DYNAMIC RELIABILITY MEASURES AND LIFE DISTRIBUTION MODELS FOR MULTISTATE SYSTEMS

1995 ◽  
Vol 02 (01) ◽  
pp. 79-102 ◽  
Author(s):  
KAI YANG ◽  
JIANAN XUE
Keyword(s):  
Markov Process ◽  
Probability Models ◽  
Reliability Measures ◽  
Distribution Models ◽  
Dynamic Reliability ◽  
Reliability Models ◽  
Reliability Parameters ◽  
Multistate System ◽  
Binary State ◽  
Semi Markov Process

This paper generalizes the dynamic binary state reliability parameters R(t), F(t), λ(t) and MTBF to corresponding dynamic multistate reliability parameter vectors R(t), F(t), λ(t) and M. Then, probability models for system lifetime used on binary state reliability models, such as exponential, Weibull, and other distributions are generalized for multistate models. Continuous time Markov process and Semi-Markov process are used to model the lifetime distribution for multistate system. Multistate reliability measures, such as R(t), F(t), λ(t), M are derived for those multistate reliability models.

scholarly journals The Renewal Process Generated By Return Times of Semi-Markov Process in Reliability Models

2017 ◽  
Vol 43 (1) ◽  
pp. 365-380
Author(s):  
Franciszek Grabski
Keyword(s):  
Markov Process ◽  
Renewal Process ◽  
First Passage Time ◽  
Return Time ◽  
Passage Time ◽  
Reliability Theory ◽  
Systems Of Equations ◽  
Reliability Models ◽  
Return Times ◽  
Semi Markov Process

Abstract The renewal process generated by the return times of semi-Markov process to a given state is considered in the paper. The return time to a state j and also a first passage time from a given state i to the state j of semi-Markov process are basic concepts that are used to determine this process. The systems of equations for distributions, expectations and secondond moments of these random variables are presented. Theorem concerning the asymptotic distribution of the considered renewal process is presented in this article. Moreover an illustrative example from the reliability theory is presented in the paper.

Redundancy Allocation for Multistate Systems With Component Dependencies and Load Sharing

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Jing Wang ◽  
Mian Li
Keyword(s):  
Markov Process ◽  
Process Model ◽  
Load Sharing ◽  
Two Component System ◽  
System Availability ◽  
Redundancy Allocation ◽  
Markov Process Model ◽  
Dependent Failures ◽  
Binary State ◽  
Semi Markov Process

Binary-state and component independent assumptions will lead to doubtful and misleading redundancy allocation schemes which may not satisfy the reliability requirements for real engineering applications. Most published works proposed methods to remove the first assumption by studying the degradation cases where multiple states of a component are from the best state to the degradation states then to the completely failed state. Fewer works focused on removing the second assumption and they only discussed dependent failures which are only a special case of component dependency. This work uses the Semi-Markov process to describe a two-component system for redundancy allocation. In this work, multiple states of a component are represented by multiple output levels, which are beyond the scope of degradation, and the component dependency is not limited to failure dependency only. The load sharing is also taken care of in the proposed work. The optimal redundancy allocation scheme is obtained by solving the corresponding redundancy allocation optimization problem with the reliability measure, the system availability, obtained through the Semi-Markov process model being constraint. Two case studies are presented, demonstrating the applicability of the propose method.

Study of functioning of relay protection system under regular check conditions

2019 ◽  
Vol 12 (1) ◽  
pp. 36-44
Author(s):  
B. P. Zelentsov ◽  
A. S. Trofimov
Keyword(s):  
Markov Process ◽  
Power Systems ◽  
Power Transmission ◽  
Relay Protection ◽  
Point Of View ◽  
Distribution Law ◽  
Reliability Parameters ◽  
A Value ◽  
Semi Markov Process ◽  
Periodic Check

