Markov and semi-Markov models in system reliability

Farahani, Ameneh; Shoja, Ahmad; Tohidi, Hamid

doi:10.1016/b978-0-323-91943-2.00010-1

Cited by 8 publications

(5 citation statements)

References 181 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…More recently, Farahani et al [20] described the use of Markov chains to carry out the analysis of time-dependent behaviours of the system and to predict the probable failure nature of industrial systems. Malhotra [21] developed a generalized method based on Markovian approach to determine different measures such as transition probabilities, mean time to failure, reliability, and availability for a two-unit cold redundant system with varied demand.…”

Section: Literature Reviewmentioning

confidence: 99%

Stochastic Approach in Performance Modelling of a Repairable Industrial System

2024

IJEM

View full text Add to dashboard Cite

This paper aims to present a quantitative investigation of a case study based on a live industrial refrigeration system exhibiting complex and dynamic behaviour such as randomness, concurrency, and time dependency. The study employs a state-space stochastic Markovian process to model the interactions among the key functional elements of the system. Furthermore, the scientific approach pursued in this study would help improve the availability of the considered plant by establishing a trade-off between investment, economy and quality. Based on the analysis of results, a framework for Decision Support Priorities (DSP) is proposed, emphasizing the criticality of various functional units. This framework could also help set and prioritize maintenance, spare parts, and human resource requirements accordingly.

show abstract

Section: Literature Reviewmentioning

confidence: 99%

Stochastic Approach in Performance Modelling of a Repairable Industrial System

2024

IJEM

View full text Add to dashboard Cite

show abstract

“…These restrictions limit the ability of KTT to model modern engineering systems effectively. Alternative approaches, such as Markov models [15] or Stochastic Petri Nets (SPN) [16,17], can be employed to overcome the assumptions. Whilst these methods can accommodate dependencies and, for SPNs, non-constant failure and repair rates are possible, both can be computationally demanding for even relatively simple systems.…”

Section: Introductionmentioning

confidence: 99%

Calculation of the System Unavailability Measures of Component Importance Using the D2T2 Methodology of Fault Tree Analysis

Andrews,

Lunt

2024

Mathematics

View full text Add to dashboard Cite

A recent development in Fault Tree Analysis (FTA), known as Dynamic and Dependent Tree Theory (D2T2), accounts for dependencies between the basic events, making FTA more powerful. The method uses an integrated combination of Binary Decision Diagrams (BDDs), Stochastic Petri Nets (SPN) and Markov models. Current algorithms enable the prediction of the system failure probability and failure frequency. This paper proposes methods which extend the current capability of the D2T2 framework to calculate component importance measures. Birnbaum’s measure of importance, the Criticality measure of importance, the Risk Achievement Worth (RAW) measure of importance and the Risk Reduction Worth (RRW) measure of importance are considered. This adds a vital ability to the framework, enabling the influence that components have on system failure to be determined and the most effective means of improving system performance to be identified. The algorithms for calculating each measure of importance are described and demonstrated using a pressure vessel cooling system.

show abstract

“…They carefully examined the benefits and drawbacks of different approaches in their study. The literature on reliability was the primary topic of Farahani et al's [18] study, with a specific emphasis on Markov and semi-Markov models. Taj and Rizwan [19] focused on reliability evaluations while modeling and evaluating a complicated industrial system with two continuously operating units.…”

Section: Introductionmentioning

confidence: 99%

Understanding the Reliability of the Complex System Having Two Standby Units: A Transdisciplinary Approach

Zaidi

2023

tjes

View full text Add to dashboard Cite

The main objective of this study is to thoroughly investigate the reliability of a complex system that consists of four components and two standby units. The complicated system is modeled using the Markov technique. The study formulates differential equations and solves them using a matrix method with the assistance of a computer program. Statistical methods, such as correlation and regression, are applied using SPSS software to understand the relationship between time and the reliability of this complex system. A statistical model is utilized to determine the system's reliability, identify potentially faulty components, and prioritize the protection of the most critical elements. The presentation of significant findings involves conducting a comprehensive analysis using tables and graphs created with Python programming language. The outcomes of this study aim to assist in identifying crucial units in various process industries, thereby facilitating the establishment of effective management policies and strategies for the optimal operation of complex and large-scale systems in the industry. This paper incorporates numerous disciplines, viewpoints, and methodologies to examine and enhance reliability in process industries. Reliability can indeed benefit from a matrix approach, which can be considered transdisciplinary. This study serves as both an introductory guide to reliability analysis for novice researchers and a survey highlighting the latest advancements in the field for experienced researchers.

show abstract

Markov and semi-Markov models in system reliability

Cited by 8 publications

References 181 publications

Stochastic Approach in Performance Modelling of a Repairable Industrial System

Stochastic Approach in Performance Modelling of a Repairable Industrial System

Calculation of the System Unavailability Measures of Component Importance Using the D2T2 Methodology of Fault Tree Analysis

Understanding the Reliability of the Complex System Having Two Standby Units: A Transdisciplinary Approach

Contact Info

Product

Resources

About