FMEA and Markov Analysis

The overall system in the figure below includes three systems: Power Supply Subsystem, Subsystem 1, and Subsystem 2. Subsystem 1 and Subsystem 2 are arranged in series, and they both need the Power Supply Subsystem to operate. The internal devices of Subsystem 1 (Device 1A and Device 1B) are arranged in parallel. The internal devices of Subsystem 2 (Device 2A and Device 2B) are arranged in series.

The individual probabilities of subsystems/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

To perform a safety analysis, you are required to follow the steps listed below: 1) Draw the system model (Reliability Block Diagram --RBD-- model).

2) Build a Markov transition model for the system. The Markov solution should include all possible states and transitions from good (success) states to failed states.

3) Based on the Markov model, calculate the probabilities of being in all possible states and the final probability of system success and failure. All probabilities of failure are expressed per operation hour.

4) Furthermore, it was decided that the subsystems can be repaired during operation. Add the repair transitions to the already developed Markov model, considering that there could be more than one subsystem repair operations performed in the same time interval.

5) Consider that Devices 1A and 1B are two FPGA actuator controllers of an aircraft flight control system. Devices 2B and 2A are in this case a control surface and its actuator, respectively. Consider also that the control surface is an elevator, which controls the aircraft pitch axis. Devices 1 and 2 have the same functionality but are manufactured by different vendors and have the code written in different languages (recall the system diversification discussion from Module 2). Perform a Functional FMEA analysis for the four devices. Keep the analysis at a higher functionality level only (i.e., the actuator controllers (Devices 1A and 1B) control the actuator (Device 2A), while the actuator (Device 2A) controls the Elevator (Device 2B). Use one of the FMEA templates given in the resources (textbook, FAA, or SAE resources). Note: Probabilities of failure for the four devices given above are not representative of an aircraft flight control system.

\begin{tabular}{|c||c|} \hline Device 1A \\ \hline Device 1B \\ \hline Subsystem 1 & Device 2A \\ \hline \hline \\ Device 2B \\ \hline \\ Subsystem 2 \\ \hline \end{tabular}