Analytical formulas of PFD and PFH calculation for systems with nonconstant failure rates

Most analytical formulas developed for the PFD and PFH calculation assume a constant failure rate. This assumption does not necessarily hold for system components that are affected by wear. This article presents methods of analytical calculations of PFD and PFH for an M-out-of-N redundancy architecture with nonconstant failure rates and demonstrates its application in a simple case study. The method for PFD calculation is based on the ratio between cumulative distribution functions and includes forecasting of PFD values with a possibility of update of failure rate function. The approach for the PFH calculation is based on simplified formulas and the definition of PFH. In both methods, a Weibull distribution is used for characteristics of the system behavior. The PFD and PFH values are obtained for low, moderate and high degradation effects and compared with the results of exact calculations. Presented analytical formulas are a useful contribution to the reliability assessment of M-out-of-N systems.

[1]  C Soares,et al.  An age-based preventive maintenance for offshore wind turbines , 2014 .

[2]  Rajendra Kumar,et al.  Accurate reliability modeling using Markov Analysis with non-constant hazard rates , 2009, 2009 IEEE Aerospace conference.

[3]  Per Hokstad,et al.  MVA Report Reliability Prediction Method for Safety Instrumented Systems – PDS Example collection , 2010 Edition , 2011 .

[4]  J Chudoba.  Modelling of dynamical dependability by using stochastic processes , 2011 .

[5]  Bernd Bertsche,et al.  Reliability in Automotive and Mechanical Engineering: Determination of Component and System Reliability , 2008 .

[6]  P. Dersin,et al.  Selecting test and maintenance strategies to achieve availability target with lowest life-cycle cost , 2008, 2008 Annual Reliability and Maintainability Symposium.

[7]  Hui Jin,et al.  New PFH-formulas for k-out-of-n: F-systems , 2013, Reliab. Eng. Syst. Saf..

[8]  Mary Ann Lundteigen,et al.  Analytical formulas of PFD calculation for systems with non-constant failure rates , 2015 .

[9]  Baek-Ju Sung.  A Design Method and Reliability Assessment of High Speed Solenoid Actuator , 2012 .

[10]  Abraham Almaw Jigar,et al.  Quantification of Reliability Performance: Analysis Methods for Safety Instrumented System , 2013 .

[11]  Eric R. Ziegel,et al.  System Reliability Theory: Models, Statistical Methods, and Applications , 2004, Technometrics.

[12]  Fares Innal,et al.  Generalized analytical expressions for safety instrumented systems' performance measures: PFDavg and PFH , 2015 .

[13]  M. Rausand.  Reliability of Safety-Critical Systems: Theory and Applications , 2014 .

[14]  Elena Rogova,et al.  Braking system redundancy requirements for moving walks , 2015, Reliab. Eng. Syst. Saf..