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Process Behavior Analysis – Understanding Variation
Steven J Mazzuca
ASQ2015-11-11
2
Why Process Behavior Analysis?
Every day we waste valuable resources because we misunderstand or
misinterpret what our data are telling us
We do this in two ways:
- We try to explain changes in the data that we should ignore because they are not
significant
- We fail to research and take action on changes in our data that we should pursue
because they are significant
There is a better way! We can improve the way we use data in our lives, make
better decisions, and do all of this with less effort than we expend today. The
key, … is Understanding Variation.
3
Variation is All Around Us
Consider Your Daily Commute to Work
Most days, the time it takes to commute to work is about the same, but those
individual times each differ by some small amount
Every so often, however, the time is significantly longer, and this is usually due
to some abnormal event like an accident, weather, construction, etc.
The small variation most days is due to a collection of “common causes,” or
sources of variation that are present at the same level, and we tend to give that
variation little thought
The exceptional variation is due to “special causes,” and we can identify these
and understand the variation they cause
4
For Commuting, We Handle This Variation Naturally, and Logically
We ignore the Common Cause Variation and intuitively understand that the
times have some natural variability in them each day
When Exceptional Variation occurs, we naturally look for the “reason”—we
want to know what happened
Unfortunately, when we look at data in our businesses, we seldom react in the
same logical manner—we assume any movement in the data must have
meaning
The reality is, all data behave this way. All data have some level of variation
that is normal, and we need to understand this variation before we can
draw proper conclusions from our data.
5
An Example: Data Comparisons in our Life
Average Temperature for July was 96.4 (F)
Suppose we are further told:
- This is 2.3 degrees higher than last July—things must be getting hotter!
- This is 3.1 degrees lower than the previous July—things must be getting colder!
The problem with both of these comparisons is that they are very limited in nature
—they provide no context!
6
Comparisons Between Two Values Can Never be Global in Nature
Unfortunately, this is how we are often presented with data, for example:
- Government Figures on inflation, unemployment, etc.
- Annual Corporate Reports
- Daily Stock Market Reports
- Monthly Customer Reports
The First Principle for Understanding Data
No data have meaning apart from their context.
7
Unfortunately, Context Alone Is Not Enough
0
5
10
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25
30
352
-Se
p
16
-Se
p
30
-Se
p
14
-Oct
28
-Oct
11
-No
v
25
-No
v
9-D
ec
23
-De
c
Daily P
ct.
Defe
cti
ve P
air
s
A Time Series Plot of Percent Defective Pairs by Day
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In Addition to Context, We Need a Method of Analysis
Data InterpretationAnalysis
Input OutputTransformation
9
Shewhart’s Solution
Walter Shewhart invented Process Behavior Analysis at AT&T’s Bell
Laboratories in the 1920’s.
Process Behavior is the Voice of the Process
- It starts with a time series
- Adds a central line for detecting shifts
- Natural process limits are computed from the data and placed symmetrically on
either side of the central line
10
As It Turns Out, There Are Two Voices That We Must Consider
The Voice of the Process tells us what the current system is capable of or in
other words what its results are expected to be if we don’t change the system.
It is represented by the natural process limits on a Process Behavior chart. It is
the extent of normal variation within the process itself.
Specifications are the Voice of the Customer. They define what the customer
expects or requires.
Comparing numbers to the Voice of the Customer will not lead to improvement of
the process--it only leads to wasted effort and confusion. In fact, in many
cases, it actually leads to a degradation of the system over time.
In other words, our best intentions are actually making
things worse, not better!
11
Understanding Variation:
An ‘Individuals’ Process Behavior chart shows the individual data points
Unless this process is changed fundamentally, it can be expected to produce between 5.8%
and 31.6% defective pairs each day, while averaging 18.7% defective pairs.
