Module spare parts ABB CI534V02 3BSE010700R1

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ABB CI534V02 3BSE010700R1

3.2.2 Solution Tevkique for Safe Failure Markov Model. The effective repair rate includes the repair for detected and undetected safe failures. Detected safe failures can be repaired on-line at a much faster rate. Undetected safe failures can only be repaired after the system is taken off-line for periodic testing. The effective repair rate is determined below. The safe failure rate can be broken down as: iS = CSXSD + (1_ CS) 'sU Where: XSD iSU Cs Safe failure rate of a component Safe detected failure rate of a component Safe undetected failure rate of a component Fraction of safe failures detected by diagnostic coverage The generalized Markov model for safe failures is shown below: Where:r 0 /-ot A2pt Failure rate from the intermediate state to the spurious trip state Repair rate when detected due to on-line testing Repair rate for off-line periodic testing This model can be simplified to the following by determining the effective repair rate. Firste MPR Associates, Inc. I M P R 320 King Street Alexandria, VA 22314 Calculation No. Pre red By Checked By 426-001-CBS-01 Where: = Effective repair rate The effective repair rate can be determined by equating the MT'YF for each model. After algebraic manipulation, the MTTF's can be shown to be equal if: 1 / (, + 0) = Cs / (Lot + 0) + (1- CS) / (@,Lpt + 0) Solving for the effective repair rate yields: A, = [(1 - Cs) /Apt.+c + C0t+ AptA03 / [CSAP, + (1- CS) A, + 0] The MTTF can be determined from the Markov model by integrating the probability for the time that the system is in a non-failed states. States 1 through 11 are the non-failed states. Therefore, the MT1FF is: - 11 MTTF= f P(t) ]dt 0 Where: Pi(t) " Probability to be in the ith state at time t A closed form solution to this model exists. From Reference 5, the MTTF is given below. Note that this solution has been verified using alternative techniques outlined in Reference 4
3.2.2 Solution Tevkique for Safe Failure Markov Model. The effective repair rate includes the repair for detected and undetected safe failures. Detected safe failures can be repaired on-line at a much faster rate. Undetected safe failures can only be repaired after the system is taken off-line for periodic testing. The effective repair rate is determined below. The safe failure rate can be broken down as: iS = CSXSD + (1_ CS) 'sU Where: XSD iSU Cs Safe failure rate of a component Safe detected failure rate of a component Safe undetected failure rate of a component Fraction of safe failures detected by diagnostic coverage The generalized Markov model for safe failures is shown below: Where:r 0 /-ot A2pt Failure rate from the intermediate state to the spurious trip state Repair rate when detected due to on-line testing Repair rate for off-line periodic testing This model can be simplified to the following by determining the effective repair rate. Firste MPR Associates, Inc. I M P R 320 King Street Alexandria, VA 22314 Calculation No. Pre red By Checked By 426-001-CBS-01 Where: = Effective repair rate The effective repair rate can be determined by equating the MT'YF for each model. After algebraic manipulation, the MTTF's can be shown to be equal if: 1 / (, + 0) = Cs / (Lot + 0) + (1- CS) / (@,Lpt + 0) Solving for the effective repair rate yields: A, = [(1 - Cs) /Apt.+c + C0t+ AptA03 / [CSAP, + (1- CS) A, + 0] The MTTF can be determined from the Markov model by integrating the probability for the time that the system is in a non-failed states. States 1 through 11 are the non-failed states. Therefore, the MT1FF is: - 11 MTTF= f P(t) ]dt 0 Where: Pi(t) " Probability to be in the ith state at time t A closed form solution to this model exists. From Reference 5, the MTTF is given below. Note that this solution has been verified using alternative techniques outlined in Reference 4

3.2.2 Solution Tevkique for Safe Failure Markov Model. The effective repair rate includes the repair for detected and undetected safe failures. Detected safe failures can be repaired on-line at a much faster rate. Undetected safe failures can only be repaired after the system is taken off-line for periodic testing. The effective repair rate is determined below. The safe failure rate can be broken down as: iS = CSXSD + (1_ CS) 'sU Where: XSD iSU Cs Safe failure rate of a component Safe detected failure rate of a component Safe undetected failure rate of a component Fraction of safe failures detected by diagnostic coverage The generalized Markov model for safe failures is shown below: Where:r 0 /-ot A2pt Failure rate from the intermediate state to the spurious trip state Repair rate when detected due to on-line testing Repair rate for off-line periodic testing This model can be simplified to the following by determining the effective repair rate. Firste MPR Associates, Inc. I M P R 320 King Street Alexandria, VA 22314 Calculation No. Pre red By Checked By 426-001-CBS-01 Where: = Effective repair rate The effective repair rate can be determined by equating the MT'YF for each model. After algebraic manipulation, the MTTF's can be shown to be equal if: 1 / (, + 0) = Cs / (Lot + 0) + (1- CS) / (@,Lpt + 0) Solving for the effective repair rate yields: A, = [(1 - Cs) /Apt.+c + C0t+ AptA03 / [CSAP, + (1- CS) A, + 0] The MTTF can be determined from the Markov model by integrating the probability for the time that the system is in a non-failed states. States 1 through 11 are the non-failed states. Therefore, the MT1FF is: - 11 MTTF= f P(t) ]dt 0 Where: Pi(t) " Probability to be in the ith state at time t A closed form solution to this model exists. From Reference 5, the MTTF is given below. Note that this solution has been verified using alternative techniques outlined in Reference 4