**2. The Simulation-Decomposition Approach**

SimDec is an analytical approach that was recently introduced to expand the explanatory capabilities of Monte Carlo by exploring inherent cause–effect links between combinations of input variable groupings and their resulting impacts on output variables [24]. While this section reviews the key steps for the decomposition of a simulation, more extensive descriptions can be found in [24–27].

The SimDec procedure constructs sub-distributions of the entire simulation output distribution by partitioning certain input variables into pre-determined states, constructing various multi-variable combinations of these states, and then clustering the simulated outputs using these partition combinations [25,27]. This process enables the construction of both an "overall" output distribution and the simultaneous projection of the decomposed multi-variable input combinations onto this figure [26]. In decomposing an overall output distribution, SimDec simultaneously highlights multi-variable combination impacts using only a single simulation run, which, thereby, circumvents the need to perform individual simulation runs to test each input combination separately. Therefore, SimDec explicitly can be considered an explicit variance reduction approach for evaluating simulated outputs [25]. The visualization from SimDec is subsequently obtained by color-coding each portion of the overall distribution represented by each of the multi-variable partitions [24,26]. Because the projected effect of each subdivided partition can be clearly visualized on the output distribution, SimDec can visually expose previously unrecognized relationships between the multi-variable input partitions and their resulting fundamental consequences on the outputs [26].

The specific algorithmic steps in SimDec are as follows [25,27]:

Step (1) From the complete set of input variables that are to be simulated in the Monte Carlo model, choose a subset of variables that are of interest for more explicit scrutiny.

Step (2) Create relevant states that correspond to different outcomes for each of the variables identified in Step 1 (e.g., good-bad, optimistic-expected-pessimistic, etc.).

Step (3) For each state of each of the variables, construct suitable numerical boundaries that correspond to that variable's possible value ranges. These boundary ranges must be mutually exclusive and collectively exhaustive for the set of states of each variable.

Step (4) Construct a listing of every possible combination of the different variable state partitions. Each combination represents a multi-variable partition of the inputs in the future decomposition.

Step (5) Perform a Monte Carlo simulation. On each simulated iteration, map the randomly generated values of each selected input variable into its corresponding partition state, then map the specific combination of all individual states for the iteration onto the corresponding multi-variable partition combination. Allocate the result of each simulated iteration to the output distribution corresponding to the "complete" simulation, while simultaneously keeping track of the decomposed state combination that produced it.

Step (6) Construct output graphs and/or tables of the simulation outputs. These graphs/tables will portray both the overall summaries of the outputs together with the state decompositions superimposed on top of the global figures.

In summary, the SimDec procedure can be used to break down the regions of the simulation's overall output distribution into a set of distinct partitions [24]. The corresponding stratification enables an effective visualization and assessment of any inherent cause–effect relationships within the simulation results [26]. The determination of which input combinations to use in any given decomposition is at the discretion of the decision-maker. SimDec can be added to any Monte Carlo study with essentially negligible additional computational overhead and can be incorporated independently of the simulation context [25]. In the subsequent sections, SimDec will be employed to analyze the impacts from a simulation model of aviation electrification.
