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Determination of tolerance level of impaired growth hormone secretion of humans

In this model it is supposed that shocks contributing additively to the amount of damage occur at random points of time. Common assumptions are that the sequence of shock amounts and the process N (t), say counting their number are stochastically independent and that the shock amounts ε1 , ε2...(Where εi is the increment of the damage caused by the i-th shock) are independent and identically distributed nonnegative random variables. The tolerance level is given by some constant β > 0 fixed on advance. The objective is to stop the cumulative damage process Sn= ε1 + ε2 +......εn before it exceeds the level β, but such that Sn is not too far apart from β. In our medical Application we have taken impaired growth hormone secretions as shocks so that the occurrence times of the “shocks” should be modeled as random.