A Novel Markov System Dynamics Framework for Reliability Analysis of Systems

Rao, M. Srinivasa; Naikan, V. N. Achuta

doi:10.1515/eqc.2009.101

Cited by 5 publications

(3 citation statements)

References 10 publications

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“…Indeed, despite the difference between the Markov and the system dynamic models in terms of the stochastic and deterministic nature of the states, due to the important similarity of Markov model with system dynamic model in terms of “state” and “transition”, these two models can be combined with each other or even in some cases converted to each other [ 14 ]. This hybrid model have been mainly used in non-medical fields and repairable systems for reliable analysis in a more realistic way [ 12 , 15 – 17 ]. In fact, in a MSD model the failure and repair or control rate of a system, which are time-varying indexes, are considered for transient availability modeling or analysis of system reliability in calculations [ 15 , 18 ].…”

Section: Introductionmentioning

confidence: 99%

“…This hybrid model have been mainly used in non-medical fields and repairable systems for reliable analysis in a more realistic way [ 12 , 15 – 17 ]. In fact, in a MSD model the failure and repair or control rate of a system, which are time-varying indexes, are considered for transient availability modeling or analysis of system reliability in calculations [ 15 , 18 ]. Due to information feedback theory, easiness of tweaking parameters to test different hypotheses and possibility of providing solutions to various problems by adjusting flow rates [ 16 ], system dynamics models are a suitable solution to eliminate computational limitations of Markov models.…”

Section: Introductionmentioning

confidence: 99%

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Predicting the natural history of metabolic syndrome with a Markov-system dynamic model: a novel approach

Rezaianzadeh

Morasae

Khalili

et al. 2021

BMC Med Res Methodol

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Background Markov system dynamic (MSD) model has rarely been used in medical studies. The aim of this study was to evaluate the performance of MSD model in prediction of metabolic syndrome (MetS) natural history. Methods Data gathered by Tehran Lipid & Glucose Study (TLGS) over a 16-year period from a cohort of 12,882 people was used to conduct the analyses. First, transition probabilities (TPs) between 12 components of MetS by Markov as well as control and failure rates of relevant interventions were calculated. Then, the risk of developing each component by 2036 was predicted once by a Markov model and then by a MSD model. Finally, the two models were validated and compared to assess their performance and advantages by using mean differences, mean SE of matrices, fit of the graphs, and Kolmogorov-Smirnov two-sample test as well as R2 index as model fitting index. Results Both Markov and MSD models were shown to be adequate for prediction of MetS trends. But the MSD model predictions were closer to the real trends when comparing the output graphs. The MSD model was also, comparatively speaking, more successful in the assessment of mean differences (less overestimation) and SE of the general matrix. Moreover, the Kolmogorov-Smirnov two-sample showed that the MSD model produced equal distributions of real and predicted samples (p = 0.808 for MSD model and p = 0.023 for Markov model). Finally, R2 for the MSD model was higher than Markov model (73% for the Markov model and 85% for the MSD model). Conclusion The MSD model showed a more realistic natural history than the Markov model which highlights the importance of paying attention to this method in therapeutic and preventive procedures.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Predicting the natural history of metabolic syndrome with a Markov-system dynamic model: a novel approach

Rezaianzadeh

Morasae

Khalili

et al. 2021

BMC Med Res Methodol

View full text Add to dashboard Cite

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“…Casi dos décadas después de Mohapatra y Roy [8], su trabajo es citado por Rao y Naikan [9], quienes presentaron un enfoque que llaman Dinámica de Sistemas Markoviano, en el que combinan los MM con la DS para realizar análisis de fiabilidad de un sistema no reparable con un único componente. Sin embargo, por las características del sistema, se trata de un problema relativamente sencillo además de incluir el supuesto de homogeneidad.…”

Section: Introductionunclassified

Modelo de dinámica de sistemas para la modelación de cadenas de Markov de tiempo Continuo – No homogéneas

Velasco

Gómez

2020

Sci. tech

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This paper treats with two modeling techniques: Nonhomogeneous Continuous-Time Markov Chains (NH-CTMC) and Systems Dynamics (SD). In general, each of these focuses on different types of problems. While the NH-CTMCare used in the modeling of stochastic processes, the SD is focused on modeling a system from functional relationships between its components. However, it is demonstrated that the concepts and tools of the SD can be effectively used in modeling of NH-CTMC by means of the building and simulating an Equivalent Systems Dynamics Model (ESDM) representing the state probabilities over time. The ESDMis based on mathematical equivalence between the two models, which is shown through an example and relevant considerations in its application are summarized. This proposal could be used to study reliability in complex systems using more simple calculations.

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Availability modeling of repairable systems using Markov system dynamics simulation

Rao¹,

Naikan

2015

International Journal of Quality &Amp; Reliability Management

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Purpose – The purpose of this paper is to propose a novel hybrid approach called as Markov System Dynamics (MSD) approach which combines the Markov approach with system dynamics (SD) simulation approach for availability modeling and to study the dynamic behavior of repairable systems. Design/methodology/approach – In the proposed approach the identification of the single unit repairable system all possible states has been performed by using the Markov approach. The remaining stages of traditional Markov analysis are highly mathematically intensive. The present work proposes a hybrid approach called as MSD approach which combines the Markov approach with SD simulation approach to overcome some of the limitations of Markov process in a simple and efficient way for availability modeling and to study the dynamic behavior of this system. Findings – The proposed framework is illustrated for a single unit repairable system. The worked out example shows the steady state point and also it gives the point, interval and steady state availabilities and also the dynamic behavior of the system. However this methodology can be extended easily for more complex multi-state maintainable systems. The results of the simulation when compared with that obtained by traditional Markov analysis clearly validate the proposed approach as an alternative approach for availability modeling of repairable systems. Practical implications – In many practical situations we require to find the time at which our system reaches steady state conditions for planning maintenance activities. The proposed MSD method in this paper is capable of finding this steady state point very easily. Originality/value – The proposed approach clearly indicates the time at which the system reaches its steady state and calculates the point, interval availabilities for planning maintenance activities. The different parties, i.e., engineers and machine operators, can jointly work with this model in order to understand the dynamic behavior of repairable systems.

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A Novel Markov System Dynamics Framework for Reliability Analysis of Systems

Cited by 5 publications

References 10 publications

Predicting the natural history of metabolic syndrome with a Markov-system dynamic model: a novel approach

Predicting the natural history of metabolic syndrome with a Markov-system dynamic model: a novel approach

Modelo de dinámica de sistemas para la modelación de cadenas de Markov de tiempo Continuo – No homogéneas

Availability modeling of repairable systems using Markov system dynamics simulation

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