Repairable failure‐delay systems with elementary structure

Abstract

SUMMARYThis paper defines repairable failure-delay systems, and gives explicit formulae for their availability. It presents models for single-component, series and parallel systems with delay at system level, and a 'rare event' approximation for availability and reliability of series systems with delay at component level. Finally, it uses a renewal terminating process for deriving the limiting distribution of the lifetime of failure-delay systems.K E I ' WORDS Failure-delay system Availability Reliability Renewal processRenewal terminating process Markov process . INTRODUCTIONA current assumption in systems reliability theory is that system failure occurs at the occurrence of a cutset (i.e. cutset occurrence at time z implies failure of system at time r ) ; we call this the simiritaneiry assumption. This assumption is realistic for many systems; some systems, however, allow a non-negligible time interval between cutset occurrence and system failure. ' -l o By relaxation of the simultaneity assumption, we have introduced a new family of reliability systems, called 'failure-delay systems' (FDS).' For these systems, if at a given moment a structural failure condition occurs (i.e. a cutset), the system fails after a critical time 7, and only if the structural failure condition is still present. This critical time 7, called the 'delay', may be either deterministic or random; in the first case, it is specified by a given value or a given function, in the second case, by a given distribution.In the literature, we can find the following systems with failure-delay: a system with fixed down time, I.' a redundant system with safety p e r i~d ,~ a semi-repairable system, and also delay operators in fault tree analysis. We formally characterized failure-delay systems in Reference 7, and evaluated their reliability. In this paper, we consider repairable failure-delay systems and evaluate their availability (instantaneous and steady-state) by an alternating renewal process. 1 , 4 . 1 1 9 1 4 An example of repairable failure-delay systems is an exothermic chemical reactor. The heat produced by the reactor is evacuated by a continuously functioning cooling circuit, to maintain the temperature in the reactor constant. When the cooling circuit fails, the temperature in the reactor increases and, if the down time exceeds a critical value 7 (the delay), the main parts of the reactor fail and a long time is needed for their repair. However, if the repair time of the cooling circuit does not exceed 7, the reactor does not fail.