Survival Probabilities for Shock and Wear Models Governed by Phase-Type Distributions

“…Reliability and maintenance policies of systems considering random component failure have been widely studied in the literature, see [6,8,10,13,19,21,22,31]. However, the most common assumption is that failures occur independently and with the same distribution, being the Poisson, renewal, or phase-type (PH) renewal processes the usual arrival processes used to model the failures.…”

Section: Introductionmentioning

confidence: 99%

Failure modeling of an electrical N-component framework by the non-stationary Markovian arrival process

Rodríguez

Lillo

Ramírez‐Cobo

2015

Reliability Engineering & System Safety

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“…Besides, the closure properties of phase-type distributions under some operations are helpful in the reliability context [2]. In the literature [3,19,27], the phase-type distribution is applied to analyze the reliability of shock models. In the literature [3,19], the interarrival time between shocks is assumed to be continuous phase-type distribution.…”

Section: Introductionmentioning

confidence: 99%

“…In the literature [3,19,27], the phase-type distribution is applied to analyze the reliability of shock models. In the literature [3,19], the interarrival time between shocks is assumed to be continuous phase-type distribution. Shocks may lead to system failure, and the system may fail due to wear.…”

Section: Introductionmentioning

confidence: 99%

Reliability modeling for dependent competing failure processes with phase-type distribution considering changing degradation rate

Lyu¹,

Wang²,

Zhang³

et al. 2021

Eksploatacja i Niezawodność – Maintenance and Reliability

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In this paper, a system reliability model subject to Dependent Competing Failure Processes (DCFP) with phase-type (PH) distribution considering changing degradation rate is proposed. When the sum of continuous degradation and sudden degradation exceeds the soft failure threshold, soft failure occurs. The interarrival time between two successive shocks and total number of shocks before hard failure occurring follow the continuous PH distribution and discrete PH distribution, respectively. The hard failure reliability is calculated using the PH distribution survival function. Due to the shock on soft failure process, the degradation rate of soft failure will increase. When the number of shocks reaches a specific value, degradation rate changes. The hard failure is calculated by the extreme shock model, cumulative shock model, and run shock model, respectively. The closed-form reliability function is derived combining with the hard and soft failure reliability model. Finally, a Micro-Electro-Mechanical System (MEMS) demonstrates the effectiveness of the proposed model.

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Survival Probabilities for Shock and Wear Models Governed by Phase-Type Distributions

Cited by 19 publications

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Dynamic assessment of multi-state systems using phase-type modeling

Dynamic assessment of multi-state systems using phase-type modeling

Failure modeling of an electrical N-component framework by the non-stationary Markovian arrival process

Reliability modeling for dependent competing failure processes with phase-type distribution considering changing degradation rate

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