Quantification of Reliability Performance: Analysis Methods for Safety Instrumented System
The reliability performance of a safety instrumented system (SIS) can be determined by several
analytical methods, such as simplified formulas, fault tree analysis and Markov analysis. These
methods are mentioned in annex B of IEC 61508-6, but this part is not normative and the user
may choose which method to use based on the specific operational characteristics of the SIS.
Moreover, since it does not provide detailed explanations, proofs and generalized formulas for
koon architecture, it is difficult for the users to understand and use it as a guideline. The purpose
of this report is to provide background and rationale for these and some other commonly
usedmethods, i.e., the PDS method and Rausand?s method, to compare them and suggest alternative methods to overcome some of their weaknesses, and to outline a procedure for their use.
This report provides detailed proofs of the IEC 61508 simplified formulas, i.e., the reliability
block diagram approach, and extend them to general koon architectures. Due emphasis is
given to critically evaluate the PDS method and several issues are discussed; for example, the
conditional relationship of DU and DD failures. As far as these failures required to be quantified
separately, as the PDS method does, an alternative formula is developed that takes this relationship
into account. Among the simplified methods the Rausand?s method is the least detailed
and the PDS method is the most. Nevertheless, the analytical and numerical results show that
these simplified methods are very similar except some slight differences resulted from the respective
levels of details they consider.
It is recognized that fault tree analysis (FTA) is always a good start during SIS reliability quantification,
especially if the SIS is in the design phase. The report sets out a procedure and explores
the proper formula in terms of correcting the optimistic approach used in the FTA. It is
also noted that a hybrid of FTA andMarkov analysis represents a SIS better since some flexibility
in the quantification can be taken care of byMarkov analysis.
Beside the advantages that has already been explored inMarkov analysis, it is acknowledged
and exemplified in the report that the model is appropriate to calculate ?the average probabilitythat the SIS fails and the process demand occurs?, whilst the existing tradition is limited to calculating
?the average probability that the SIS fails? without directly taking the process demands
All these and other existing methods in the area assume constant failure rate though it is,
indeed, unrealistic. This report introduces a new approach to quantify SIS reliability performance
under the assumption of other lifetime distributions and is demonstrated thoroughly
with Weibull distribution. The approach is verified both analytically and numerically for accuracy.
Furthermore, the report establishes a simple procedure that may help users to choose the
most adequate method, among the methods covered in this report, based on the specific operational
characteristics of the SIS. This is further demonstrated in a case study.
Finally, the limitations of the present work are noted and suggestions for some areas of further
researches are given.
Place, publisher, year, edition, pages
Institutt for matematiske fag , 2013. , 159 p.
IdentifiersURN: urn:nbn:no:ntnu:diva-22517Local ID: ntnudaim:8394OAI: oai:DiVA.org:ntnu-22517DiVA: diva2:649761
Tyssedal, John Sølve, FørsteamanuensisRausand, Marvin