The Life Cycle of a Trend
Steven S Prevette
Fluor Hanford Environment Safety and Health
ASQ Certified Quality Engineer
509-373-9371
http://www.hanford.gov/safety/vpp/trend.htm
The aim of this paper is to provide assistance on establishing a statistical baseline for a
work process. Baselines are necessary in order to determine if and when a trend has
developed in the work process being monitored. Baselines serve as a predictor of future
performance.
This paper is written with the assumption that your organization is making use of
Statistical Process Control (SPC) to monitor work performance. This paper focuses on
one aspect of SPC, determination of the baseline average line for a performance indicator
chart. For general information on SPC, please refer to
http://www.hanford.gov/safety/vpp/trend.htm
Trending or a work process or process element can result in continual improvement in
performance of work. The life-cycle-of-a trend is a cyclical effort. The figure below
provides an overview of this SPC trending tool.
0. Gestation:
Choose a Measure
Gather data
4. Maturity:
Data stabilizes
1. Establish Baseline
Take action
to correct,
reinforce,
or stabilize
Establish
Expectations,
Routine
Monitoring
3. Youth:
Determine special
cause(s)
2. Birth:
A trend is
detected
0. Gestation
The very first step (“stage zero”) in trending a set of data from a work process is to setup
the initial control chart from available data. Many organizations have massive amounts
of data about existing processes, but have never analyzed it. Having decided upon what
process element(s) to measure, the initial data set is gathered. Preferably, there should be
at least 25 or more data points collected over time. Even if you do not have 25 points, it
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SS Prevette
is still worth proceeding, but a reasonable attempt should be made to retrieve 25 time
intervals of data. Data intervals may be based upon time (weekly, monthly, quarterly) or
upon numbers of units produced.
Choosing a Measure
Choosing what to measure should not be a daunting task. If one carefully reviews the
stated business objectives, mission statement, vision statement, contractual clauses of the
organization, one can find measures. Promises of timeliness and accuracy can lend
themselves to development into measurable indicators. Common factors also include
safety, financial, achievement of schedules and milestones. This review is then further
refined into “operational definitions”. Operational definitions supply sufficient detail
such that data gatherers can go forth and collect and collate the data, and have a
reasonable expectation that the result is repeatable and measures what was intended. No
data set is ever “perfect”, so try to plan ahead with a good, agreed upon definition. Most
disagreements over performance results arise from a lack of firm definition of how to
retrieve the data in the first place.
Gathering Data
In many cases one will find that existing reporting systems can be utilized. Many
organizations are awash in data, but the data have never been analyzed or put to use.
There is an advantage to using existing data, as it has already been paid for, and historic
data for establishment of the baseline should be available.
An “operational definition” for each measure should be established. This is the agreed
upon definition as to what data will be collected and under what criteria. For example, if
you desire to trend the amount of corrective maintenance performed, you will need to
define what is the unit to be counted (such as number of work packages) and what makes
a maintenance item be considered “corrective maintenance”. The operational definition
can be based upon existing fields and conventions in the existing reporting system.
Analysis of reporting system data also serves to validate the data quality of the reporting
system. Automation of data gathering can save time, money, and have improved
accuracy and traceability of results. However, do not only focus on the data that are
immediately on hand. It may be necessary to establish new data sources to reflect the
total performance of the organization. See
http://www.hanford.gov/safety/vpp/busobj2.htm for further ideas on choosing measures.
Good questions to ask when developing measures include:
o What are my customer’s needs and wants?
o If I were gone on vacation for a month, what data would I look at upon
return?
o What are my critical success factors?
o What have been causes of historical crises and failures?
Data for control charts should be independent from time increment to time increment.
For example, inventory in a warehouse at the end of this month is highly dependent upon
Life Cycle of a Trend
SS Prevette
the inventory at the end of last month. Run charts can be plotted of the inventories, but it
can be better to analyze the flow rates through the warehouse (incoming and outgoing).
When gathering the data, do not “cumulate” the data (such as summing year-to-date).
Also, the original time order of the data should be maintained.
Choosing Data Reporting Intervals
The monthly time increment for data gathering and reporting is very common. But one
should consider the following when establishing the reporting interval.

What is the longest time you could withstand (from a risk perspective) with an
undetected trend? If a trend started the day following the closure of data collection,
how long could you continue to operate without substantial risk? One should
recognize that there may be other anecdotal signals of a trend that may provide
backup and trigger an early analysis cycle.

It may be appropriate to shorten the time interval (such as from monthly to weekly) in
order to gain a sufficient volume of data points (25 minimum).

