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

Elena Rogova*, Gabriel Lodewijks, Mary Ann Lundteigen

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

12 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)373-382
JournalJournal of Risk and Reliability: Proceedings of the Institution of Mechanical Engineers, Part O
Issue number4
Publication statusPublished - 2017


  • analytical formulas
  • average frequency of dangerous failures
  • average probability of failure on demand
  • nonconstant failure rates
  • Reliability assessment
  • Weibull distribution


Dive into the research topics of 'Analytical formulas of PFD and PFH calculation for systems with nonconstant failure rates'. Together they form a unique fingerprint.

Cite this