45 Frontiers of performance: using a mathematical model to discover unobservable performance limits in a pre-hospital and retrieval service

Aim

We aimed to establish if a validated computer model could derive otherwise unobservable performance limits for a physician-led pre-hospital and retrieval service.

Methods

Using our previously validated model for the ?ScotSTAR Emergency Medical Retrieval Service (EMRS), we randomly simulated varying numbers of primary pre-hospital and secondary retrieval missions using the MATLAB software suite Simulink program. The parameters of simultaneous retrieval rate and number of missed primary missions were calculated and plotted. The 45o tangent of the corresponding exponential curve was identified and used as the performance frontier.

Results

Based on the current system demand, the number of missed primaries rose exponentially above a performance frontier of 400 missed primaries per year on a total of 1550 completed primary missions per year (corresponding to 15% absolute service utilisation). However, the simultaneous retrieval rate for both primary and secondary retrieval rose exponentially above 12% at 810 primary missions per year (corresponding to 13% utilisation).

Conclusion

These results provide a useful insight into potential system performance, and its limitations. When combined with forecasting of service growth and demand, they provide useful guidance on what a service may be able to achieve. By knowing the limits of achievable performance, we can also work to derive an absolute number of missions as a specification limit. Furthermore, they illustrate the importance of maintaining relatively low service utilisation in order to achieve rapid response to critically ill or injured patients.

Conflict of interest

None declared.

Funding

Scottish Ambulance Service ScotSTAR

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