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- The operational scenario
- Re-analyzing the model for the beam losses.
- Updating the model.
- Beam loss and normal conclusion.

- The general model.
- Some approximations for managing complexity.

- Trading-off safety performance (a case study).
- Conclusions.

Roberto Filippini AB-BT

Roberto Filippini AB-BT

The model.

- The system includes the BLM, the BICs, the beam permit loop and the LBDS. The BEM is included in the LBDS.
- The BIC6 is kept separated from the other BICs, for the function of sending a dump request to the LBDS.
- Failure rates are assumed constant.
Beam Losses

- The likelihood of having beam losses at a certain portion is uniformly distributed along the ring and involves only one BLM at a time.
- Beam losses average rate is assumed 1/48h (200days).
Analysis.

- The probability of being available at the time of a beam loss (continuous operation, no planned dump requests).

Roberto Filippini AB-BT

Distribution of a single beam loss

Probability of the number of beam loss events respect to time t

Probability a beam loss occurred in[0,t]

Beam Loss Events

Roberto Filippini AB-BT

Markov Chain

Roberto Filippini AB-BT

1-R(t)

T1

T2

Tn

P(X3): System not available at a Beam loss

1-R(m)

Model parameters setting

E{T i+1 – Ti }= 48h

E{N(t)} = 100, (t = 4800h)

P(X3): Mean System Unreliability after 100 missions of mean duration T = 48h

Roberto Filippini AB-BT

About the model:

- The single mission terminates at a beam loss and restarts only if it has been successfully terminated.
- The overall process (one year) is a sequence of dump requests at the time of the beam loss. It is a Markov renewalprocess.
What is to update:

- The mission has a finite duration T due to the planned dump requests:
- The system configuration at a planned dump requests is in part different form the configuration needed for a beam loss.

Roberto Filippini AB-BT

Markov Chain

Roberto Filippini AB-BT

1-R(t)

1-R(t)

1-R(t)

Unavailable at a beam loss occurred in [0,10] : P(X4)

Unavailable at a planned dump request at any time: P(X2)+P(X3)

Mission aborts distribution due to a beam loss (1/48h) over 400 missions

Probability of unsafe dump at time t=10

At time t =10h the unavailability of the system BIC1-Permit Loop-BIC6-LBDS is added

Roberto Filippini AB-BT

About the model:

- More realistic reliability figures are obtained.
- Reliability over 1 year involves a more complex renewal process.
- System is as good as new at the start of a mission.
- Surveillance (BET, etc…) not yet included.
The next step: to include surveillance:

- Benefits: reduction of the system failure rate.
- Drawbacks: generation of dump requests.
Approximations are necessary for managing complexity.

- For the reliability of a single operation.
- For the reliability over one year.

Beam Loss Model: Unreliability over 400 missions (10h each)

Beam Loss and Planned dump requests Model: Unreliability over 400 missions (10h each)

Roberto Filippini AB-BT

Assumptions during a single mission

- A1: The probabilities are evaluated at time t = T.
- A2: All the cases leading to a dump requests are modeled and analyzed separately.
- A3: The system reliability R(T) is calculated with respect to the system configuration at the time of a dump request.
Assumptions over one year

- A4: The system is as good as new after the check (no aging and wearing).
- A5: We assume 400 LHC operation cycles per year (average).
The approximations 1,2,3 lead to a lower bound for the system reliability over one mission. The assumptions 4 can be relaxed.

Roberto Filippini AB-BT

Roberto Filippini AB-BT

- Analysis of safety and average number of false dumps of the MKD (LBDS) over one year.

Roberto Filippini AB-BT

Not-Homogeneous Markov Chain

Roberto Filippini AB-BT

Modeling assumptions

- BEM, triggering and re-triggering systems have not been included.
- The data acquisition channels going to the BET are identical and fail always safe (dump request).
- Constant failure rates.
- The length of an LHC operation (the mission) is 10h.
- After the post mortem the system is as good as new.

Roberto Filippini AB-BT

Roberto Filippini AB-BT

- The beam loss model was updated considering the conclusion due to a planned dump request
- The model is very compact although complex in the transition rates.
- To manage things at higher level needs approximations.
- The next steps:
- To analyze the contribution of surveillance in terms of safety gain and false dumps per year as shown for the MKD system.
- Sensitivity analysis and trade-off studies (safety against false dumps) of the most critical systems.

Roberto Filippini AB-BT