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+# System Uncertainty Analysis Using Monte Carlo Simulations
+
+## Overview
+
+This project provides a framework for performing Monte Carlo analysis on systems that utilize various sensors and instrumentation. It allows users to represent complex systems where calculations are performed on sensor data and evaluates the impact of sensor uncertainties on overall system performance.
+
+The tool performs:
+
+- **Monte Carlo Analysis**: Evaluates the uncertainty of the entire system by simulating sensor errors.
+- **Sensitivity Analysis**: Analyzes the impact of individual sensor errors on the system output.
+- **Range Analysis**: Studies how variations in sensor input ranges affect the system.
+
+An example report generated by this tool is included in the repository ([System Uncertainty Report.pdf](System_Uncertainty_Report.pdf)).
+
+## Features
+
+- **Customizable Sensor Models**: Define sensors with specific error characteristics.
+- **Complex System Equations**: Represent the system's governing equations using sensor inputs.
+- **Parallel Processing**: Utilize multiple processes to speed up simulations.
+- **Visualization**: Generate plots for sensitivity and range analyses.
+
+## How It Works
+
+### 1. Define Sensors and Errors
+
+Each sensor is modeled with its true value and associated error characteristics. Error parameters can include:
+
+- **Static Error Band**
+- **Repeatability**
+- **Hysteresis**
+- **Non-linearity**
+- **Temperature Effects**
+- **Full-Scale Output (FSO)**
+
+Example of defining sensor errors:
+
+```
+pt_1_errors = {
+    "k": 2,  # Number of standard deviations
+    "fso": 100,  # Full-scale output
+    "static_error_band": 0.15,  # % of FSO
+    "repeatability": 0.02,  # % of FSO
+    "hysteresis": 0.07,  # % of FSO
+    "non-linearity": 0.15,  # % of FSO
+    "temperature_zero_error": 0.005,  # % of FSO per degree
+    "temperature_offset": 30,  # Degrees off from calibration
+}
+```
+
+### 2. Create Sensor Instances
+
+Sensors are instantiated using the defined error characteristics:
+```
+pressure_transmitter_1 = PressureTransmitter(25, pt_1_errors, name="PT 1")
+pressure_transmitter_2 = PressureTransmitter(20, pt_1_errors, name="PT 2")
+temperature_sensor_1 = RTD(250, RTD_1_errors, name="RTD 1")
+flow_speed = TurbineFlowMeter(10, flow_1_errors, name="Flow Sensor 1")
+pipe_diameter = PhysicalInput(1, pipe_diameter_error, name="Pipe Diameter")
+```
+
+### 3. Define the System Equation
+
+The system's governing equation is defined using the sensor instances. For example:
+```
+combined_input = math.pi * density_lookup * flow_speed * (pipe_diameter / 12 / 2) ** 2
+```
+
+### 4. Perform Monte Carlo Analysis
+
+The SystemUncertaintyMonteCarlo class is used to perform the analysis:
+```monte_carlo = SystemUncertaintyMonteCarlo(combined_input)
+
+monte_carlo.perform_system_analysis(monte_carlo_settings={
+    "num_runs": num_of_tests,
+    "num_processes": num_of_processes
+})
+```
+
+### 5. Perform Sensitivity and Range Analyses
+Sensitivity Analysis evaluates the impact of individual sensor errors:
+
+```
+monte_carlo.perform_sensitivity_analysis(
+    input_to_analyze=flow_speed,
+    gain_settings=[1, 2, 3, 4, 5],
+    monte_carlo_settings={
+        "num_runs": sensitivity_analysis_num_runs,
+        "num_processes": num_of_processes
+    }
+)
+```
+
+Range Analysis studies the effect of varying sensor inputs:
+```
+monte_carlo.perform_range_analysis(
+    input_to_analyze=pressure_transmitter_1,
+    range_settings=[28, 31, 20],  # Start, Stop, Number of Points
+    monte_carlo_settings={
+        "num_runs": range_analysis_num_runs,
+        "num_processes": num_of_processes
+    }
+)
+```
+
+### 6. Generate Reports
+
+After the analyses, a detailed report is generated summarizing the findings:
+```
+monte_carlo.save_report()
+```