Motivated by the observation that small events can cause large crises, Rudolph and Repenning7
developed a system dynamics model drawing on source data from several case studies of large-scale disasters such as those of Tenerife and the USS Vincennes
. Drawing primarily on Weick’s theoretical analysis3
as the initial source data, the model formulations translate the text-based constructs and theoretical relationships into the system dynamics language of stocks, flows, and feedback. The paper carefully develops the causal feedback structure of the model, explains the mathematical formulations, and provides access to the fully documented model. Here, we provide a summary of the model, highlighting some key features, and focus attention on the results of simulation analyses that may have some bearing on managerial practices in the ED.
The original model7
grounded in source data from disasters is based on several key assumptions that are likely quite consistent with most ED contexts. First, the model assumes the organization faces a continuing, possibly varying, stream of non-novel interruptions. The definition of an interruption follows Mandler’s: any unanticipated event, external to the individual, that temporarily or permanently prevents completion of some organized action, thought sequence, or plan.25
Second, the model focuses on interruptions for which the organization has an appropriate response within its existing repertoire, that is, the interruptions are non-novel interruptions. Resolving a non-novel interruption still requires significant cognitive effort,26
first to shift to an active mode of cognition and then to execute the three processes of attention to determine which interruptions are considered, activation to trigger the necessary knowledge, and strategic processes to prioritize goals and allocate resources.1
However, the difficulty of resolving an interruption can vary widely. For example, the stream of interruptions an EP faces might include a question from a nurse to confirm a medication order, which could be readily and quickly handled, as well as a request to read an electrocardiogram (ECG), which might be more time-consuming and cognitively taxing. The model captures this variability in the time required to resolve different interruptions by interpreting the unit in the flow of interruptions not as the raw number of interruptions, but as the number of component mental steps needed to resolve interruptions. So, in the above example, reading an ECG may constitute many interruption units, whereas answering a simple question might be interpreted as only a few units of interruption. The model also assumes that resolving pending interruptions is required for ongoing survival of both the physical and social functioning of the organization. Finally, the model does not include the primary task being interrupted, but instead focuses on organizational performance as a function of the ability to resolve interruptions.
The model synthesizes three main ideas, each of which when taken alone is a relatively uncontested statement, but which when taken together form the basis for some important and somewhat counterintuitive dynamics. The first of these ideas is that interruptions are not processed instantaneously, but instead accumulate while pending resolution. is a stock and flow and feedback diagram using the standard icons of system dynamics to represent the relevant system structure.27,28
At the top of the diagram, we see the stream of incoming interruptions represented as the interruption arrival rate
and depicted with a pipe and valve icon, signaling a flow variable. Interruptions accumulate in the stock of interruptions pending,
represented with a rectangle, until they are resolved as depicted by the outflow net interruption resolution rate
. Thus, the stock of interruptions pending is increased by the interruption arrival rate and decreased by the net interruption resolution rate. The dynamics of stocks are often conceptualized as akin to the dynamics of the level of water in a bathtub.29–31
The stock of interruptions pending will increase any time the interruption arrival rate exceeds the net interruption resolution rate, just as the level of water in a bathtub increases any time the inflow from the water spigot exceeds the outflow through the drain of the bathtub. Examples of accumulated unresolved interruptions in the ED include requests to come visit a patient, alerts that new test results are available, and pages that signal incoming stroke alert patients. To resolve each of these interruptions requires cognitive and physical effort that will take time and energy. Because interruptions may arrive at a rate that is greater than that at which they are resolved, unresolved interruptions can accumulate.
Figure 1 A model of disaster dynamics. Reprinted from “Disaster Dynamics: Understanding the Role of Quantity in Organizational Collapse,” by Rudolph and Repenning, published in Administrative Science Quarterly (Vol. 47, 2002) by permission of Administrative (more ...)
The second main idea underlying the causal structure of the model is that accumulating interruptions increase the levels of stress on the individuals in the organization. Unresolved interruptions do not disappear, but instead continue to wait for resolution. Mental bookkeeping becomes more challenging, raising the risks of losing situational awareness or committing fixation errors.32
Moreover, the time pressure these accumulations generate may decrease access to inert knowledge, increase errors, or trigger a maladaptive problem-solving routine.1,33–35
This notion is an important conceptual step that distinguishes the present work from many traditional studies of stress and performance that consider stress as an independent variable, exogenously manipulated or viewed as imposed by forces outside the system under study. Rather, given that accumulating interruptions cause increases in stress, the level of stress at any given time is largely determined by the organization’s past performance. Stress and performance become part of a feedback system in which stress affects the current performance and the consequences of past performance, as captured by the stock of interruptions pending, affect stress. In , stress
is modeled as the mismatch between the desired resolution rate
, which depends on interruptions pending and a desired resolution time
, and the normal resolution rate,
which reflects a sense of performance under typical unstressed conditions. As pending interruptions increase, so does the desired resolution rate, increasing the model variable stress as well.