Increasing the amount of reporting (increasing the frequency of data gathering and
reporting) has several costs. One must consider the cost to gather, analyze, and
publish the data. Also, one may discover that by the time a report is generated, one or
more reporting time intervals have elapsed if the reporting interval is too short.

Many organizations use a time interval basis for reporting. However, if one is
measuring characteristics of items produced, it may make more sense to report in
increments of output produced. For example, one may choose to plot a new datum
after each fifth item produced. This is the basis for xbar-R control charts.
If one is counting items or events, adjust the time interval for the analysis in order to keep
the average rate above 1.0 per time interval. As an alternative, low rate trending (see
http://www.hanford.gov/safety/vpp/lowrate.htm) could be used.
1. Establish the Baseline
The baseline on a control chart consists of the average (center) line, a three-standard
deviation Upper Control Limit (UCL) and a three-standard deviation Lower Control
Limit (LCL). A procedure for choosing the proper form of control chart, and calculating
the baseline and control limits is available at http://www.hanford.gov/safety/vpp/spc.htm.
An example control chart is portrayed below.
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UCL
16
14
Average Line
Performance Data
12
10
8
6
4
LCL
2
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
0
In general, it is best to use all of the data you have. At a minimum, one should keep at
least 25 points on hand prior to discontinuing use of older data. If you have less than 25,
use what you have.
The goal is to establish one or more baseline time intervals with no trends within the
interval. Experience has indicated a rule of thumb called the “MW Rule” for how many
data points are needed to establish a “good” baseline. For purposes of this paper,
“goodness” reflects the capability of the baseline to serve in detecting future trends. That
is, once a baseline is established, and later a trend is detected, it is not likely that the trend
was due to there being too few data points in the baseline, causing the baseline to have
been inaccurate.
The “MW” Rule
A rule of thumb is that one needs at least three changes of direction in the data within a
baseline (“MW” Rule)
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“MW” Rule
2
1
3
Empirical experience is that if the data have made three changes of direction (like a letter
“M” or “W”), then there are sufficient data to generate a baseline. It is also desirable for
the resulting average line to pass between the “corners” or vertices. In the example
above, the average line will have corner “2” above and corners “1” and “3” below.
The Initial Baseline
Try to use the first 25 points for the baseline. If 25 points were not available (either due
to lack of data, or trends within the data), use the “MW” rule. It can be worth leaving
some recent data out of the baseline, for testing the suitability of the baseline. Also, in
some reporting systems the current data are incomplete or subject to change.
With less than 25 points the resulting control limits can be quite “soft” and should be
viewed with some skepticism until proven to be valid. Achieving a run of 25 points, with
no statistically significant changes against the average and control limits would serve to
“validate” the control limits. Note that it is not necessary to recalculate the average and
control limits once you reach 25 (or any other number). One only recalculates the
baseline following a statistically significant change.
Plot the data, and add the initial average and control limits as appropriate to the chart
type. Next, apply the following detection rules. An suggested set of rules to use are:






One point outside the control limits
Two out of Three points two standard deviations above/below average
Four out of Five points one standard deviation above/below average
Seven points in a row all above/below average
Ten out of Eleven points in a row all above/below average
Seven points in a row all increasing/decreasing.
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Several other sets of rules exist (for example, Dr. Wheeler uses 8 in a row instead of 7).
Also, some may choose to implement the easier rules first (such as points outside the
control limits and seven in a row) prior to implementing the more difficult rules.
Whatever the choice, one should determine the set of rules they will use and stick to it.
When one of these rules is triggered”, it can be considered a “trend”. In most
requirements referring to “trends” or “trending”, a “trend” is something that has changed,
or something that is “new” that should reviewed, causal factors determined, and actions
taken. The statistical criteria above provide a method to separate a “trend” from ongoing
random noise in the data.
If there are not statistically significant changes detected in the initial baseline, the
baseline should be accepted, and utilized for reporting. However, in many cases there
will be trends detected. These trends represent shifts and the question “What happened”
should be asked. The process should be investigated and the causes of the trends
determined. Appropriate actions should be taken to bring the process “under control”.
However, even if the current process has trends within it, it is necessary to determine
some baseline to work with such that one can detect further trends. If the initial attempt
to establish average and control limits results in trends being identified, the following
strategies can be utilized to establish a valid baseline.
Cleaning Up the Baseline
If the initial baseline has a trend within it, recalculate the average and control limits
through the following strategies:




Drop data off of the beginning
Drop data off of the end
Drop individual datum point(s) out
Split into two or more baselines
Note that the complete data set should still be plotted on the chart, we are only making a
choice as to what data to include in the average and control limit calculations.
If zeroes are causing problems:



