Transcript causal loop diagrams
System Dynamics
Causal Loop Diagrams
Morteza Bazrafshan
Causal Loop Diagrams
Feedback is one of the core concepts of system dynamics. Yet our mental models often fail to include the critical feedbacks determining the dynamics of our systems. In system dynamics we use several diagramming tools to capture the structure of systems, including
causal loop diagrams (CLD)
and
stock and flow maps
. CLDs are excellent for: • Quickly capturing your hypotheses about the causes of dynamics ; • Eliciting and capturing the mental models of individuals or teams; • Communicating problem.
the important feedbacks you believe are responsible for a
CAUSAL DIAGRAM NOTATION
A causal diagram consists of variables connected by arrows denoting the causal influences among the variables. Variables are related by
causal links ,
shown by arrows. Each causal link is assigned a polarity, either positive (+) or negative (-) to indicate how the dependent variable changes when the independent variable changes. The important loops are highlighted by a
loop identifier
which shows whether the loop is a positive (
reinforcing
) or negative (
balancing
) feedback.
CAUSAL DIAGRAM NOTATION
Note that the loop identifier circulates in the same direction as the loop to which it corresponds. A positive link means that if the cause increases, the effect increases
above what it would otherwise have been
,
and if the cause decreases, the effect decreases
below what it would otherwise have been
.
In the previous example an increase in the fractional birth rate means the birth rate (in people per year) will increase above what it would have been, and a decrease in the fractional birth rate means the birth rate will fall below what it would have been. A negative link means that if the cause increases, the effect decreases
below what it would otherwise have been
,
and if the cause decreases, the effect increases
above what it would otherwise have been
.
In the example, an increase death rate in the average lifetime of the population means the (in people per year) will fall below what it would have been, and a decrease in the average lifetime means the death rate will rise above what it would have been. Link polarities describe the structure of the system. They do not describe the behavior of the variables.
That is, they describe what would happen
IF
there were a change.
CAUSAL DIAGRAM NOTATION
They do not describe what actually happens .
The fractional birth rate might increase; it might decrease the causal diagram doesn't tell you what
will
happen. Rather, it tells you what
would
happen if the variable were to change.
An increase in a cause variable increase.
does not necessarily mean the effect will actually There are two reasons : First, a variable often has happens you need to know more than one input how all the inputs are . To determine changing .
what actually
When assessing the polarity of individual links, assume all other variables are constant
Second, and more importantly, stocks and flows causal loop diagrams do not distinguish between the accumulations of resources in a system and the rates of change that alter those resources An increase birth rate does in the birth rate will increase the population not decrease the population .
, but a decrease in the Births can only increase the population, they can never reduce it.
CAUSAL DIAGRAM NOTATION
Similarly, the negative polarity of the link from the death rate to population indicates that the death rate subtracts from the population.
A drop in the death rate does not add to the population.
A drop in deaths means fewer people die and more remain alive: the population is higher
than it would otherwise have been.
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Causation versus Correlation
•Every link relationships in your diagram must represent (what you believe to be) between the variables.
causal •You must not include correlations between variables .
•A system dynamics model must enough that the mimic the structure of the real system well model behaves the same way the real system would .
•Behavior includes not only replicating to circumstances and policies that are historical experience entirely novel .
but also responding •Correlations among variables reflect the past
behavior
of a system.
• Though sales of ice cream are positively correlated with the murder rate, you may not include a link from ice cream sales to murder in your models.
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Causation versus Correlation
•many correlations underlying are more causal structure .
subtle , and it is often difficult to determine the •A great deal of scientific research haystack of correlations: seeks the genuine causal needles in a huge - Does vitamin C cure the common cold?
- Can eating oat bran reduce cholesterol, and if it does, will your risk of a heart attack drop?
- Does economic growth lead to lower birth rates, or is the lower rate attributable to literacy, education for women, and increasing costs of child rearing?
- Do companies with serious quality improvement programs earn superior returns for stockholders?
•Modelers are causal, must take extra care to consider whether the relationships in their models no matter how strong the correlation , how high the R 2 , or how great the statistical significance of the coefficients in a regression may be.
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Labeling Link Polarity
Be sure to label the polarity of every link in your diagrams.
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Determining Loop Polarity
Imagine a small disturbance in
one
of the variables.
-If the disturbance propagates around the loop to then the loop is positive .
reinforce the original change , -If the disturbance propagates around the loop to the loop is negative .
oppose the original change , then There are two methods for determining whether a loop is positive or negative: 1-
Count the Number of Negative Links -
The fast method always works. . .
except when it doesn't !
