Similar convergence curves are obtained at different time moments but are not presented here, due to space limitation.

The good stabilization of state probabilities at is manifested. Similar results are found at different time moments. At t = 80 years, the variances are, ,, ,, and for ‘initial’, ‘micro - crack’, ‘circumferential’, ‘radial’, ‘leak’, and ‘rupture’ states, respectively. The sample mean and variance of the estimated state probabilities are calculated. To investigate the convergence of the simulation model, the realizations have been subdivided into N = 20 subsamples of 50000 each. The simulation model has been executed times over a component lifetime years, in line with the original study. temperature and pressure) have not been modeled in the crack initiation process and have been inexplicitly modeled in the crack propagation process by means of a uniform distribution of the transition rate. It is noted that in the original study, the uncertainties of the external influencing factors (e.g. The simulation model supported by a Petri net description of the degradation process has been applied to the case study presented above, with the same parameter settings as in. It is noted that in their formulation, the transition rates, and are time-dependent. The detailed information about the definitions of the transition rates can be found in.

The Petri net representing the multi-state physics model of the crack growth process, is given in Fig. The circumferential crack grows relatively evenly around the circumference, potentially leading to a rupture. The radial crack mainly grows outward from the initiation site towards the outer diameter the process can lead to a leak and potentially to rupture. The crack growth has two steps (1) crack initiation, (2) crack propagation. The latter two types can lead to the rupture of the component. Cracks can grow from the inner to the outer diameter of the dissimilar metal welds in one of the three major morphologies: axial, radial, and circumferential. The case study refers to the cracking process in an Alloy 82/182 dissimilar metal weld in a primary coolant system of a nuclear power plant. It is noted that the derived distributions and, may have complicated mathematical expressions under these circumstances, the Markov Chain Monte Carlo technique can be used to sample random values. to the execution of the simulation algorithm, an estimate of the state probability vector is computed by dividing the total number of visits to each state by the total number of simulations :, where is the total number of visits to state i at time t.

Simio simulation crack