Leave runs of 7 or more zeroes out (they will always be below average)
Lengthen the data interval (i.e. from monthly to quarterly)
Try “Low Rate Trending” (http://www.hanford.gov/safety/vpp/lowrate.htm)
Chart Examples:
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1. Three data points removed from the beginning of the data set, leaving a stable baseline
from the fourth point onwards:
2. Three data points removed from the end of the data. In this case, there is a current
trend that needs to be acted upon, and there are not enough data to determine a new
baseline (there is only one change in direction in the three recent points).
3. Two data points within the data have been removed, and the remaining data used to
construct the baseline. The special causes of these two points should be investigated to
determine if they could recur. If they can recur, one would need to be careful with the
validity of predicting future performance using this baseline (or at least put a clarifier on
the prediction that as long as these special causes do not recur, this is the prediction).
Life Cycle of a Trend
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4. The data have been split into two baselines. A permanent decrease in the level
appears to have occurred. The current baseline does have three changes in direction, so it
is believed that this is a valid prediction of future performance. The cause for the
decrease should be determined.
5. Below is an example of “low rate trending” from Dr. Wheeler’s Understanding
Variation, the Key to Managing Chaos. The first chart is based upon counting events per
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month, and does not show a trend. The second chart is based upon trending the time
between events, and does show an increasing trend.
Sep-05
May-05
Jan-05
Sep-04
May-04
Jan-04
Sep-03
May-03
Jan-03
Sep-02
May-02
Jan-02
May-01
Jan-01
Sep-01
Number of Events per Month
5
4
3
2
1
0
4
Rate per Year, between Events
3
2
1
0
The x-chart Standard Deviation
The sample standard deviation formula (“stdev” in Excel) can be used for determining
the standard deviation of x-charts. The traditional method uses the moving range of the
data, which most statistical texts prefer. With either method, one does need to check for
outliers in the data, which can cause the control limits to be too far from the average and
fail to detect the trend. An example follows. After removing the datum point that is
close to the UCL, the recalculated UCL shows that the point is an outlier and justifies
removing it from the baseline. As always, the special cause for the outlier should be
determined.
With Outlier in the Average and Stdev
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With Outlier Removed
Establish Expectations, perform routine monitoring
Once the baseline is established, management should determine if the baseline is
“acceptable”. In manufacturing, this is referred to as determining the “process
capability”. Since the baseline is the prediction of future performance, can the
organization continue to prosper (or continue to have crises, as the case may be) if current
performance continues? If current performance is indeed “acceptable”, the management
expectation that should be established is to maintain current performance. If not, then the
expectation that should be established is that improvement is needed. Further, the
expectation (or goal) is that a significant improving trend needs to occur.
In order to improve performance when the process is stable, one will need to review the
common causes of the results, found in the work process elements, across the entire
baseline time interval. This should provide insight as to how to improve the process. For
organizations that pledge to “continual improvement” in principle, there should be a
manageable number of indicators of the work process elements identified as “needing
improvement”. As improvement is achieved, it may be appropriate to shift the
improvement focus to other work process element indicators. Deciding those indicators
that are acceptable as is and those in need of improvement is a rudimentary form of risk
management. High-risk areas should be targeted for improvement. Low-risk areas that
can be accepted “as is” are simply monitored and action is only taken if a non-improving
trend occurs.
During routine monitoring and reporting, the data are gathered using the operational
definitions previously established, at the time interval previously established. During
each reporting cycle, the new data are plotted and reviewed against the trending rules to
see if a trend has developed. This trend could be due to an unforeseen change, or due to
actions taken to improve the process.
The charts are published routinely. Note that there is nothing special about the end of the
calendar year or fiscal year. The data continue to be plotted by their reporting interval.
In some cases where management focuses upon fiscal or calendar year, a text box with
the value of the current and past fiscal year average may be useful, at least until
management completely shifts to reading the control chart only.
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SS Prevette
The baselines are not shifted unless a significant trend per the trending rules develops. A
baseline is “innocent until proven guilty” and is only proven guilty using your established
trend rules.
Some organizations desire to have “executive summaries” and/or color coding of results.
The following phrases and color codes could be utilized for standardized, consistent
wording:




Data are stable, at a good baseline value (“Green”)
Data are stable, improvement is needed (“Yellow”)
There is an improving trend (“Green”)
There is a non-improving trend (“Red”)
Birth of a Trend
Your agreed upon set of trend detection rules are utilized in order to detect the birth of
the trend. To review, the set of rules to consider are:






