Probability of Failure of Safety-Critical Systems Subject to Partial Tests

TL;DR

This paper introduces formulas for assessing the failure probability of MooN safety systems under partial and full testing, including methods for parameter estimation and test strategy optimization, demonstrated with a 2006 system example.

Contribution

It provides new formulas for failure probability assessment of MooN systems with partial tests, along with parameter estimation and test strategy optimization methods.

Findings

Approximate 10% reduction in total PFD through optimized partial test scheduling.

Formulas enable failure rate estimation from feedback data.

Enhanced testing strategies improve system safety performance.

Abstract

A set of general formulas is proposed for the probability of failure on demand (PFD) assessment of MooN architecture (i.e. k-out-of-n) systems subject to proof tests. The proof tests can be partial or full. The partial tests (e.g. visual inspections, partial stroke testing) are able to detect only some system failures and leave the others latent, whereas the full tests refer to overhauls which restore the system to an as good as new condition. Partial tests may occur at different time instants (periodic or not), up to the full test. The system performances which are investigated are the system availability according to time, the PFD average in each partial test time interval, and the total PFD average calculated on the full test time interval. Following the given expressions, parameter estimations are proposed to assess the system failure rates and the partial test effectiveness according to feedback data from previous test policies. Subsequently, an optimization of the partial test strategy is presented. In the 2oo6 system given as example, an improvement of about 10% of the total PFD average has been obtained, just by a better (non-periodic) distribution of the same number of partial tests, in the full test time interval.