- In a complex diagram it is all too easy to negative links in a loop.
miscount the number of - And it is easy to mislabel the diagram.
the polarity of links when you first draw - Counting the number of negative signs is errors.
unlikely to reveal these
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
2-
Trace the Effect of a Change around the Loop -
trace the effect of a around the loop.
Attractiveness
small change in one of the variables as it propagates
Cumulative
any variable
Profits Number of Competitors Market Share Unit Costs Price Price Pressure to Clean Up Environment Environmental Quality Cleanup Effort Net Withdrawals Bank Cash Reserves Perceived Solvency of Bank
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
CHALLENGE Assigning Link Polarities
Consider the attractiveness of a product to customers as it depends on various attributes of the product. Assign link polarities.
Quality
What feedback product?
loops might be created as product attractiveness changes the demand for the firm's
Price Delivery Delay Product Attractiveness Functionality
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Mathematics of Loop Polarity
When you determine theory as loop polarity , you are calculating what is known in
the sign of the open loop gain of the loop
.
control The term "gain" refers to the strength of the signal returned by the loop: - A gain of two means a change in a variable is doubled each cycle around the loop - A gain of negative 0.5 means the disturbance propagates around the loop to oppose itself with a strength half as large.
The term " open loop " means the gain is calculated for just one feedback cycle Consider an arbitrary feedback loop consisting of n variables, X 1 , … ,X n .
let X 1 denote the variable you choose. When you break the loop, X 1 input, X 1 I and output, X 1 O splits into an The open loop gain is defined as the (partial) derivative of X 1 O with respect to X 1 I
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Mathematics of Loop Polarity
The polarity of the loop is the sign of the open loop gain:
Polarity of loop = SGN(∂X 1 O / ∂X 1 I )
The open loop gain is calculated by the chain rule from the gains of the individual links:
SGN(∂X 1 O / ∂X 1 I ) = SGN[(∂X 1 O / ∂X n ) (∂X n / ∂X n-1 ) … (∂X 2 / ∂X 1 I )
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
All Links Should Have Unambiguous Polarities
- Sometimes people say a link other parameters can be either positive or negative or on where the system is operating.
, depending on -If demand is highly elastic , a higher price means less revenue increase in price causes demand to fall more than 1%.
because a 1% - When you have trouble assigning a clear and unambiguous polarity to a link it usually means there is variables.
more than one causal pathway connecting the two
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
CHALLENGE
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Name Your Loops
To help navigate your the audience network of loops, it's helpful to give each important feedback a number and a name .
Numbering the loops RI, R2, B1, B2, and so on helps your audience find each loop as you discuss it.
Causal by diagram developed engineers and managers in a workshop designed to explore the delivery causes of late for their organization's design work.
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Variable Names 1- Variable Names Should Be Nouns or Noun Phrases
The actions (verbs) are captured by the causal links connecting the variables.
A causal diagram captures the has
actually
happened but structure of the system what
would
, not its behavior-not what happen if other variables changed in various ways.
Incorrect Correct Costs Rise + Price Rises Costs + Price
Adding the verb " rises " to the diagram presumes costs will only rise .
It is confusing to talk of a decrease in costs rising or a fall in price increases.
Are prices rising, rising at a falling rate, or falling?
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Variable Names 2 Variable Names Must Have a Clear Sense of Direction
Choose names for which the variables that meaning of an increase or decrease is clear can be larger or smaller .
, Without a clear sense of direction for the variables you will not be able to assign meaningful link polarities .
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Variable Names 3 Choose Variables Whose Normal Sense of Direction Is Positive
Avoid the use of variable names containing etc.) prefixes indicating negation (non, un,
Incorrect Correct Costs + Losses Costs Profit Criticism + Unhappiness Criticism Happiness
Standard accounting practice is Profit = Revenue - Costs , so the better variable name is Profit, which falls when costs rise and rises when costs fall.
criticism may make you unhappy, but it is confusing to speak of rising unhappiness
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Tips for Causal Loop Diagram Layout
To maximize the clarity and impact of your causal diagrams, you should follow some basic principles of graphic design: 1. Use curved lines for information feedbacks. Curved lines help the reader visualize the feedback loops.
2. Make important loops follow circular or oval paths .
3. Organize your diagrams to minimize crossed lines .
4. Don't put circles , hexagons , or other symbols around the variables in causal diagrams. 5. Iterate . Since you often won't know what all the variables and loops will be when you start, you will have to redraw your diagrams, often many times, to find the best layout.
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Choose the Right Level of Aggregation
Causal loop diagrams are designed to communicate the central feedback structure of your dynamic hypothesis.
