🏥 ER Wait Time Simulation – What Statistics Teaches Engineers
Scenario:
You're a systems engineer at EmereTy Hospital. You must plan ER staffing using wait time data.
Patients arrive randomly, and wait times vary. Can you make smart decisions using data?
💡 What You Learn While You Play
Sample: The 60 patients in your simulation today. This is a manageable set of data collected to estimate larger trends.
Population: All potential ER patients who might come in during any hour, day, or season.
Why a sample? It's costly and impractical to track every single patient, so we collect and analyze samples to make predictions — this is called statistical inference.
Mean and percentiles: These help us determine what a typical wait time is (mean) and understand patient experience (percentiles show where most patients fall).
Median: The 50th percentile. It divides the sample in half and is less sensitive to extreme values.
Variability: Not all patients wait the same amount of time. Standard deviation and percentiles help you understand the spread in wait times and plan for high and low demand hours.
Max Wait Time: Useful in identifying worst-case scenarios. Engineers must consider system extremes to plan safety buffers.
Overcrowded Cases: Shows how often the system fails to meet expectations (e.g., >60 minutes). This reveals if resources are insufficient.
Engineers' Role: Design smarter, more efficient systems — from staffing to layout — using this data. Whether in hospitals, factories, or power grids, statistics helps engineers predict, optimize, and control.
Distribution Shape: The histogram helps you visually identify patterns, such as whether wait times are normal, skewed, or multimodal.
Real-world relevance: This simulation mirrors real ER challenges — statistics helps hospitals reduce patient risk, improve satisfaction, and avoid costly overstaffing or delays.