Inference algorithms for the useful life of safety instrumented systems under small failure sample data

Qi Mao, Haiqing Wang*, Ming Yang, Jason Hu

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Safety instrumented systems(SIS) have been widely used in petroleum and chemical plants to detect and respond to dangerous events and prevent them from developing into accidents. The in-service time of SIS does not exceed its useful life is one of the crucial assumptions of IEC functional safety standards. The testing method recommended in the IEC standard is essentially a chi-square testing, where the testing effect is proportional to the sample size and, therefore, not suitable for testing the type of data distribution under small samples. In this paper, a rapid inference method of useful life (RIUL) is proposed to: i) determine whether the distribution type of failure data is exponential under small samples with the help of Anderson-Darling testing, and ii) use the Bayesian sequential testing method for estimating the useful life. The sequential posterior odds ratio testing is introduced to test the equipment failure rate one by one. The proposed RIUL approach is applied to the liquid-level protection circuit of the hot high-pressure separator. The engineering simulation results show that compared with IEC standard methods, the proposed method can be performed with fewer failure data, providing a theoretical basis for reasonable maintenance and replacement of equipment.
Original languageEnglish
Pages (from-to)783-790
Number of pages8
JournalProcess Safety and Environmental Protection
Publication statusPublished - 2023

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • Failure rate
  • Reliability
  • Safety instrumented systems
  • Small samples
  • Useful life


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