Fluctuation Analysis of a Soft-Extreme Shock Reliability Model

Dshalalow, Jewgeni H.; White, Ryan T.

doi:10.3390/math10183312

Cited by 4 publications

(2 citation statements)

References 22 publications

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“…Dshalalow and White [4] in 2022 studied a mixed system with aging, soft, and critical shocks. The aging process was defined as linear with a deterministic slope and it was combined with soft shocks that accelerated aging, and such a cumulative aging process sooner or later crossed a sustainability threshold.…”

Section: Analysis Of Related Literaturementioning

confidence: 99%

Discrete and Continuous Operational Calculus in N-Critical Shocks Reliability Systems with Aging under Delayed Information

Dshalalow,

Aljahani

2023

Mathematics

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We study a reliability system subject to occasional random shocks of random magnitudes W0,W1,W2,… occurring at times τ0,τ1,τ2,…. Any such shock is harmless or critical dependent on Wk≤H or Wk>H, given a fixed threshold H. It takes a total of N critical shocks to knock the system down. In addition, the system ages in accordance with a monotone increasing continuous function δ, so that when δT crosses some sustainability threshold D at time T, the system becomes essentially inoperational. However, it can still function for a while undetected. The most common way to do the checking is at one of the moments τ1,τ2,… when the shocks are registered. Thus, if crossing of D by δ occurs at time T∈τk,τk+1, only at time τk+1, can one identify the system’s failure. The age-related failure is detected with some random delay. The objective is to predict when the system fails, through the Nth critical shock or by the observed aging moment, whichever of the two events comes first. We use and embellish tools of discrete and continuous operational calculus (D-operator and Laplace–Carson transform), combined with first-passage time analysis of random walk processes, to arrive at fully explicit functionals of joint distributions for the observed lifetime of the system and cumulative damage to the system. We discuss various special cases and modifications including the assumption that D is random (and so is T). A number of examples and numerically drawn figures demonstrate the analytic tractability of the results.

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Section: Analysis Of Related Literaturementioning

confidence: 99%

Discrete and Continuous Operational Calculus in N-Critical Shocks Reliability Systems with Aging under Delayed Information

Dshalalow,

Aljahani

2023

Mathematics

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“…N-Critical Shocks Models. As a DCFP with multiple processes involved, an N-critical model, along with aging and soft shocks, was studied in 2022 by Dshalalow and White [ 13 ]. The aging process was defined as linear with a deterministic slope, and it was combined with soft shocks that accelerated aging, and such a cumulative aging process sooner or later crossed a sustainability threshold.…”

Section: Introductionmentioning

confidence: 99%

Dependent Competing Failure Processes in Reliability Systems

Dshalalow,

Aljahani,

White

2024

Entropy

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This paper deals with a reliability system hit by three types of shocks ranked as harmless, critical, or extreme, depending on their magnitudes, being below H1, between H1 and H2, and above H2, respectively. The system’s failure is caused by a single extreme shock or by a total of N critical shocks. In addition, the system fails under occurrences of M pairs of shocks with lags less than some δ (δ-shocks) in any order. Thus, the system fails when one of the three named cumulative damages occurs first. Thus, it fails due to the competition of the three associated shock processes. We obtain a closed-form joint distribution of the time-to-failure, shock count upon failure, δ-shock count, and cumulative damage to the system on failure, to name a few. In particular, the reliability function directly follows from the marginal distribution of the failure time. In a modified system, we restrict δ-shocks to those with small lags between consecutive harmful shocks. We treat the system as a generalized random walk process and use an embellished variant of discrete operational calculus developed in our earlier work. We demonstrate analytical tractability of our formulas which are also validated, through Monte Carlo simulation.

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A novel shock-dependent preventive maintenance policy for degraded systems subject to dynamic environments and N-critical shocks

XiaoHua

Bai

2023

Reliability Engineering & System Safety

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Fluctuation Analysis of a Soft-Extreme Shock Reliability Model

Cited by 4 publications

References 22 publications

Discrete and Continuous Operational Calculus in N-Critical Shocks Reliability Systems with Aging under Delayed Information

Discrete and Continuous Operational Calculus in N-Critical Shocks Reliability Systems with Aging under Delayed Information

Dependent Competing Failure Processes in Reliability Systems

A novel shock-dependent preventive maintenance policy for degraded systems subject to dynamic environments and N-critical shocks

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