An Engineer's Mathematical Approach to Designing an Emergency Room Decontamination Area for Weapons of Mass Destruction Casualties

This study will focus on the potential requirements for an emergency response facility in case of weapons of mass destruction casualties proposing mathematical models. A complete emergency room layout will be designed taking the following analyses and requirements into consideration: quality function development (QFD) and product layout; average number of patients in the system, average time in the system, average number of patients in the waiting queue and average time waiting in the queue. Our analysis showed that, assuming 150 patients per day for 2 days with average service time of 14 minutes with two lines running. λ = 75 arrivals/day = 0.0521 arrivals/min. µ = 2 patients/14min = 0.1429 patients/min. Average number of patients in system (waiting and being served). Ls = λ / (µ - λ) = 0.574 patients. Average time in system (waiting and service time) Ws = 1 / (µ - λ) = 11.02 min. Average number of patients waiting in queue. Lq = λ² / µ (µ - λ) = 0.209 patients Average time waiting in queue, Wq = λ / µ (µ - λ) = 4.016 min. From our model, we conclude to set up an engineer's perfect ER response we need: Having a stable patient and unstable patient track will make it easy to respond to the emergency. Patients requiring the emergency track feature would be dropped off before the vehicle shower at contaminated stabilizing rooms. Time of service: waiting 14 minutes with an average of 2 patients waiting in line to be served. This is an initial study having a flow of 150 patients arriving over a long time period and it is an attempt to apply a mathematical model to a multidisciplinary approach to a clinical potential discussion.