A Risk-Based Universal Calibration Interval Model Using Monte Carlo Simulation

Sustainable manufacturing requires modern intelligent approaches to monitoring products of the manufacturing process. An integral part of intelligent manufacturing is the measurement of geometric parameters of products, which allows diagnosing the state of the manufacturing process, optimizing it and predicting its further development. For these reasons, it is necessary to monitor the condition of measuring instruments, as decision-making is based on the data provided by them. Calibration intervals of measuring instruments are commonly defined using fixed time-based rules that are not explicitly linked to measurement uncertainty growth or conformity risk. This practice may lead to either unnecessary recalibration or an increased probability of using out-of-tolerance instruments. In this study, a Monte Carlo-based methodology for determining recalibration intervals is proposed, in which recalibration decisions are derived from the probabilistic evolution of measurement error over time. Measurement uncertainty is modeled as a time-dependent stochastic process combining calibration uncertainty, drift behavior, and repeatability. Monte Carlo simulation is used to propagate uncertainty and to estimate both the expanded uncertainty and the probability that the measurement error exceeds the maximum permissible error (MPE). The recalibration interval is defined as the earliest time at which this probability exceeds a predefined acceptable risk threshold. A numerical experiment using realistic synthetic data representative of a typical dimensional measuring instrument demonstrates that probability-based and uncertainty-based criteria may lead to substantially different recalibration intervals. The results confirm that risk-informed recalibration intervals provide a more transparent and metrologically justified alternative to fixed schedules while remaining fully compatible with ISO/IEC 17025 and GUM principles. The proposed approach is instrument-agnostic and readily applicable in calibration laboratories and industrial measurement systems.