703 research outputs found
A complex multi-state k-out-of-n: G system with preventive maintenance and loss of units
In this study, a multi-state k-out-of-n: G system subject to multiple events is modeled through a Markovian Arrival Process with marked arrivals. The system is composed initially of n units and is active when at least k units are operational. Each unit is multi-state, each of which is classified as minor or major according to the level of degradation presented. Each operational unit may undergo internal repairable or non-repairable failures, external shocks and/or random inspections. An external shock can provoke extreme failure, while cumulative external damage can deteriorate internal performance. This situation can produce repairable and non-repairable failures. When a repairable failure occurs the unit is sent to a repair facility for corrective repair. If the failure is non-repairable, the unit is removed. When the system has insufficient units with which to operate, it is restarted. Preventive maintenance is employed in response to random inspection. The system is modeled in an algorithmic and computational form. Several interesting measures of performance are considered. Costs and rewards are included in the system. All measures are obtained for transient and stationary regimes. A numerical example is analyzed to determine whether preventive maintenance is profitable, financially and in terms of performance.Junta de Andalucía (Spain) FQM-307Ministerio de Economía y Competitividad (España) MTM2017-88708-PEuropean Regional Development Fund (ERDF
Markov and Semi-markov Chains, Processes, Systems and Emerging Related Fields
This book covers a broad range of research results in the field of Markov and Semi-Markov chains, processes, systems and related emerging fields. The authors of the included research papers are well-known researchers in their field. The book presents the state-of-the-art and ideas for further research for theorists in the fields. Nonetheless, it also provides straightforwardly applicable results for diverse areas of practitioners
A complex multi-state system with vacations in the repair
A complex multi-state system subject to wear failure and given
preventive maintenance is considered. Various internal levels of degradation
are assumed. The repair facility is composed of a repairperson, who may take
one or more vacations during the period considered. A policy is established
for the repairperson’s vacation time. Two types of task may be performed by
the repairperson: corrective repair and preventive maintenance. All
embedded times in the system are phase type distributed. The transient and
stationary distributions are determined and several reliability measures are
developed in a matrix-algorithmic form. Costs and rewards are included in
the model. The results are implemented computationally with Matlab. A
numerical example shows that the distribution of vacation time can be
optimised according to the net reward established.Junta de Andalucía, Spain, FQM-307Ministerio de Economía y Competitividad, España, under Grant MTM2017−88708−PEuropean Regional Development Fund (ERDF
Optimizing a Multi-State Cold-Standby System with Multiple Vacations in the Repair and Loss of Units
A complex multi-state redundant system with preventive maintenance subject to multiple
events is considered. The online unit can undergo several types of failure: both internal and those
provoked by external shocks. Multiple degradation levels are assumed as both internal and external.
Degradation levels are observed by random inspections and, if they are major, the unit goes to a
repair facility where preventive maintenance is carried out. This repair facility is composed of a single
repairperson governed by a multiple vacation policy. This policy is set up according to the operational
number of units. Two types of task can be performed by the repairperson, corrective repair and
preventive maintenance. The times embedded in the system are phase type distributed and the
model is built by using Markovian Arrival Processes with marked arrivals. Multiple performance
measures besides the transient and stationary distribution are worked out through matrix-analytic
methods. This methodology enables us to express the main results and the global development in
a matrix-algorithmic form. To optimize the model, costs and rewards are included. A numerical
example shows the versatility of the model
A discrete MMAP for analysing the behaviour of a multi-state complex dynamic system subject to multiple events.
A complex multi-state system subject to different types of failures, repairable and/or nonrepairable, external shocks and preventive maintenance is modelled by considering a discrete
Markovian arrival process with marked arrivals (D-MMAP). The internal performance of the
system is composed of several degradation states partitioned into minor and major damage
states according to the risk of failure. Random external events can produce failures throughout
the system. If an external shock occurs, there may be an aggravation of the internal degradation, cumulative external damage or extreme external failure. The internal performance and the
cumulative external damage are observed by random inspection. If major degradation is
observed, the unit goes to the repair facility for preventive maintenance. If a repairable failure
occurs then the system goes to corrective repair with different time distributions depending on
the failure state. Time distributions for corrective repair and preventive maintenance depend on
the failure state. Rewards and costs depending on the state at which the device failed or was
inspected are introduced. The system is modelled and several measures of interest are built into
transient and stationary regimes. A preventive maintenance policy is shown to determine the
effectiveness of preventive maintenance and the optimum state of internal and cumulative
external damage at which preventive maintenance should be taken into account. A numerical
example is presented, revealing the efficacy of the model. Correlations between the numbers of
different events over time and in non-overlapping intervals are calculated. The results are
expressed in algorithmic-matrix form and are implemented computationally with Matlab.Junta de Andalucía, Spain, under the grant FQM307Ministerio de Economía y Competitividad, España, MTM2017-88708-PEuropean Regional Development Fund (ERDF
Bounding steady-state availability models with phase type repair distributions
We propose a method to obtain bounds for the steady-state availability using Markov models in which only a small portion of the state space is generated. The method is applicable to models with phase type repair distributions and involves the solution of only 4 linear systems of the size of the generated state space, independently on the number of “return” states. A numerical example is presented to illustrate the method.Postprint (author’s final draft
Bounding steady-state availability models with group repair and phase type repair distributions
We propose an algorithm to obtain bounds for the steady-state availability using Markov
models in which only a small portion of the state space is generated. The algorithm is applicable
to models with group repair and phase type repair distributions and involves the solution of only
four linear systems of the size of the generated state space, independently on the number of
“return” states. Numerical examples are presented to illustrate the algorithm and compare it
with a previous bounding algorithm.Postprint (published version
A survey of the machine interference problem
This paper surveys the research published on the machine interference problem since the 1985 review by Stecke & Aronson. After introducing the basic model, we discuss the literature along several dimensions. We then note how research has evolved since the 1985 review, including a trend towards the modelling of stochastic (rather than deterministic) systems and the corresponding use of more advanced queuing methods for analysis. We conclude with some suggestions for areas holding particular promise for future studies.Natural Sciences and Engineering Research Council (NSERC) Discovery Grant 238294-200
Розрахунок інтенсивності потоку відмов дубльованої системи з паралельним резервуванням
Розглянуто проблему розрахунку інтенсивності потоку відмов для дубльованої відновлюваної системи з паралельним резервуванням. Інтенсивність потоку відмов системи пропонується визначати шляхом застосування спеціального методу, який ґрунтується на марковській моделі на основі розширення простору станів. Коректність такого підходу перевірено методом Монте-Карло.The paper is devoted to problem of failure intensity calculation for doubled repairable system with parallel redundancy. Failure intensity determination is suggested by using special method for extended Markov reliability model. The correctness for such approach is verified by Monte-Carlo method
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