Observation probability estimation of dead-time models using Monte Carlo simulations

One of difficulties of working with pulse mode detectors is dead time and its distorting effect on measuring with the random process. Three different models for description of dead time effect are given, these are paralizable, non-paralizable, and hybrid models. The first two models describe the behaviour of the detector with one degree of freedom. But the third one which is a combination of the other two models, with two degrees of freedom, proposes a more realistic description of the detector behaviour. Each model has its specific observation probability. In this research, these models are simulated using the Monte Carlo method and their individual observation probabilities are determined and compared with each other. The Monte Carlo simulation, is first validated by analytical formulas of the models and then is utilized for calculation of the observation probability. Using the results, the probability for observing pulses with different time intervals in the output of the detector is determined. Therefore, it is possible by comparing the observation probability of these models with the experimental result to determine the proper model and optimized values of its parameters. The results presented in this paper can be applied to other pulse mode detection and measuring systems of physical stochastic processes.