A complex multi-state k-out-of-n: G system with preventive maintenance and loss of units

Castro, Juan Luis

doi:10.1016/j.ress.2020.106797

Cited by 24 publications

(11 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From the first equation of (20) taking into account the initial condition, it follows sπ 0 (s) − 1 = −λ 0 π0 (s) + h(s) b(s + λ 1 ), and therefore, taking into account the expression for h(s), it follows…”

Section: Reliability Function Of 2-out-of-n Systemmentioning

confidence: 99%

“…A review of the most recent works on the reliability study of repairable k -out-of-n systems showed that these studies either focus on non-time-dependent reliability characteristics [5,17,23,28] or are based on assumptions of exponential [29] or PH-type distributions [4,20] of the repair time of the system's components. The latter contain models that can easily be reduced to Markov processes with a discrete set of states.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

ON RELIABILITY FUNCTION OF A K-OUT-OF-N SYSTEM WITH GENERAL REPAIR TIME DISTRIBUTION

Rykov

Kozyrev

Filimonov³

et al. 2020

Prob. Eng. Inf. Sci.

View full text Add to dashboard Cite

The reliability study of k-out-of-n systems is of interest both from theoretical and practical points of view. Applications of such models can be seen in many real-world phenomena, including telecommunication, transmission, transportation, manufacturing, and services. A probabilistic study of a real-world k-out-of-n system often helps to develop an optimal strategy for maintaining high system-level reliability. There are many investigations devoted to the reliability-centric analysis of such systems. We consider a mathematical model of a repairable k-out-of-n system that works until k of its n components have failed. During the system's life cycle, its components are repaired with the help of a single repair facility. It is supposed that the components' lifetimes have an exponential distribution and their repair times have a general distribution. The proposed model is intended to be applied to the description of operation of unmanned rotorcraft high-altitude platforms and to be validated with the help of an experimental prototype. For the considered system, we propose an algorithm for calculation of the reliability function, and for special cases, k = 2 and k = 3, its closed-form representation is given. A numerical investigation is performed for special cases. The obtained results are a first step toward the sensitivity analysis of reliability characteristics of k-out-of-n systems to the shape of the repair time distributions of their components.

show abstract

Section: Reliability Function Of 2-out-of-n Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

ON RELIABILITY FUNCTION OF A K-OUT-OF-N SYSTEM WITH GENERAL REPAIR TIME DISTRIBUTION

Rykov

Kozyrev

Filimonov³

et al. 2020

Prob. Eng. Inf. Sci.

View full text Add to dashboard Cite

show abstract

“…The MAP as a model for the arrival of failures is introduced in [26], and it is applied in [27][28][29][30], for studying different reliability systems. In [31], a system under shocks, damages, and other elements is modeled by a Markovian arrival process with marked arrivals.…”

Section: Introductionmentioning

confidence: 99%

Analysis of k-Out-of-N-Systems with Different Units under Simultaneous Failures: A Matrix-Analytic Approach

Montoro-Cazorla

Pérez‐Ocón

2022

Mathematics

View full text Add to dashboard Cite

An N-system with different units submitted to shock and wear is studied. The shocks cause damage and, eventually, simultaneous failures of several units. The units can also fail due to internal failures. At random times, the system is inspected, and the down units are simultaneously replaced by identical ones. The arrival of shocks is governed by a Markovian arrival process. The operational times and the interarrival times between inspections follow phase-type distributions. The generator of the multidimensional Markov process modeling the system is constructed. This is performed introducing indicator functions for the different transition rates among the units using the algorithm of Kronecker. This is a general Markov process that can be applied for modeling different reliability systems depending on the structure of the units and how the systems operate. The general model is applied to the study of k-out-of-N systems, calculating the main performance measures. A practical example is presented showing the approximation of the model to a system with units following different Weibull distributions.

show abstract

“…This class of distributions was introduced by Neuts [1,2] and allows the modeling of complex problems in an algorithmic and computational way. It has been widely applied in fields such as engineering to model complex systems [3][4][5], queueing theory [6], risk theory [7] and electronics engineering [8].…”

Section: Introductionmentioning

confidence: 99%

A Complex Model via Phase-Type Distributions to Study Random Telegraph Noise in Resistive Memories

et al. 2021

View full text Add to dashboard Cite

A new stochastic process was developed by considering the internal performance of macro-states in which the sojourn time in each one is phase-type distributed depending on time. The stationary distribution was calculated through matrix-algorithmic methods and multiple interesting measures were worked out. The number of visits distribution to a determine macro-state were analyzed from the respective differential equations and the Laplace transform. The mean number of visits to a macro-state between any two times was given. The results were implemented computationally and were successfully applied to study random telegraph noise (RTN) in resistive memories. RTN is an important concern in resistive random access memory (RRAM) operation. On one hand, it could limit some of the technological applications of these devices; on the other hand, RTN can be used for the physical characterization. Therefore, an in-depth statistical analysis to model the behavior of these devices is of essential importance.

show abstract

A complex multi-state k-out-of-n: G system with preventive maintenance and loss of units

Cited by 24 publications

References 29 publications

ON RELIABILITY FUNCTION OF A K-OUT-OF-N SYSTEM WITH GENERAL REPAIR TIME DISTRIBUTION

ON RELIABILITY FUNCTION OF A K-OUT-OF-N SYSTEM WITH GENERAL REPAIR TIME DISTRIBUTION

Analysis of k-Out-of-N-Systems with Different Units under Simultaneous Failures: A Matrix-Analytic Approach

A Complex Model via Phase-Type Distributions to Study Random Telegraph Noise in Resistive Memories

Contact Info

Product

Resources

About