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Portfolio for Safety-Directed Design of a Brake-By-Wire System for Car
Coursework for 661985 – Safety Critical Systems
Part 2 –Dynamic Reliability Analysis and System Adaptation for Electronic Stability

The Portfolio explores the iterative design of a Brake-By-Wire (BBW) system for cars.
This is Part 2 of the assignment and continues this exploration with dynamic reliability analysis,
considering adaptation of the system to prevent skidding for electronic stability purposes. Part2 is worth
60% of the Portfolio.
You will analyse this architecture using Markov Models. Calculation of reliability involves programming
exercises.
We continue to examine the systems presented in Part 1. Its architecture for the system is given in Figure 1
below:
Figure 1: The proposed architecture of the BBW system
System Specification
• The BBW features separate braking on each wheel.
• All components of the system are powered by a common power supply (PS).
• An electromechanical pedal (PL) receives the braking demand from the driver and sends this as a
message (PLm) to two pedal nodes PN1, and PN2.
• Two replicas of the message are sent by each pedal node to buses B1 and B2. PN1 sends PN1m,
while PN2 sends PN2m.
• Four Wheel nodes (WN1 … WN4) each read those four identical messages (PN1B1m, PN2B1m,
PN1B2m, PN2B2m) from the two buses.
• As long as one of the messages is received a wheel node can create the braking output applied to
the corresponding wheel (WN1b ... WN4b).
PN1
PN2
PS
PLm
B1 B2
PN1m
PN2m
PN1B1m, PN2B1m
PN1B2m, PN2B2m
WN1b
WN2b
WN3b
WN4b
p
p p
p p
p
PL
PN1B1m, PN2B1m
PN1B1m, PN2B1m
PN1B1m, PN2B1m
PN1B2m, PN2B2m
PN1B2m, PN2B2m
PN1B2m, PN2B2m 2
Failures
Each component in this system has only one failure mode that shares the name of the component. For
example:
• The failure mode of component PS is PS
• The failure mode of component B1 is B1
The failure mode of each component leads to the omission of all outputs. For example:
• If PS fails, you get O-p (Omission of p)
• If B1 fails, you get O-PN1B1m and O-PN2B1m
• Regarding the dynamic reliability analysis:
o It is assumed that all components have two states Operational and Failure.
o It is assumed that the system is completely healthy at the starting point.
o The failure distribution of all components is exponential with constant failure rates.
In the absence of component failures, all four wheels apply the braking output and the car brakes correctly.
When components fail, the system may fail to brake on one or more wheels. The effects vary depending on
the number of wheel failures. For example:
• If one wheel fails, the car brakes sufficiently but is likely to skid off its course.
In this case, to correct the skidding failure, an electronic stability program could release the wheel
that is diagonal to the wheel that fails to brake. The car then brakes slowly, and the stopping
distance is increased.
• If all wheels fail, then the car experiences catastrophic loss of braking.
Assignment Tasks
Based on this design:
1. Only consider the independent failure modes of the 4 Wheels in the BBW and assume that the rest
of the system is perfect. Each wheel failure will lead the BBW to hazardous states of asymmetrical
braking. In each of the 4 cases, skidding prevention is applied by locking the diagonal wheel leading
to moving the system to a corresponding recovery state with reduced braking capacity. We assume
that the skidding prevention mechanism is perfect, i.e. the probability of its failure is zero. We also
assume that any further wheel failure from asymmetrical braking or recovery states will lead the
BBW to a single terminally failed state. Draw a Markov model and explain the model construction
procedure (15 marks).
2. Consider that in [1]. all wheels have the same failure rates of 0.0001 failure per hour and provide a
Python code to calculate and visualise the reliability curve for 2000 hours (15 marks).
3. Only consider the failure modes of PL, PN1, PN2, B1, B2, and PS, assuming that the wheels are
perfect. Draw a Markov model which shows how the system moves into a state of complete loss of
braking and explain the model construction procedure. (15 marks).
4. Consider that in [3], all failure modes have the same failure rate of 0.000623 failure/hours. Provide
a Python code to calculate and visualise the reliability curve for 2000 hours. (20 marks).
5. Consider only failure modes of B1 and B2 and Assume all other components are perfect. Also,
assume they are repairable with a failure rate of 0.0002 and a repair rate of 0.01 repair per hour.
Construct a new Markov model to evaluate the Availability and MTBF of the Bus subsystem. Please
provide a Python code for steady-state availability and MTBF calculation. The intention is to only
evaluate the availability and MTBF of the Bus sub-system. (20 marks)
6. Consider only the failure modes of PN1 and PN2 and assume all other components are perfect. Only
focus on the reliability of pedal nodes and explain how we can improve the reliability using
reconfigurable Triple Modular Redundancy (TMR) architecture supported with three hot standby 3
redundancies. For all components, please consider the fixed failure rate of 0.000432. Construct a
new Markov model to evaluate the reliability of the Pedal Node subsystem. Please provide a Python
code for reliability calculation and visualise the unreliability curve for 3000 hours (15 marks).
Notes:
• Explain your solutions in [1-6] above with a short paragraph of text to show your understanding.
Avoid verbosity. Up to 30% of marks will be deducted for lack of explanation.
• For computational problems [2, 4, 5 and 6], please submit your Python code in separate files. These
files should be named according to the question number (e.g., Question2.py, Question4.py, etc.).
Please ZIP the files with the final report and submit it as a single-file submission.
• Ensure your code is runnable. If your code cannot be executed due to errors, it will be examined
manually, and marks will be awarded based on the effort and correctness of the approach.