scholarly journals BIRNBAUM CRITICALITY AND IMPORTANCE MEASURES FOR MULTISTATE SYSTEMS WITH REPAIRABLE COMPONENTS

2020 ◽  
pp. 1-21
Author(s):  
Arne Bang Huseby ◽  
Martyna Kalinowska ◽  
Tobias Abrahamsen
Keyword(s):  
Markov Processes ◽  
Life Cycles ◽  
System Structure ◽  
System Model ◽  
Composite Measures ◽  
Multistate System ◽  
Multistate Systems ◽  
Semi Markov Processes ◽  
Repairable Components ◽  
Forward Looking

We suggest four new measures of importance for repairable multistate systems based on the classical Birnbaum measure. Periodic component life cycles and general semi-Markov processes are considered. Similar to the Birnbaum measure, the proposed measures are generic in the sense that they only depend on the probabilistic properties of the components and the system structure. The multistate system model encodes physical properties of the components and the system directly into the structure function. As a result, calculating importance is easy, especially in the asymptotic case. Moreover, the proposed measures are composite measures, combining importance for all component states into a unified quantity. This simplifies ranking of the components with respect to importance. The proposed measures can be characterized with respect to two features: forward-looking versus backward-looking and with respect to how criticality is measured. Forward-looking importance measures focus on the next component states, while backward-looking importance measures focus on the previous component states. Two approaches to measuring criticality are considered: probability of criticality versus expected impact. Examples show that the different importance measures may result in unequal rankings.

SEMI-MARKOV EMBEDDABLE RELIABILITY STRUCTURES AND APPLICATIONS TO LOAD-SHARING k-OUT-OF-n SYSTEMS

2013 ◽  
Vol 20 (02) ◽  
pp. 1350007 ◽  
Author(s):  
MARIO HELLMICH
Keyword(s):  
Markov Processes ◽  
Load Sharing ◽  
Sharing Rule ◽  
Reliability Modeling ◽  
Life Distributions ◽  
Semi Markov Processes ◽  
Repairable Components

This paper deals with the application of nonhomogeneous semi-Markov processes in reliability modeling. The notion of a semi-Markov embeddable reliability structure is introduced and discussed. As an example, load-sharing k-out-of-n : G systems of equal components with arbitrary life distributions under the equal load-sharing rule are treated in the context of semi-Markov embeddable systems. Besides some discussion about load-life models, the case of repairable components is to some extent treated as well.

scholarly journals Quantum Semi-Markov Processes

2008 ◽  
Vol 101 (14) ◽  
Author(s):  
Heinz-Peter Breuer ◽  
Bassano Vacchini
Keyword(s):  
Markov Processes ◽  
Semi Markov Processes

scholarly journals A continuous-time semi-markov bayesian belief network model for availability measure estimation of fault tolerant systems

2008 ◽  
Vol 28 (2) ◽  
pp. 355-375 ◽  
Author(s):  
Márcio das Chagas Moura ◽  
Enrique López Droguett
Keyword(s):  
Hybrid Model ◽  
Markov Processes ◽  
Continuous Time ◽  
Fault Tolerant ◽  
Numerical Procedure ◽  
Bayesian Belief Networks ◽  
Operational Conditions ◽  
Fault Tolerant Systems ◽  
Semi Markov Processes ◽  
Availability Measure

In this work it is proposed a model for the assessment of availability measure of fault tolerant systems based on the integration of continuous time semi-Markov processes and Bayesian belief networks. This integration results in a hybrid stochastic model that is able to represent the dynamic characteristics of a system as well as to deal with cause-effect relationships among external factors such as environmental and operational conditions. The hybrid model also allows for uncertainty propagation on the system availability. It is also proposed a numerical procedure for the solution of the state probability equations of semi-Markov processes described in terms of transition rates. The numerical procedure is based on the application of Laplace transforms that are inverted by the Gauss quadrature method known as Gauss Legendre. The hybrid model and numerical procedure are illustrated by means of an example of application in the context of fault tolerant systems.

Cumulative constrained sojourn times in semi-Markov processes with an application to pensionable service

1978 ◽  
Vol 15 (3) ◽  
pp. 531-542 ◽  
Author(s):  
Izzet Sahin
Keyword(s):  
Markov Processes ◽  
Sojourn Time ◽  
Working Life ◽  
Partial Coverage ◽  
Sojourn Times ◽  
Semi Markov Processes

This paper is concerned with the characterization of the cumulative pensionable service over an individual's working life that is made up of random lengths of service in different employments in a given industry, under partial coverage, transferability, and a uniform vesting rule. This characterization uses some results that are developed in the paper involving a functional and cumulative constrained sojourn times (constrained in the sense that if a sojourn time is less than a given constant it is not counted) in semi-Markov processes.

Sign in / Sign up

Export Citation Format

Share Document