This paper presents an analysis of the effects of noise and precision on a simplified model of the clarinet driven by a variable control parameter. In a previous work [5], the dynamic oscillation threshold of a simplified model of a clarinet is obtained analytically. In the present article, the sensitivity of the dynamic threshold on precision is analyzed as a stochastic variable introduced in the model. A new theoretical expression is given for the dynamic thresholds in presence of the stochastic variable, providing a fair prediction of the thresholds found in finite-precision simulations. The dynamic thresholds are found to depend on increase rate and are independent on the initial value of the parameter, both in simulations and in theory.