The system in the figure below includes three sub-systems: Power Supply, Sub-system 1, and Sub-system 2, and works as a series system. The internal devices of Sub-system 1 are arranged in parallel, whereas the devices of Sub-system 2 are arranged in series. Device 1A Device 2A
Device 1B Device 2B
Sub-system1 Sub-system2
Power Supply
The individual probabilities of sub-systems/devices being in failed states are as follows .
Power Supply: 0.005
Device 1A: 0.25
Device 1B: 0.25
Device 2A: 0.025
Device 2B: 0.025
1) Draw the system model (RBD model).
2) Build a Markov transition model for the system at the sub-system level only (i. e., the Markov model should include a three-component series system). The Markov solution should include all possible states and transitions from good (success) states to failed states.
3) Calculate the probabilities of being in all possible states and the final probability of system success and failure.
4) Furthermore, it was decided that the sub-systems can be repaired during operation. Add the repair transitions to the already developed Markov model, considering that there could be more than one sub-system repair operations performed in the same time interval. 3) 4)