While the objective of structural design is to achieve stability with an appropriate level of reliability, the design of systems for structural health monitoring is performed to identify a configuration that enables acquisition of data with an appropriate level of accuracy in order to understand the performance of a structure or its condition state. However, a rational standardized approach for monitoring system design is not fully available. Hence, when engineers design a monitoring system, their approach is often heuristic with performance evaluation based on experience, rather than on quantitative analysis. In this contribution, we propose a probabilistic model for the estimation of monitoring system effectiveness based on information available in prior condition, i.e. before acquiring empirical data. The presented model is developed considering the analogy between structural design and monitoring system design. We assume that the effectiveness can be evaluated based on the prediction of the posterior variance or covariance matrix of the state parameters, which we assume to be defined in a continuous space. Since the empirical measurements are not available in prior condition, the estimation of the posterior variance or covariance matrix is performed considering the measurements as a stochastic variable. Moreover, the model takes into account the effects of nuisance parameters, which are stochastic parameters that affect the observations but cannot be estimated using monitoring data. Finally, we present an application of the proposed model to a real structure. The results show how the model enables engineers to predict whether a sensor configuration satisfies the required performance.