This process demonstrates a state which is considered predictable
18.7
31.6
5.8
0
5
10
15
20
25
30
35
2-Sep
16-Sep
30-Sep
14-Oct
28-Oct
11-Nov
25-Nov
9-Dec
23-Dec
Dai
ly P
ct. D
efec
tive
Pai
rs
12
Signals Help Us to Identify Exceptional Variation
Points that fall outside the upper and lower natural process limits
A consecutive run of 8 points all below or above the central line
Trends of 6 points in a row, all increasing or decreasing
Non-random behavior
13
Point above the natural process limit Point below the natural process limit
Run above the mean (8 consecutive points) Run below the mean (8 consecutive points)
Trend up (6 consecutive points) Trend down (6 consecutive points)
Examples of Exceptional Variation
Tickets
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451-J
ul-07
15-J
ul-07
29-J
ul-07
12-A
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9-S
ep-0
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ov-0
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ov-0
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an-0
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Tickets
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1-J
ul-07
15-J
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29-J
ul-07
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ug-0
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9-S
ep-0
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ep-0
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ct-
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21-O
ct-
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4-N
ov-0
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ct-
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ep-0
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14
Two Types of Mistakes
1. Interpreting common cause variation as if it were exceptional cause
2. Interpreting exceptional cause variation as if it were common cause
Process Behavior Analysis strikes an economic balance between
these two types of mistakes
15
Process Behavior Analysis - Step 1
Plot the Data and their Average on an Individuals Chart
The value for July of year three is 28 and is the highest
value that has ever occurred. BUT -- is it exceptional?
28
20.04
10
15
20
25
30Ja
n
Mar
May
Ju
l
Sep
Nov
Ja
n
Mar
May
Ju
l
Sep
Nov
Ja
n
Mar
May
Ju
l
Ind
ivid
ual
Valu
es (
X)
(break in line is only to make chart easier to quickly interpret, not that data is missing)
16
Process Behavior Analysis - Step 2
Generate Moving Range Values to Understand Variation
We need to filter out the common cause variation
To do that, we have to measure the variation month-to-month
This is done using successive differences, known as Moving Ranges (mR)
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Year One 19 27 20 16 18 25 22 24 17 25 15 17
Moving Range Values8 7 4 2 7 3 2 7 8 10 2
17
Process Behavior Analysis - Step 3
Plot the Moving Range (mR) Values and their Average
The center line is the average of the moving range data points. The Moving Ranges are
plotted as a time series as well. The first two years were used here for the average.
4.35
0
5
10
15
Jan
Apr Ju
lOct
Jan
Apr Ju
lOct
Jan
Apr Ju
l
mR
18
The Base for Process Behavior Analysis
The Individuals Chart and Moving Range Chart
28
20.04
10
15
20
25
30
Jan
Mar
May
Jul
Sep
Nov
Jan
Mar
May
Jul
Sep
Nov
Jan
Mar
May
Jul
Ind
ivid
ual
Valu
es (
X)
4.35
0
5
10
15
Jan
AprJu
lO
ctJa
nApr
Jul
Oct
Jan
AprJu
l
mR
Individuals
Chart
Moving
Range
Chart
19
Process Behavior Analysis - Step 4
Calculate the Natural Process Limits for the Individuals Chart
The Upper and Lower Natural Process Limits (UNPL and LNPL) for the
Individuals Chart are computed by
- multiplying the Average Moving Range by 2.66 and
- adding and subtracting that value from the Central Line of the Individuals chart
UNPL(Individual) = Average of the Individuals + (2.66 x Average Moving Range)
= 20.04 + (2.66 x 4.35 ) = 31.6
LNPL(Individual) = Average of the Individuals - (2.66 x Average Moving Range)
= 20.04 - (2.66 x 4.35 ) = 8.5
20
Process Behavior Analysis - Step 5
Plot the Upper and Lower Natural Process Limits on the Individuals Chart
Note that based on this process behavior chart, the value “28” is NOT significant!
If “28” does not meet our needs; we should not look at the event, but rather we
should look at the process as a whole.