They are not intended to be equations.
descriptions of a model at the detailed level of the Having and too much detail makes it how the different loops interact hard to see the overall feedback loop .
structure Having too little detail makes it hard for your audience to grasp the logic evaluate the plausibility and realism of your model.
and If your audience doesn't grasp the logic of a causal link, you should make some of the intermediate variables more explicit .
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Don't Put All the Loops into One Large Diagram
Short-term memory can hold 7+- 2 chunks of information at once.
This puts a rather sharp limit on the effective size and complexity of a causal map.
Resist the temptation to put all the loops you and your clients have identified single comprehensive diagram.
into a Build up your model in stages , with a series of smaller causal loop diagrams .
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Make the Goals of Negative Loops Explicit
All negative feedback loops have goals .
All negative loops function by comparing the actual state to the goal , then initiating a corrective action in response to the discrepancy.
There are exceptions to the principle of showing the goals of negative loops.
Consider the death rate loop . The goal of the death rate loop is implicit (and equal to zero: in the long run, we are all dead).
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Indicate Important Delays in Causal Links
Delays are critical in creating dynamics.
Delays give systems inertia , can create oscillations , and are often responsible for trade-offs between the short- and long-run effects of policies.
Your causal diagrams should include delays that are hypothesis or significant relative to your time horizon.
important to the dynamic
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Distinguish between Actual and Perceived Conditions
Often there are significant perception differences of that state by the between the actors in the system .
true state of affairs and the There may be delays caused by reporting and measurement processes.
There may be noise, measurement error, bias, and distortions .
Example: There may be significant delays in assessing quality and in changing management's opinion about product quality.
Separating perceived and actual conditions helps prompt questions such as: -How long does it take to measure quality ?
-To change management's opinion about quality even after the data are available?
-To implement a quality improvement program ?
- To realize results?
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Distinguish between Actual and Perceived Conditions
DEVELOPING CAUSAL DIAGRAMS FROM INTERVIEW DATA
Much of the interviews data a modeler uses to develop a dynamic hypothesis comes from and conversations with people in organizations.
There are many techniques available to gather data from members of organizations, including: - Surveys - Interviews - Participant observation - Archival data - And so on Once you've done your interviews, you must be able to extract of the system from the statements of the interview subjects.
the causal structure Formulate variable names so that they sense of direction ).
correspond closely to the actual words used by the person you interviewed, while still adhering to the principles for proper variable name selection described above ( noun phrases, a clear and positive
DEVELOPING CAUSAL DIAGRAMS FROM INTERVIEW DATA
Process Improvement
The following two quotes carried out in an are actual interview automobile company transcripts developed in fieldwork in the United States.
The managers , from two different component plants company, describe why the in the same division of the yield of their lines was persistently low and why it had been so difficult to get process improvement programs off the ground In the minds of the [operations team leaders] they had to hit their pack counts [daily quotas]. This meant if you were having a bad day and your yield had fallen. .
. You had to run like crazy to hit your target. You could say, "You are making 20% garbage, stop the line and fix the problem," and they would say, "I can't hit my pack count without running like crazy." They could never get ahead of the game.
Manager at Plant A
Supervisors never had time to make improvements or do preventive maintenance on their lines. . . they had to spend all their time just trying to keep the line going, but this meant it was always in a state of flux. . . because everything was so unpredictable. It was a kind of snowball effect that just kept getting worse.
Supervisor at Plant B
DEVELOPING CAUSAL DIAGRAMS FROM INTERVIEW DATA
Process Improvement
Develop a single causal diagram capturing the dynamics described by the interviews.
Build your diagram around the basic physical structure shown below
Example: MANAGING YOUR WORKLOAD
Problem Definition
Consider the process of managing your workload: -A student ( imagine yourself ) must balance activities , a personal life , and sleep .
classes and assignments with outside - During the semester you attend classes, do the readings, and hand in assignments as they are due - You probably try to work harder if you think your grades are lower than you desire and take more time off when you are sleepdeprived.
There are two basic policies you can follow: (1) The ant strategy: never put off until tomorrow what you can do today (2) the grasshopper tomorrow.
strategy: never do today what can be put off until
Example: MANAGING YOUR WORKLOAD
Problem Definition
- The ant works builds up a large steadily backlog throughout the semester as work is assigned and never of assignments.
- As a result, the ant avoids the end of semester under control, and is able to stay well rested .
crunch , keeps the workweek - Because the ant gets enough sleep, of time to participate in outside activities productivity .
is high, and the ant has plenty - The ant's grades improve steadily throughout the term.
- The grasshopper, in contrast, defers the work until the last minute.
