Related to an innovative cleaning device for cleaning hydrogenerator heat exchangers that does not require the interruption of generation (turning off the turbines), this article discusses two alternative schemes to estimate the minimum number of cleaning cycles required to ensure that all tubes of the heat exchanger will be visited at least once by the cleaning artifacts used by the conceived online cleaning system. The technique makes use of abrasive sponge balls transported by the cold working fluid of the exchanger to remove scale that accumulates inside the exchanger tubes during its operation. The main purpose of this study is to guide the hydrogenerator field operator in setting up the automation system of the exchanger cleaning system. In a first attempt, a negative binomial probability distribution function was investigated to estimate the number of tries needed to obtain a number of success events, with equal probability of success, after running a number of Bernoulli's experiments, where the last is considered the success case. Getting closer to the physical reality of the problem studied, a Monte Carlo method simulation, making use of a high number of repetitions (10 x 106), appeared to be a consistent mathematical formulation to anticipate the smallest number of cleaning cycles meeting the posed assumption.