Safety-critical systems in various industries such as transportation or nuclear energy have been paid more attention with the development of societies due to increased attachment of importance to the life of human, their property, and nature. While developing such systems, detailed availability and safety characteristics are to be taken into account in parallel with architectural design decisions such as synchronization between different computing units or real-time task management. For fulfilling top-level requirements in international standards, ambitious quantitative targets like 0.012 FIT for HW units are to be reached where the industry has difficulties to achieve it. In this paper, this problem is handled by proposing an augmented Markov model for diverse architectures that is superior to the formulas provided in the main safety standard IEC 61508 and previous studies. With the proposed method it is possible to cover all safety-relevant states, which leads to more accuracy and lower hazard rates helping to reach these ambitious quantitative targets. Besides, the reliability parameters are investigated and optimized to increase safety performance. Consequently, the proposed novel model including enhanced reliability parameters is used for an industry application, namely safety-critical computer used for unmanned metro and high-speed rail transportation. The result obtained by the proposed model is compared with the results obtained using state of art models in literature and using the formulas in IEC 61508. As domain independent references IEC 61508 and Markovian approach are used in the paper, this study is applicable to other safety critical areas such as automotive or avionic industry.