Topics of the Presentation

1. 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

2. System DescriptionOperational Scenario Roberto Filippini AB-BT

3. 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

4. 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

5. The Beam Loss ModelMarkov Chain Markov Chain Roberto Filippini AB-BT

6. 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

7. 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

8. Updating ModelBeam Loss and Planned Dump Requests Markov Chain Roberto Filippini AB-BT

9. 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

10. 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

11. 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

12. The General ModelPutting All Together Roberto Filippini AB-BT

13. 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

14. The MKD ModelRedundancy, Surveillance, Post mortem Not-Homogeneous Markov Chain Roberto Filippini AB-BT

15. 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

16. MKD AnalysisResults Over One Year (400 Missions) Roberto Filippini AB-BT

17. 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