Shock and wear degradating systems under three types of repair

Montoro-Cazorla, Delia; Pérez‐Ocón, Rafael

doi:10.1016/j.amc.2012.05.053

Cited by 13 publications

(5 citation statements)

References 10 publications

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“…Neuts et al 24 first investigated this type of model under the assumption that a Poisson process governs external failures and that the lifetime between shocks and repair times after failures follow PH distributions. Furthermore, Montoro-Cazorla et al 29 , Montoro-Cazorla, and Pe´rez-Oco´n [30][31][32] considered shock and wear systems under different types of repair by combining random shock with wear-out as an additional failure mode and ignoring the size of damage caused by a single shock. The PH distribution is widely used to characterize the lifetime of the system and the time between shocks.…”

Section: Introductionmentioning

confidence: 99%

Analyze periodic inspection and replacement policy of a shock and wear model with phase-type inter-shock arrival times using roots method

Tang

2023

Proceedings of the Institution of Mechanical Engineers, Part O:

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We consider a shock and wear model in which the inter-shock arrival process is a phase-type (PH) renewal process, and the system’s lifetime is generally distributed. The system has two competing failure modes. One failure mode is due to random shocks, which cause failure by overloading the system. The other failure mode is owning to wear-out failures, which usually happen after the system has run for many cycles. System failure is not self-announcing and remains undiscovered unless an inspection is performed. The intervals between successive inspections are identical and equal to T time units. If a system failure is detected, the corrective repair or replacement is conducted immediately. If the system is found working at inspection, preventive maintenance will be carried out to prolong its useful life. Furthermore, to model the occurrence of events with an underlying monotonic trend, the extended geometric process (EGP) is employed to account for the impact of different types of failures on the system’s degradation. Moreover, for establishing the cost rate function in our model, the counting process generated from a PH renewal shock process is studied in detail using the roots method and formula for calculating residues. Based on these results, the survival function and other characteristics of the system are further investigated. Finally, numerical examples that determine the optimal inspection period T[Formula: see text] and the optimal replacement policy N[Formula: see text], which minimizes the long-run average cost rate, are presented.

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Section: Introductionmentioning

confidence: 99%

Analyze periodic inspection and replacement policy of a shock and wear model with phase-type inter-shock arrival times using roots method

Tang

2023

Proceedings of the Institution of Mechanical Engineers, Part O:

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“…This measure is of interest in the power transmission line reliability. The replacement policy K was applied in [15], where a system with a limited number of repairs before a replacement is presented. Phase-type distributions and Markov renewal processes are used more and more in the literature due to their generality in applications and the versatility of the calculations.…”

Section: Introductionmentioning

confidence: 99%

“…These papers determined the number of preventive maintenance before the system replacement or the planned replacement time to minimize the expected cost rate, respectively. Meanwhile, authors in [15] pointed out the optimal number of corrective repairs prior to the reposition of the system; other studies of effectiveness are [25][26][27][28][29], and so on.…”

Section: Introductionmentioning

confidence: 99%

Optimizing Costs in a Reliability System under Markovian Arrival of Failures and Reposition by K-Policy Inspection

Montoro-Cazorla

Pérez‐Ocón

2022

Mathematics

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This paper presents an N warm standby system under shocks and inspections governed by Markovian arrival processes. The inspections detect the number of down units, and their replacement is carried out if there are a minimum K of failed units. This is a policy of the type (K,N) used in inventory theory. The study is performed via the up and down periods of the system (cycle); the distribution of these random times and the expected costs for each period comprising the cycle are determined on the basis of individual costs due to maintenance actions (per inspection and replacement of every unit) and others due to operation or inactivity of the system, per time unit. Intermediate addressed calculus are the distributions of the number of inspections by cycle and the expected cost involving every inspection, depending on the number of replaced units. The system is studied in transient and stationary regimes, and some reliability measures of interest and the cost rate are calculated. An optimization of these quantities is performed in terms of the number K in a numerical example. This general model extends to many others in the literature, and, by using the matrix-analytic method, compact and algorithmic expressions are achieved, facilitating its potential application.

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“…From then on, the PH distribution have been frequently applied in queuing theory, statistics signal analysis and inventory theory and so on. In recent years, the PH distribution has also been used in reliability field by several Spanish scholars (see references [20][21][22][23][24][25][26][27][28][29][30], and references contained therein). Repairable systems are usually studied in the continuous time case; nevertheless, not all systems can be continuously monitored, and they must be observed at certain epochs.…”

Section: Introductionmentioning

confidence: 99%

A cold standby repairable system with working vacations and vacation interruption following Markovian arrival process

Liu

Cui

Wen

et al. 2015

Reliability Engineering & System Safety

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Shock and wear degradating systems under three types of repair

Cited by 13 publications

References 10 publications

Analyze periodic inspection and replacement policy of a shock and wear model with phase-type inter-shock arrival times using roots method

Analyze periodic inspection and replacement policy of a shock and wear model with phase-type inter-shock arrival times using roots method

Optimizing Costs in a Reliability System under Markovian Arrival of Failures and Reposition by K-Policy Inspection

A cold standby repairable system with working vacations and vacation interruption following Markovian arrival process

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