The third main idea asserts that the influence of stress on performance is captured by an inverted U-shaped relationship, as is posited by the Yerkes Dodson law.36
When stress is low, small increases result in an increase in performance, but the favorable effects of stress on performance continue only up to a point, after which further increases cause performance to deteriorate.37–39
The Yerkes Dodson law, based on experiments applying varying intensities of electrical shocks to mice running through a maze, has a long history in psychological research and has been used to describe the effects of anxiety, arousal, drive, motivation, activation, and reward and punishment on performance, problem solving, coping, and memory.39–41
shows the Yerkes Dodson curve separated into its upward- and downward-sloping components. The insert labeled positive effect of stress
describes the upward-sloping portion of the Yerkes Dodson curve. The causal arrow from the variable stress
to the positive effect of stress
indicates that as stress increases, so too does the effect of stress, and the causal arrow from the positive effect of stress
to the net interruption resolution rate
indicates that as this effect increases, so does the net interruption resolution rate
. This portion of the model operationalizes the idea that increasing stress increases performance (i.e., interruption resolution rate). Eventually, the peak of the Yerkes Dodson curve is reached, and increasing stress further causes performance to deteriorate. The insert labeled negative effect of stress
describes the downward-sloping portion of the Yerkes Dodson curve, and the causal arrow from negative effect of stress
to the net interruption resolution rate
indicates that as this effect increases, the interruption resolution rate decreases.
The links among interruptions pending, the desired resolution rate, stress, the effects of stress, and the net interruption resolution rate form feedback loops that govern the organization’s response to variations in the interruption arrival rate. shows two feedback loops corresponding to the two regions of the Yerkes Dodson curve. To understand the diagram, consider a scenario in which an ED experiences a surge in interruptions compared to the baseline levels during normal operating conditions. The surge constitutes a rapid increase in the interruption arrival rate. These interruptions are not processed and resolved instantaneously, but instead accumulate in the stock of interruptions pending. As the stock of interruptions pending increases, the ED practitioners notice and interpret these interruptions and consequently experience an increase in their desired resolution rate for these pending interruptions. As the desired resolution rate rises above the normal resolution rate, stress (as it is modeled here) increases. Practitioners get more focused, experience autonomic arousal, and ratchet up their performance as in the upward-sloping portion of the Yerkes Dodson curve. In , increasing stress causes an increase in the positive effect of stress, which then in turn causes an increase in the interruption resolution rate. With a higher interruption resolution rate the stock of interruptions pending decreases. Beginning with an increase in interruptions pending and tracing the process around to the resulting decrease in interruptions pending, we see that the response represented by this feedback loop offsets, or balances out, the initial increase. We call this a balancing feedback loop and label it in with the letter B for balancing. Balancing feedback loops act to correct deviations, regulate performance, or move systems toward their target conditions. Common examples of balancing feedback loops in other contexts include thermostatic control of room temperature, homeostasis, and eating in response to pangs of hunger. Balancing loops bring stability to systems. In the context of this example, the stress-induced enhancement in performance is a stabilizing response that helps the ED to restore normal operating conditions in the wake of the surge of interruptions.
The system response changes considerably when the stress level rises enough to trigger the downward-sloping portion of the Yerkes Dodson curve. Consider an ED experiencing larger or longer-lasting surges than described above, such that the stock of interruptions pending accumulates to a level high enough to push the ED into the region where the negative effects of stress dominate. The increase in stress that results from increases in interruptions pending now causes a decline in the interruption resolution rate, and as the interruption arrival rate continues, the stock of interruptions pending grows still further. Beginning with the increase in interruptions pending and tracing around the feedback loop, we have an increase in the desired resolution rate that causes an increase in stress, which in turn causes more negative effects of stress, reducing the interruption resolution rate and resulting in further increases in the stock of interruptions pending. The response represented by this feedback loop amplifies or reinforces the original increase. We call this a reinforcing feedback loop and label it with the letter R in . Reinforcing feedback loops generate growth or decline at increasing rates of change, and they generate instability in systems. Common examples of reinforcing feedback loops include compounding interest, population growth, and the contagious spread of infectious disease. In the context of , when stress levels increase, at first the balancing loop determines the overall behavior of the system, but when stress becomes high enough, the reinforcing loop begins to determine the system’s behavior. This transition is a shift in loop dominance and is key to understanding the dynamics of quantity-induced crises. We turn next to simulation experiments to highlight these important dynamics.