Jan
-14
3-F
eb-1
4
17-
Feb
-14
3-M
ar-1
4
17-
Mar
-14
31-
Mar
-14
14-
Ap
r-14
28-
Ap
r-14
12-
May
-14
No
. of
Inci
den
ts /
Co
un
t
Number of incidents - Run Chart
67.933
UCL92.660
LCL
43.207
30
40
50
60
70
80
90
100
6-J
an-1
4
20-
Jan
-14
3-F
eb-1
4
17-
Feb
-14
3-M
ar-1
4
17-
Mar
-14
31-
Mar
-14
14-
Ap
r-14
28-
Ap
r-14
12-
May
-14
26-
May
-14
9-J
un
-14
23-
Jun
-14
7-J
ul-
14
21-
Jul-
14
No
. of
Inci
den
ts /
Co
un
t
Number of incidents - C Chart (Trial Limits)
67.050
UCL91.615
LCL42.485
30
40
50
60
70
80
90
100
6-J
an-1
4
20-
Jan
-14
3-F
eb-1
4
17-
Feb
-14
3-M
ar-1
4
17-
Mar
-14
31-
Mar
-14
14-
Ap
r-14
28-
Ap
r-14
12-
May
-14
26-
May
-14
9-J
un
-14
23-
Jun
-14
7-J
ul-
14
21-
Jul-
14
4-A
ug-
14
18-
Au
g-14
1-S
ep-1
4
15-
Sep
-14
29-
Sep
-14
No
. of
Inci
den
ts /
Co
un
t
Number of Incidents - C Chart
Type of data
Variables dataAttributes data
Multiple Observations
Single Observation
ClassificationCount
Here is an example of the SPC charts you’d expect when measuring count data i.e. No. of incidents.
Produced by Forid Alom
30.701%
UCL
35.515%
LCL
25.886%
20%
22%
24%
26%
28%
30%
32%
34%
36%
38%
40%
Jan
-14
Feb
-14
Mar
-14
Ap
r-14
May
-14
Jun
-14
Jul-
14
Au
g-14
Sep
-14
Oct
-14
No
v-14
Dec
-14
Jan
-15
Feb
-15
Mar
-15
Ap
r-15
May
-15
Jun
-15
Jul-
15
Au
g-15
Sep
-15
Oct
-15
No
v-15
Dec
-15
Did
No
t A
tten
d /
%
% of Did Not Attend (DNA) Appointments - P Chart32.500%
UCL
37.103%
LCL
27.898%
20%
22%
24%
26%
28%
30%
32%
34%
36%
38%
40%Ja
n-1
4
Feb
-14
Mar
-14
Ap
r-14
May
-14
Jun
-14
Jul-
14
Au
g-14
Sep
-14
Oct
-14
No
v-14
Dec
-14
Jan
-15
Feb
-15
Mar
-15
Did
No
t A
tten
t /
%
% of Did Not Attend (DNA) Appointments - P Chart (Trial Limits)
20%
22%
24%
26%
28%
30%
32%
34%
36%
38%
Jan
-14
Feb
-14
Mar
-14
Ap
r-1
4
May
-14
Jun
-14
Jul-
14
Au
g-1
4
Sep
-14
Did
No
t A
tten
d /
%
% of Did Not Attend (DNA) Appointments - Line chart
33.924%
20%
22%
24%
26%
28%
30%
32%
34%
36%
38%
Jan
-14
Feb
-14
Mar
-14
Ap
r-14
May
-14
Jun
-14
Jul-
14
Au
g-14
Sep
-14
Oct
-14
Did
No
t A
tten
d /
%
% of Did Not Attend (DNA) Appointments - Run Chart
APPENDIX 5 – Chart Example 2 (Classification Data)
Page 18Contents Page
Type of data
Variables dataAttributes data
Multiple Observations
Single Observation
ClassificationCount
Here is an example of the SPC charts you’d expect when measuring classification data i.e. DNA %
Month DNA Total Appts % DNA
Jan-14 351 963 36.45%Feb-14 328 932 35.19%Mar-14 268 826 32.45%Apr-14 272 803 33.87%May-14 338 912 37.06%Jun-14 277 862 32.13%Jul-14 303 877 34.55%
Aug-14 212 624 33.97%Sep-14 271 817 33.17%Oct-14 300 976 30.74%Nov-14 258 903 28.57%Dec-14 256 816 31.37%Jan-15 247 917 26.94%Feb-15 281 952 29.52%Mar-15 291 906 32.12%Apr-15 350 942 37.15%May-15 249 741 33.60%Jun-15 286 845 33.85%Jul-15 251 960 26.15%
Aug-15 201 830 24.22%Sep-15 193 770 25.06%Oct-15 243 918 26.47%Nov-15 193 903 21.37%Dec-15 222 985 22.54%
Produced by Forid Alom
184.838
UCL276.678
LCL92.998
50
100
150
200
250
300
Jan
-14
Feb
-14
Mar
-14
Ap
r-14
May
-14
Jun
-14
Jul-
14
Au
g-14
Sep
-14
Oct
-14
No
v-14
Dec
-14
Jan
-15
Feb
-15
Mar
-15
Ap
r-15
May
-15
Jun
-15
Jul-
15
Au
g-15
Sep
-15
Oct
-15
No
v-15
Dec
-15
Jan
-16
Sick
nes
s /
Day
s
Days lost due to staff sickness - I Chart186.918
UCL309.561
LCL
64.275
50
100
150
200
250
300
350Ja
n-1
4
Feb
-14
Mar
-14
Ap
r-14
May
-14
Jun
-14
Jul-
14
Au
g-14
Sep
-14
Oct
-14
No
v-14
Dec
-14
Jan
-15
Feb
-15
Mar
-15
Sic
kness /
Days
Days lost due to staff sickness - I Chart (Trial Limits)
182.813
50
100
150
200
250
300
Jan
-14
Feb
-14
Mar
-14
Ap
r-14
May
-14
Jun
-14
Jul-
14
Au
g-14
Sep
-14
Oct
-14
Sick
nes
s /
Day
s
Days lost due to staff sickness - Run Chart
50
100
150
200
250
300
Jan
-14
Feb
-14
Mar
-14
Ap
r-1
4
May
-14
Jun
-14
Jul-
14
Au
g-1
4
Sep
-14
Sick
ne
ss /
Day
s
Days lost due to staff sickness - Line chart
APPENDIX 5 – Chart Example 3 (Variables Data)
Page 19Contents Page
Type of data
Variables dataAttributes data
Multiple Observations
Single Observation
ClassificationCount
Here is an example of the SPC charts you’d expect when measuring variables data i.e. sickness days
Date Sickness (Days)01-Jan-14 252
01-Feb-14 108
01-Mar-14 120
01-Apr-14 130
01-May-14 175
01-Jun-14 183
01-Jul-14 230
01-Aug-14 220
01-Sep-14 183
01-Oct-14 201
01-Nov-14 262
01-Dec-14 189
01-Jan-15 203
01-Feb-15 128
01-Mar-15 220
01-Apr-15 198
01-May-15 156
01-Jun-15 134
01-Jul-15 148
01-Aug-15 198
01-Sep-15 169
01-Oct-15 170
01-Nov-15 197
01-Dec-15 242
01-Jan-16 203
Produced by Forid Alom