Accuracy of all instrument has been traditionally defined as the sum of the precision and the bias. Recently, this notion was generalized to estimators [Bagajewicz, M. (2005a). On the definition of software accuracy in redundant measurement systems. AIChE Journal, 51(4), 1201-1206]. The definition was based on the maximum undetected bias and ignored the frequency of failure, thus providing an upper bound. In more recent work [Baga jevvicz, M. (2005b). On a new definition of a stochastic-based accuracy concept of data reconciliation-based estimators. In European Symposium on Computer-Aided Process Engineering Proceeding (ESCAPE)], a more realistic concept of expected value of accuracy was presented. However, only the timing of failure and the condition of failure was sampled. In this paper 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. (C) 2007 Elsevier Ltd. All rights reserved.