First failure time of dependent parallel systems with safety periods

Shanthikumar, J. George

doi:10.1016/0026-2714(86)90238-6

Cited by 12 publications

(1 citation statement)

References 11 publications

(9 reference statements)

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“…Reliability models involving dependent geometric sums can be found in the literatue, e.g. Shanthikumar and Sumita [9] or Shanthikumar [7] and the references there.…”

Section: Zenbue (Nwue) Iff J Lz(u)du 5 ( 2 )Zzfz (T) For T 2 0 Zehnbmentioning

confidence: 99%

Ageing properties of certain dependent geometric sums

Kováts¹,

Móri²

1992

Journal of Applied Probability

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We study some distribution properties of a random sum of i.i.d. non-negative random variables, where the number of terms is geometrically distributed and not independent of the summands. The results are applied to the system failure time of a one-unit system with a single spare and repair facility. In such a system when the operating unit fails it is immediately replaced by the spare and sent to the repair facility. The system continues operating until the first time when the failed unit has not yet been repaired by the failure of the operating unit. Certain ageing properties such as NBU, NWU, NBUE, NWUE, HNBUE, HNWUE, L+ and L– are shown to be inheritable from the working time of the operating unit to the system lifetime.

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“…Reliability models involving dependent geometric sums can be found in the literatue, e.g. Shanthikumar and Sumita [9] or Shanthikumar [7] and the references there.…”

Section: Zenbue (Nwue) Iff J Lz(u)du 5 ( 2 )Zzfz (T) For T 2 0 Zehnbmentioning

confidence: 99%

Ageing properties of certain dependent geometric sums

Kováts¹,

Móri²

1992

Journal of Applied Probability

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Repairable failure‐delay systems with elementary structure

Limnios

1992

Appl. Stochastic Models Data Anal.

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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.

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A Survey and Analysis of the Application of the Laplace Transform to Present Value Problems

Grubbström

Yinzhong

1991

Modelling for Financial Decisions

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First failure time of dependent parallel systems with safety periods

Cited by 12 publications

References 11 publications

Ageing properties of certain dependent geometric sums

Ageing properties of certain dependent geometric sums

Repairable failure‐delay systems with elementary structure

A Survey and Analysis of the Application of the Laplace Transform to Present Value Problems

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