- The grasshopper's time for parties and workweek is low outside activities .
at the beginning of the term, providing lots of - The grasshopper can stay reasonably schedule because the workweek is low.
well rested despite a heavy social - But because the grasshopper doesn't do the work as fast as it is assigned, the assignment backlog steadily builds up.
Example: MANAGING YOUR WORKLOAD
Problem Definition
-Eventually, it's crunch time , and the grasshopper starts putting in perhaps pulling a few all-nighters .
long hours , - Unfortunately, as sleep suffers , energy and productivity fall.
- The rate and quality of work suffers.
-Grades plummet , and the term ends before the grasshopper work , perhaps leading the grasshopper to plead for extensions can finish all the from the faculty.
Example: MANAGING YOUR WORKLOAD
ant strategy
Example: MANAGING YOUR WORKLOAD
grasshopper strategy
Example: MANAGING YOUR WORKLOAD
Identifying Key Variables
-Assignment rate:
term (tasks/week).
the rate at which professors assign work throughout the
-Work completion rate:
the rate at which tasks are completed (tasks/week).
-Assignment backlog:
the number of tasks that have been assigned but not yet completed (tasks).
-Grades:
the grade received for work handed in (0-100 scale).
-Workweek:
the number of hours spent on academic work, including classes, reading, homework, projects, etc. (hours/week).
-Energy level:
measures how well rested the student is. Arbitrary scale from 0-100% where 100% = fully rested and 0 = comatose).
Other variables could be added, but this set provides a reasonable starting point for conceptualization of the feedback structure governing the dynamics.
Example: MANAGING YOUR WORKLOAD
Developing the Causal Diagrams
The Assignment Rate is assumed to be exogenous : Once a student has signed up for a set of courses, the assignment rate is determined. Classes can sometimes be dropped , but this possibility is ignored for now.
Example: MANAGING YOUR WORKLOAD
Developing the Causal Diagrams
Example: MANAGING YOUR WORKLOAD
Developing the Causal Diagrams
If work reading , pressure is high , the student may choose to skip classes , or give cut corners less complete answers , skim some to the questions in assignments.
Work pressure depends on the complete the work assignment backlog and the Time Remaining to
Example: MANAGING YOUR WORKLOAD
Developing the Causal Diagrams
The two most basic options available to a student faced with are:
Calendar Time Assignment Rate + Backlog B2 Work Completion Rate -
high work pressure
+
(1)
+ Time
work longer hours , thus increasing the
Corne r
completion rate and reducing the backlog (2) work faster
Due Date
by spending less time on each task, speeding
Effort Devoted
and reducing the backlog (the Corner Cutting loop B2).
-
the completion rate
+
Sustained high workweeks cut into sleep and the satisfaction of other needs
B1
(eating, exercise, human companionship, etc.), causing the student's Energy Level to fall .
R1 M idnight Oil Burnout
A tired student must spend longer than a well-rested one to complete a task with a given level of quality.
+ Workweek Delay Energy Level
Example: MANAGING YOUR WORKLOAD
Developing the Causal Diagrams Time Assignment + Work Rate
Reducing the effort
Calendar
devoted to each assignment also has
Backlog Rate
side effects
+ +
.
-
Putting less effort into each task does allow assignments to be time but
+ Time
reduces the Quality of Work ,
B2
lowering the student's completed in less Grades .
Work
When grades fall, there is pressure to boost the effort put into each task.
Due Effort Devoted Productivity Date Pressure to Assignments +
The negative Quality Control loop prevents effort and quality from falling too far
R1
even when work pressure is high
B3 Burnout B1 Grades Quality Control M idnight Oil + + R2 Quality of Work + Too Tire d to Think + Workweek Delay Energy Level
Example: MANAGING YOUR WORKLOAD
Assignment Rate Developing the Causal Diagrams Calendar Backlog Time -
If all else fails, the
+
exhausted student
Work Completion Rate + + B2
can appeal to the faculty for relief,
+ Corne r Cutting
Usually, such requests are accompanied beyond the student's control:
Date M y Hom e w ork Work Pressure
by stories
-
of bad luck
Effort Devoted to Assignments +
" "
My dog ate my homework
,"
My hard disk crashed Extensions +
,“
B3
"
My roommate had a nervous breakdown
."
Control +
and
R1 Burnout
hardship
Productivity + B1 M idnight Oil
If the is faculty slipped are moved by these tales of tragedy and woe (a big if), the
Quality of +
, making more time available and reducing work pressure.
R2 +
due date Note that slipping the deadline
Too Tire d
, because it lowers work pressure, may actually
Energy
cause the workweek to fall and the effort devoted to each assignment to rise, both reducing the completion rate and causing work pressure to build up again.
Workweek Delay Level