The average unavailability and the average unconditional failure intensity of safety-instrumented systems represent the main performance indicators of safety integrity. This paper employs an approach based on the exploitation of the availability expression to obtain both performance measures in a simultaneous and straightforward way for any KooN configuration. The implementation of such an approach is generalized to take into account the contribution of common cause failures using any parametric model. The validation of the obtained results is verified through their application using several architectures and using Beta Factor and Binomial Failure Rate models to handle such type of dependent events. Therefore, the contribution of this paper lies in proposing one single formula that can be used to estimate the two main safety integrity’s performance indicators for any KooN architecture using any kind of common cause failures parametric model.

Spectral domain formulation is provided for the analysis of rectangular stacked patches printed on a substrate characterized by dielectric and magnetic uniaxial anisotropy. Detailed analytical expressions of the dyadic Green’s functions are derived. Galerkin’s procedure is applied to solve the electric field integral equations, and the resonance characteristics are determined by solving the characteristic equation. Numerical results show that the influence of the magnetic anisotropy on the resonant frequencies is highly dependent on the permeability of the medium, where for a non-magnetic medium, the impact of the existing anisotropy was found negligible. However, for a magnetic medium, the anisotropy has a large impact on the resonant frequencies. Moreover, the influence of each of the components of the permeability tensor has been also reported.

Spectral domain formulation is provided for the analysis of rectangular stacked patches printed on a substrate characterized by dielectric and magnetic uniaxial anisotropy. Detailed analytical expressions of the dyadic Green’s functions are derived. Galerkin’s procedure is applied to solve the electric field integral equations, and the resonance characteristics are determined by solving the characteristic equation. Numerical results show that the influence of the magnetic anisotropy on the resonant frequencies is highly dependent on the permeability of the medium, where for a non-magnetic medium, the impact of the existing anisotropy was found negligible. However, for a magnetic medium, the anisotropy has a large impact on the resonant frequencies. Moreover, the influence of each of the components of the permeability tensor has been also reported.

Spectral domain formulation is provided for the analysis of rectangular stacked patches printed on a substrate characterized by dielectric and magnetic uniaxial anisotropy. Detailed analytical expressions of the dyadic Green’s functions are derived. Galerkin’s procedure is applied to solve the electric field integral equations, and the resonance characteristics are determined by solving the characteristic equation. Numerical results show that the influence of the magnetic anisotropy on the resonant frequencies is highly dependent on the permeability of the medium, where for a non-magnetic medium, the impact of the existing anisotropy was found negligible. However, for a magnetic medium, the anisotropy has a large impact on the resonant frequencies. Moreover, the influence of each of the components of the permeability tensor has been also reported.

Spectral domain formulation is provided for the analysis of rectangular stacked patches printed on a substrate characterized by dielectric and magnetic uniaxial anisotropy. Detailed analytical expressions of the dyadic Green’s functions are derived. Galerkin’s procedure is applied to solve the electric field integral equations, and the resonance characteristics are determined by solving the characteristic equation. Numerical results show that the influence of the magnetic anisotropy on the resonant frequencies is highly dependent on the permeability of the medium, where for a non-magnetic medium, the impact of the existing anisotropy was found negligible. However, for a magnetic medium, the anisotropy has a large impact on the resonant frequencies. Moreover, the influence of each of the components of the permeability tensor has been also reported.