Traditionally, accuracy of an instrument is defined as the sum of the precision and the bias (Miller, 1996). Recently, Bagajewicz (AiChe journal, 2005a) proposed a new definition of accuracy which relies on the ability of the gross error detection technique to detect gross errors rather than the actual bias an instrument has. The accuracy was defined based on the maximum undetected bias, hence it represented the worst-case scenario and did not reflect the sensor's frequency of failure. In more recent work (Bagajewicz, 2005b), the definition of accuracy was modified to include expected undetected biases and the frequency of failure. However, only the timing of failure and the condition of failure were sampled. In this work, we extend the Monte Carlo simulations to also sample the size of the gross errors and we provide new insights on the evolution of biases through time. Miller, R. W. Flow Measurement Engineering Handbook, McGraw-Hill, New York, (1996). Bagajewicz M. On the Definition of Software Accuracy in Redundant Measurement Systems. AIChE Journal. Vol 51, No 4., pp. 1201-1206 (2005a). Bagajewicz, M., On a New Definition of a Stochastic-based Accuracy Concept of Data Reconciliation-Based Estimators ESCAPE-15 proceeding (European Symposium on Computer-Aided Process Engineering). (2005b).