An analytical model of the operation of the relay protection of power systems is presented, which takes into account such types of failures as unwanted operation, failure to operate, as well as defects dangerous from the point of view of unwanted operation and failure to operate. Operability checks of relay protection of power systems are conducted with a constant period. The listed events can be divided into two groups: random and regular ones. The presence of random and regular components of events of recovery of relay protection of power systems can be correctly taken into account in the framework of the apparatus of the theory of Markov processes. The model is based on the description of the process of operation of relay protection of power transmission line by a semi-Markov process. The functioning of the system in time is presented in the form of cycles. The cycle of the functioning of the system consists of a subset, where the system is functioning and verifi ed, and a subset, in which it is restored. The model is implemented in a graph with 9 states. Probabilities of events describe the process of changing states on a discrete set of states of relay protection of the power system. The probability of a change of states is the initial characteristic of a semi-Markov process. This model has enabled to obtain the dependence of operation and reliability parameters on the frequency of regular checks. It is established that the frequency of regular checks with the exponential distribution law overstates the value of the unavailability factor, since the time of the onset of a periodic check is greater than the mathematical expectation of a given value of the periodic check under a random distribution law. With a signifi cant time between checks, or in absence of periodic checks, the unavailability factor tends to a value that does not depend on the way of setting the time between periodic checks.

Partially observable semi-Markov reward processes

1993 ◽  
Vol 30 (3) ◽  
pp. 548-560 ◽  
Author(s):  
Yasushi Masuda
Keyword(s):  
Markov Process ◽  
Counting Process ◽  
Probabilistic Interpretation ◽  
Real Domain ◽  
Semi Markov Process ◽  
Reward Process ◽  
Markov Reward ◽  
Partially Observable ◽  
Joint Behavior

The main objective of this paper is to investigate the conditional behavior of the multivariate reward process given the number of certain signals where the underlying system is described by a semi-Markov process and the signal is defined by a counting process. To this end, we study the joint behavior of the multivariate reward process and the multivariate counting process in detail. We derive transform results as well as the corresponding real domain expressions, thus providing clear probabilistic interpretation.

Probabilistic Assessment of Wind Farm Active Power Based on Monte-Carlo Simulation

2013 ◽  
Vol 291-294 ◽  
pp. 536-540 ◽  
Author(s):  
Xin Wei Wang ◽  
Jian Hua Zhang ◽  
Cheng Jiang ◽  
Lei Yu
Keyword(s):  
Monte Carlo ◽  
Power Output ◽  
Wind Farm ◽  
Active Power ◽  
Assessment Methods ◽  
Probabilistic Methods ◽  
Model Parameters ◽  
Probability Assessment ◽  
Reliability Models ◽  
Reliability Parameters

The conventional deterministic methods have been unable to accurately assess the active power output of the wind farm being the random and intermittent of wind power, and the probabilistic methods commonly used to solve this problem. In this paper the multi-state fault model is built considering run, outage and derating state of wind turbine, and then the reliability model of the wind farm is established considering the randomness of the wind speed, the wind farm wake effects and turbine failure. The active wind farm output probability assessment methods and processes based on the Monte Carlo method. The related programs are written in MATLAB, and the probability assessment for active power output of a wind farm in carried out, the effectiveness and adaptability of built reliability models and assessment methods are illustrated by analysis of the effects of reliability parameters and model parameters on assessment results.

scholarly journals Reliability and Random Lifetime Models of Planetary Gear Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Peng Gao ◽  
Liyang Xie ◽  
Wei Hu
Keyword(s):  
Load Distribution ◽  
Planetary Gear ◽  
Working Process ◽  
Random Load ◽  
Working Mechanism ◽  
Dynamic Reliability ◽  
Reliability Models ◽  
Process Failure ◽  
Failure Dependence ◽  
Gear Systems

Conventional reliability models of planetary gear systems are mainly static. In this paper, dynamic reliability models and random lifetime models of planetary gear systems are developed with dynamic working mechanism considered. The load parameters, the geometric parameters, and the material parameters are taken as the inputs of the reliability models and the random lifetime models. Moreover, failure dependence and dynamic random load redistributions are taken into account in the models. Monte Carlo simulations are carried out to validate the proposed models. The results show that the randomness of the load distribution is obvious in the system working process. Failure dependence has significant influences on system reliability. Moreover, the dispersion of external load has great impacts on the reliability, lifetime distribution, and redundancy of planetary gear systems.

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