One point outside the control limits
Two out of Three points two standard deviations above/below average
Four out of Five points one standard deviation above/below average
Seven points in a row all above/below average
Ten out of Eleven points in a row all above/below average
Seven points in a row all increasing/decreasing.
The example charts below demonstrate a trend which has been discovered following
establishment of the initial baseline.
Initial Stable Process
Average = 9.5
(Oct 98 - Oct 00)
20
15
25 points in a
stable baseline
10
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SS Prevette
Aug-01
Jun-01
Apr-01
Feb-01
Dec-00
Oct-00
Aug-00
Jun-00
Apr-00
Feb-00
Dec-99
Oct-99
Aug-99
Jun-99
Apr-99
Feb-99
Dec-98
0
Oct-98
5
Initial Indication of Trend
Average = 9.5
(Oct 98 - Oct 00)
2 of 3 at
2 standard
deviations
above average,
circled
20
15
10
Aug-01
Jun-01
Apr-01
Feb-01
Dec-00
Oct-00
Aug-00
Jun-00
Apr-00
Feb-00
Dec-99
Oct-99
Aug-99
Jun-99
Apr-99
Feb-99
Dec-98
0
Oct-98
5
Youth
Any trends should be reported through the routine performance report. The chart itself
should be annotated. A general practice is to circle those data points that make up the
trend. Special notifications to responsible management may be necessary to flag that the
trend exists.
Once the trend has been detected, the special cause(s) of the trend should be determined.
Note that the cause might turn out to be the result of a previous improvement action
implemented by management. “Root cause” analyses techniques may be useful.
Comparison of the common causes in force during the stable time interval (Oct 98 to Nov
00 in this case) to the special causes in force during the trend (Dec 00 and Jan 01) may
provide insight. Ishikawa (fishbone) diagrams can also be useful for analyzing cause and
effect.
Note that ONLY looking at the data from the trend may result in a conclusion that was
not the reason for the trend. For example, while investigating bearing failures one
company discovered that there was a contaminate in the bearing grease of the failed
bearings. A great campaign was instituted to eliminate the contamination. There was no
effect on bearing failures. An analysis of “good” bearings found the same contamination
existed.
Take Action
After reviewing the special causes, management should determine if action is needed. If
no action is needed, the trend is monitored in order to determine when and at what value
it stabilizes.
In organizations with “corrective action management” (such as required by CFR
830.122), non-improving trends should be reviewed to see if they are “adverse”. Many
corrective action management policies require adverse trends to be documented and the
corrective actions documented. Improving trends should be reinforced in order to
maximize the shift in the improving direction.
Life Cycle of a Trend
SS Prevette
Lessons learned from all trends should be reviewed for application in other processes.
Maturity
As time progresses, and actions are taken, the data will eventually stabilize at a new level.
The charts below follow on the discussion of the previous data example. The next chart
shows more data received for the trend (which has increased to seven points in a row
above average), but has not yet stabilized.
Waiting for
3 changes of
Direction
More Data Gathered
Average = 9.5
(Oct 98 - Oct 00)
> 7 months in a row
above average
20
15
10
Aug-01
Jun-01
Apr-01
Feb-01
Dec-00
Oct-00
Aug-00
Jun-00
Apr-00
Feb-00
Dec-99
Oct-99
Aug-99
Jun-99
Apr-99
Feb-99
Dec-98
0
Oct-98
5
Cycle back to step 1 – Establish Baseline
In the last chart below, three changes of direction of the new data have occurred,
satisfying the “MW” rule. Therefore, new baseline average and control limits are
established. The circle around the trend is removed, as the shift in the average line now
accounts for the trend.
It should be noted that in some cases the data will return to the old baseline, and it may
not be necessary to calculate a new baseline. This is a judgment call on the part of the
analyst. Eventually, it will become obvious as to whether a new baseline is needed, as
further trends would be detected by the trending rules.
Life Cycle of a Trend
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Average = 9.5
(Oct 98 - Oct 00)
New Baseline Established
Average = 13
(Dec 00 - Aug 01)
20
15
10
Aug-01
Jun-01
Apr-01
Feb-01
Dec-00
Oct-00
Aug-00
Jun-00
Apr-00
Feb-00
Dec-99
Oct-99
Aug-99
Jun-99
Apr-99
Feb-99
Dec-98
0
Oct-98
5
With the new baseline established, one continues on with the life-of-a-trend cycle. This
“life cycle”, if executed in a routine, consistent manner, will be of great assistance in
generating continual improvement for the practicing organization.
-----------------------------------------------------------------------------------------------------References:
Quality Control and Industrial Statistics, Acheson Duncan
The New Economics and Out of the Crisis, W. Edwards Deming
Peer Reviews:
Peer Review comments from Rich DeRoeck, Alpha Industries; Phil Monroe, DEMCOM
Consulting; and Gary Reid, Department of Energy Rocky Flats were incorporated.
Life Cycle of a Trend
SS Prevette