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Topics of the Presentation. 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.

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Topics of the presentation

Topics of the Presentation

  • 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


System description operational scenario

System DescriptionOperational Scenario

Roberto Filippini AB-BT


The beam loss model basic assumptions

The Beam Loss ModelBasic Assumptions

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


The beam loss model modeling the beam loss event

The Beam Loss ModelModeling the Beam Loss Event

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


The beam loss model markov chain

The Beam Loss ModelMarkov Chain

Markov Chain

Roberto Filippini AB-BT


The beam loss model results

1-R(t)

T1

T2

Tn

The Beam Loss ModelResults

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


The beam loss model comments

The Beam Loss ModelComments

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


Updating model beam loss and planned dump requests

Updating ModelBeam Loss and Planned Dump Requests

Markov Chain

Roberto Filippini AB-BT


Updating model results at the end of a 10h operation

1-R(t)

1-R(t)

1-R(t)

Updating ModelResults at the End of a 10h Operation

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


Updating model comments

Updating ModelComments

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


The model including surveillance assumptions

The Model Including SurveillanceAssumptions

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


The general model putting all together

The General ModelPutting All Together

Roberto Filippini AB-BT


Mkd a case study epac paper

MKDA Case Study (EPAC Paper)

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

Roberto Filippini AB-BT


The mkd model redundancy surveillance post mortem

The MKD ModelRedundancy, Surveillance, Post mortem

Not-Homogeneous Markov Chain

Roberto Filippini AB-BT


Mkd analysis assumptions

MKD AnalysisAssumptions

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


Mkd analysis results over one year 400 missions

MKD AnalysisResults Over One Year (400 Missions)

Roberto Filippini AB-BT


Conclusions

Conclusions

  • 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


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