Assessment of the Maintenance of the Effectiveness of Safety Schemes by Inspection and Age-replacement of Protective Devices

Expressions are derived for quantities measuring deficienciesoccurring in the protective capabilities of safety schemes comprisedof devices which are subject to random failure. The devicesare assumed to be prone to two modes of failure, one which isreadily detectable in service, and one which is undetectablein service. The expressions take into account the effects ofpreventive maintenance procedures in which devices are inspectedat regularly spaced times to discover and renew devices whichhave failed "detectably", and also devices are replaced aftera specified age in service to mitigate the effects of "undetectable"failures. These expressions are evaluated for devices havingconstant failure rate (i.e. exponential failure distributions)for both modes of failure; and also for a constant "detectable"-failurerate and an increasing "undetectable"-failure rate (i.e. representedby a second order gamma function failure distribution).