28
20.04
31.6
8.5
5
10
15
20
25
30
35
Ja
n
Ma
r
Ma
y
Ju
l
Se
p
No
v
Ja
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Ma
r
Ma
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Ju
l
Se
p
No
v
Ja
n
Ma
r
Ma
y
Ju
l
Ind
ivid
ua
l V
alu
es
(X
)
+ 2.66 x 4.35
- 2.66 x 4.35
21
Process Behavior Analysis - Step 6
Calculate the Natural Process Limit for the Moving Range Chart
The Moving Range Chart only has an Upper Natural Process Limit, which is
computed by multiplying the Average Moving Range by 3.27
- UNPL(Moving Range) = 3.27 x Average Moving Range
= 3.27 x 4.35 = 14.2
22
Process Behavior Analysis - Step 7
Plot the Upper Natural Process Limit on the Moving Range Chart
There is no Lower Natural Process Limit on the Moving Range chart because we computed the
positive difference between successive points
- the red line is the extent of normal period-to-period variation
- The green line is the average period-to-period variation
Conclusion: there are no Moving Range “signals” (no evidence of an “unpredictable” situation)
4.35
14.2
0
5
10
15
Jan
Apr Ju
lOct
Jan
Apr Ju
lOct
Jan
Apr Ju
l
mR 3.27 x 4.35
23
Process Behavior Analysis - Step 8
The MOST IMPORTANT Step: Interpret the Data
Question: Can’t This Process Do Better?
Answer: No - the natural month-to-month
variation in this process guarantees that the
overall range for the process will be as wide
as it is
Improvement will only come as a result of
changing the overall system—seeking
explanations for extreme values within the
limits is a waste of time and resources!
Asking the question “Why did the 28
occur?” is a non-value added activity,
because the process is behaving
predictably. We call this “chasing noise”
– chasing after explanations for data
points that are actually within predictable
limits.
28
20.04
31.6
8.5
5
10
15
20
25
30
35
Ja
n
Ma
r
Ma
y
Ju
l
Se
p
No
v
Ja
n
Ma
r
Ma
y
Ju
l
Se
p
No
v
Ja
n
Ma
r
Ma
y
Ju
l
Ind
ivid
ua
l V
alu
es
(X
)
4.35
14.2
0
5
10
15
Jan
Apr Ju
lOct
Jan
Apr Ju
lOct
Jan
Apr Ju
l
mR
24
Some Rules of Thumb for Process Behavior Analysis
More data is better than less data, but never let a small amount of data keep
you from drawing a Process Behavior chart. Simply understand that the
natural process limits are ‘soft’ until the number of data points increases.
Start with all the data, plot one set of limits, and see what the chart says.
If there are no signals, and you have 10-15 data points, set the limits and keep
them until the data indicate there has been a change.
If there is a signal, investigate it immediately. Your data are trying to tell you
something!
Remember, you don’t get any credit for computing the limits, you get credit for
taking action! Process Behavior Analysis is a tool, not an end in itself.
25
When to Adjust Natural Process Limits
Natural process limits are not often adjusted
- They are NOT automatically adjusted, e.g., at the beginning of each year or at the
beginning of a project
Before we can adjust the limits, we need to answer four “natural process limit
adjustment questions”:
1. Do the data indicate a change has occurred? Is there aa) Run above the mean (8 consecutive points)
b) Run below the mean (8 consecutive points)
c) Trend up (6 consecutive points)
d) Trend down (6 consecutive points)
2. Do we understand the cause of the change?
3. Is the change expected to continue?
4. Is the change desirable – is it in the right direction?
If we can answer “Yes” to all of these questions, it is appropriate to re-
compute the limits, starting with the first point that indicated a change in the
process.
26
But, Aren’t Specifications Important?
Yes! They are the “Voice of the Customer,” but …
They don’t help us understand how to improve, so …
We must work to align the processes to the specifications
Results are IN Compliance
with Specification
Results are OUT of Compliance
with Specification
Process is
Predictable
Ideal State – Process
Behavior Charts help
maintain the process in this
state
Threshold State - Must change
the process (more likely) or
change the specifications
(occasionally)
Process is
NOT
predictable
Brink of Chaos – Quality of
process could change to be
out of specification at any
time; prediction not
possible
State of Chaos – Must first get
process to be predictable (in
control)
Voice of the Customer
Voice
of
the
Process
27
In Order to Meet the Customer’s Needs, the Voice of the Process
Must be Aligned with the Voice of the Customer. For example…
Measurement A
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17
19
21
23
25
27
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Time Interval
Un
its
Customer
Specification
This process is not capable of
consistently meeting the customer’s
needs. Corrective actions are to
reduce variability or move the
process center line up (shifting the
aim).
