Individual doctors treat individual patients. This results in individual times for the similar activity of the individual full-time employee, all of which are different – individual times. Because of this characteristic, it is unrepeatable. Consequence: Medical activity time is unplannable.
What mathematical approach is there to partially ‘solve’ the problem?
In the 1st step:
Because the times are individual, they vary. Scattering can be represented as an ordinal time probability.
Ordinal means in probability:
- The „Laplace“- experiment is invalid.
- There are ‘n’ individual, delimited event spaces that are infinitely large in themselves.
- The events in the event space are integrated, i.e. not independent.
- Each new event generates new integrated probabilities. Etc
The advantages:
- Probabilities are distance-free. In principle, there are no idle times.
- Planned time and real time are identical. There is no unreal demand..
- n ranks are combined ‚nn=x’ times in m halls. This makes minimum time and even com-bination visible.
- Planned and real time are linked by ordinal conditional probability. It enables reliable time estimates, the condition for the digital twin.
In the 2nd step:
The actual end time of the current operation must be predicted for the real time sequence. This can be achieved with a time prediction of >95% (= statistical certainty) if the structure of each operation consisting of qualitatively different sub-activities (skin incision, insertion of Laparoscope, CO2 introduction, appendix removal,..) is used. If the time for each partial activity is measured using a sensor, its ordinal time probability can be calculated. The con-ditional ordinal time probability for the ordinal time probability of the overall operation is calculated based on the probability of the partial operation. This is calculated for each part-ial activity when it is completed.
The more of the partial activities are completed in the current overall course of the operat-ion, the more the sequence of calculated conditional ordinal time probabilities increases. They ‘multiply’ and the more reliable the time forecast becomes with regard to the end of the overall operation. The result is a reliable, probable time (End) (>95%). This was previ-ously not possible with arithmetic time calculations.
Since the end of the operation is now known, the following applies: (END – START) = OP-duration. It can now be calculated in real time.
This condition has made a digital twin possible.
Additional advantage – All time-relevant patient individualities are included in the probability sequence of the partial activities. You lose the incalculable surprise effect. The current time forecasts are reliable and PARETO time optimisation can also control the optimum schedule prognostically.