## Materials and Methods  
### Study Design, Setting, & Data  
This study leverages 23 years of data from the U.S. Department of Energy on average price per kilowatt hour [18], average dollars per gallon for regular conventional gasoline [19], the distribution of vehicle miles driven per year [20], base manufacturer suggested retail prices (MSRP) [21], maintenance factors, insurance estimates, and simulation with design of experiments parameters to investigate life-cycle costs for electric and non-plugin hybrid vehicles. The study also includes time series forecasts for cents per kilowatt hour (cpkWh) and dollars per gallon to use in simulating an 8-year vehicle lifespan. While vehicles may last longer, the average length of ownership is approximately 6.5 years [22]. Further, electric battery warranties are often only 8 years [23]. The study includes base MSRP data as acquisition costs and forecasting of both cpkWh and cents per gallon of regular gasoline to estimate ownership costs. Maintenance is accounted for by applying 3.5 cents per mile for electric vehicles and 6 cents per mile for hybrids, although this is imprecise [24]. Insurance costs may be higher or lower depending on car value and insurance company, so a fixed value of 5% based on initial cost of the car is assigned. Electric vehicles depreciate at a more rapid rate than hybrid vehicles [25]. Over four years, gasoline cars retained on average 45% of their value, while electric vehicles just above 25% after adjustment for any Federal tax credit. It is unknown what the depreciation on new cars will be after an 8-year lifespan will be; however, it is assumed that the decay over the next four years will match the previous four, 0.45 remaining \(\times\) 0.65 decay rate = 0.29 residual for gasoline cars and 0.25 remaining \(\times\) 0.75 decay rate = 0.19 for electric cars. The setting for this study is the entirety of the United States, although the analysis is readily parsed to any individual state for which data are gathered. For generalization, all coding is provided. Data sources for costs derive primarily from the U.S. Department of Energy. Simulation Sets, Parameters, Stochastic Variables, Deterministic Variables, Formulae, and Flowcharts  
Sets. Three index sets are used in the simulation. The first index, \(i\), counts the number of simulation iterations, \(i\) = {1, 2,..., 25} (see _Simulation Iterations_ under results). The second index, \(t\), counts the day of the year, \(t\) = {1, 2,..., 365}. The third index, \(y\), counts the number of years in the simulation, \(y\) = {1, 2,..., 8}. Design of Experiments Parameters. The simulation leverages design of experiments (DOE) parameters that include miles per kilowatt hour (mpKh) design factor and miles per gallon (mpg) for gasoline powered cars. Daily miles driven is included as a probability distribution. Cost in cents per kilowatt hour (cpkWh) and in cents per gallon of fuel are forecasted as explicated in the results section for each month in the simulation, and those monthly estimates are applied to each day within the month. All DOE parameters are investigated within reasonable ranges as demonstrated through analysis of datasets. The parameter range of mpkWh for new electric cars derived from an analysis of EVadoption [26]. The distribution of interest was the daily mpkWh because it provides a mechanism for assessing comparative efficiency of vehicles when coupled with a time series analysis of cost per kWh. The minimum efficiency for 2018 electric cars based on distance and battery size is 2.89 mpKh (Tesla Model X P1000, Palo Alto, CA, USA), and the maximum is 4.43 mpKh for the Hyundai Ioniq Electric, Seoul, South Korea. Thus, the DOE parameter is fixed simplistically within the range of 3 to 5 to represent a feasible engineering range. The hybrid vehicle mpg parameter was evaluated using top 10, highest MPG hybrid vehicles provided by Fueleconomy.gov [27]. Due to mpg ties, there are actually 11 vehicles on this list.