Out of specification!
28
Summary: Understanding Variation
Before we can interpret data, we must have a method of analysis
Process Behavior Analysis provide just such a method, as they focus on the
behavior of the process
The purpose of analysis is insight, and the best analysis is the simplest one
that provides the needed insight
29
Analysis of Temperature Trends at Mohonk Mohonk is one of the oldest continuously operating meteorological stations in
the US.
It has been in operation since 1896.
For the ease of display I calculated three sets of data:
- Average of the average daily temperatures over each calendar year.
- Average of the daily low temperatures over each calendar year.
- Average of the daily high temperatures over each calendar year.
30
Annual Average Temperature (F)
30
40
50
60
1896
1902
1907
1912
1917
1922
1927
1932
1937
1942
1947
1952
1957
1962
1967
1972
1977
1982
1987
1992
1997
2002
2007
Deg
rees (
F)
Annual Average Temperature (F) Mean Upper Natural Process Limit Low er Natural Process Limit
Temperature Trend Analysis – Mean calculated on full data set.
31
Temperature Trend Analysis – 14 Year Mean Calculation (1896 – 1909)
Annual Average Temperature (F)
40
50
60
1896
1902
1907
1912
1917
1922
1927
1932
1937
1942
1947
1952
1957
1962
1967
1972
1977
1982
1987
1992
1997
2002
2007
Deg
rees (
F)
Annual Average Temperature (F) Mean Upper Natural Process Limit Low er Natural Process Limit
32
Temperature Trend Analysis – 14 Year Mean Calculation (1896 – 1909)
Annual Average Mininum Temperature (F)
30
40
50
1896
1902
1907
1912
1917
1922
1927
1932
1937
1942
1947
1952
1957
1962
1967
1972
1977
1982
1987
1992
1997
2002
2007
Deg
rees (
F)
Annual Average Mininum Temperature (F) Mean
Upper Natural Process Limit Low er Natural Process Limit
Signal: 1920 seems to have been an exceptionally cold year. (33.95 F)
33
Temperature Trend Analysis – 14 Year Mean Calculation (1896 – 1909)
Annual Average Maximum Temperature (F)
50
60
1896
1902
1907
1912
1917
1922
1927
1932
1937
1942
1947
1952
1957
1962
1967
1972
1977
1982
1987
1992
1997
2002
2007
Deg
rees (
F)
Annual Average Maximum Temperature (F) Mean
Upper Natural Process Limit Low er Natural Process Limit
Signal: 1904 seems to have been an exceptionally cold year. (50.98 F)
34
Analysis of Temperature Trends at Mohonk For the ease of display I calculated three sets of data:
- Average of the average daily temperatures over each calendar year.
- Average of the daily low temperatures over each calendar year.
- Average of the daily high temperatures over each calendar year.
Each set of data identified different signals.
All data sets identified a signal in last several years.
We don’t know what if any effects are contained in the data.
- Solar Sunspot Activity (11 year cycle)
- Volcanic Eruptions
- Industrial Pollution
- Other industrial effects (deforestation, greenhouse gases, cities, etc)
There seems to be a warming trend.
35
Solar Energy Is Not Constant
36
A century of Mohonk’s weather records suggest a
warming trend.
•Preliminary analysis of the Preserve’s weather data shows that the average
temperature has risen about two degrees over the past 110 years.
•Composed of more than 40,000 days of weather observations, these records
comprise the collection of the Preserve’s Mohonk Lake Cooperative Weather Station,
established in 1896 by the U.S. Weather Bureau (now the National Weather Service).
•Weather readings at Mohonk began in the mid-1880s, taken by the Smiley family,
founders of the neighboring Mohonk Mountain House, and are now continued by
Preserve research staff.
•Beginning in the late 1970s, data collection expanded to include regular monitoring
the pH of precipitation, lakes, and streams.
•Why is this data important?
To identify the extent of global climate change, researchers need access to
reliable data covering the longest period possible.
• The Preserve’s weather data is dependable because the station has been in the
same, comparatively stable location for over a century and the same protocol has
been followed by the relatively few people involved in collecting the data.
http://www.mohonkpreserve.org/index.php?weatherdata
