Steady-state availability analysis of repairable mechanical systems with opportunistic maintenance by using Semi-Markov process

2014 ◽  
Vol 5 (4) ◽  
pp. 664-678 ◽  
Author(s):  
Girish Kumar ◽  
Vipul Jain ◽  
O. P. Gandhi
Keyword(s):  
Steady State ◽  
Markov Process ◽  
Mechanical Systems ◽  
Opportunistic Maintenance ◽  
Availability Analysis ◽  
Semi Markov Process

scholarly journals Degrading systems availability analysis: analytical semi-Markov approach

2021 ◽  
Vol 23 (1) ◽  
pp. 195-208
Author(s):  
Varun Kumar ◽  
Girish Kumar ◽  
Rajesh Kumar Singh ◽  
Umang Soni
Keyword(s):  
Steady State ◽  
Degradation Mechanism ◽  
Continuous Process ◽  
Mechanical Systems ◽  
Embedded Markov Chain ◽  
Steady State Probability ◽  
Opportunistic Maintenance ◽  
System Availability ◽  
Availability Analysis ◽  
Complex Mechanical Systems

This paper deals with modeling and analysis of complex mechanical systems that deteriorate with age. As systems age, the questions on their availability and reliability start to surface. The system is believed to suffer from internal stochastic degradation mechanism that is described as a gradual and continuous process of performance deterioration. Therefore, it becomes difficult for maintenance engineer to model such system. Semi-Markov approach is proposed to analyze the degradation of complex mechanical systems. It involves constructing states corresponding to the system functionality status and constructing kernel matrix between the states. The construction of the transition matrix takes the failure rate and repair rate into account. Once the steady-state probability of the embedded Markov chain is computed, one can compute the steady-state solution and finally, the system availability. System models based on perfect repair without opportunistic and with opportunistic maintenance have been developed and the benefits of opportunistic maintenance are quantified in terms of increased system availability. The proposed methodology is demonstrated for a two-stage reciprocating air compressor with intercooler in between, system in series configuration.

Loss tandem networks with blocking - a semi-Markov approach

2010 ◽  
Vol 58 (4) ◽  
pp. 673-681
Author(s):  
W. Oniszczuk
Keyword(s):  
Steady State ◽  
Markov Process ◽  
Markov Model ◽  
Markov Models ◽  
State Graph ◽  
State Equations ◽  
Semi Markov Process ◽  
Tandem Networks ◽  
Measures Of Effectiveness

Loss tandem networks with blocking - a semi-Markov approachBased on the semi-Markov process theory, this paper describes an analytical study of a loss multiple-server two-station network model with blocking. Tasks arrive to the tandem in a Poisson fashion at a rate λ, and the service times at the first and second stations are non-exponentially distributed with means sAand sB, respectively. Between these two stations there is a buffer with finite capacity. In this type of network, if the buffer is full, the accumulation of new tasks (jobs) by the second station is temporarily suspended (blocking factor) and tasks must wait on the first station until the transmission process is resumed. Any new task that finds all service lines at the first station occupied is turned away and is lost (loss factor). Initially, in this document, a Markov model of the loss tandem with blocking is investigated. Here, a two-dimensional state graph is constructed and a set of steady-state equations is created. These equations allow the calculation of state probabilities for each graph state. A special algorithm for transforming the Markov model into a semi-Markov process is presented. This approach allows calculating steady-state probabilities in the semi-Markov model. In the next part of the paper, the algorithms for calculation of the main measures of effectiveness in the semi-Markov model are presented. Finally, the numerical part of this paper contains an investigation of some special semi-Markov models, where the results are presented of the calculation of the quality of service (QoS) parameters and the main measures of effectiveness.

scholarly journals Semi-Markov-Based Approach for the Analysis of Open Tandem Networks with Blocking and Truncation

2009 ◽  
Vol 19 (1) ◽  
pp. 151-164 ◽  
Author(s):  
Walenty Oniszczuk
Keyword(s):  
Steady State ◽  
Markov Process ◽  
Markov Model ◽  
Markov Models ◽  
Network Models ◽  
State Graph ◽  
State Equations ◽  
Semi Markov Process ◽  
Tandem Networks ◽  
Measures Of Effectiveness

Semi-Markov-Based Approach for the Analysis of Open Tandem Networks with Blocking and TruncationThis paper describes an analytical study of open two-node (tandem) network models with blocking and truncation. The study is based on semi-Markov process theory, and network models assume that multiple servers serve each queue. Tasks arrive at the tandem in a Poisson fashion at the rate λ, and the service times at the first and the second node are non-exponentially distributed with meanssAandsB, respectively. Both nodes have buffers with finite capacities. In this type of network, if the second buffer is full, the accumulation of new tasks by the second node is temporarily suspended (a blocking factor) and tasks must wait on the first node until the transmission process is resumed. All new tasks that find the first buffer full are turned away and are lost (a truncation factor). First, a Markov model of the tandem is investigated. Here, a two-dimensional state graph is constructed and a set of steady-state equations is created. These equations allow calculating state probabilities for each graph state. A special algorithm for transforming the Markov model into a semi-Markov process is presented. This approach allows calculating steady-state probabilities in the semi-Markov model. Next, the algorithms for calculating the main measures of effectiveness in the semi-Markov model are presented. In the numerical part of this paper, the author investigates examples of several semi-Markov models. Finally, the results of calculating both the main measures of effectiveness and quality of service (QoS) parameters are presented.

scholarly journals Asymptotic performance of a multistate coherent system

1988 ◽  
Vol 20 (01) ◽  
pp. 241-243 ◽  
Author(s):  
Srinivas Iyer
Keyword(s):  
Steady State ◽  
Markov Process ◽  
Coherent System ◽  
Renewal Processes ◽  
Asymptotic Performance ◽  
System Availability ◽  
Performance Function ◽  
Semi Markov Process ◽  
Mutually Independent ◽  
Steady State Performance

An expression for the asymptotic or steady-state performance function is derived for a multistate coherent system when each component changes states in time according to a semi-Markov process, the stochastic processes being mutually independent. This generalizes the expression for system availability of a binary coherent system when the components are governed by mutually independent alternating renewal processes.

Asymptotic performance of a multistate coherent system

1988 ◽  
Vol 20 (1) ◽  
pp. 241-243 ◽  
Author(s):  
Srinivas Iyer
Keyword(s):  
Steady State ◽  
Markov Process ◽  
Coherent System ◽  
Renewal Processes ◽  
Asymptotic Performance ◽  
System Availability ◽  
Performance Function ◽  
Semi Markov Process ◽  
Mutually Independent ◽  
Steady State Performance

An expression for the asymptotic or steady-state performance function is derived for a multistate coherent system when each component changes states in time according to a semi-Markov process, the stochastic processes being mutually independent. This generalizes the expression for system availability of a binary coherent system when the components are governed by mutually independent alternating renewal processes.

Insensitivity of steady-state distributions of generalized semi-Markov processes by speeds

1978 ◽  
Vol 10 (04) ◽  
pp. 836-851 ◽  
Author(s):  
R. Schassberger
Keyword(s):  
Steady State ◽  
General System ◽  
State Distribution ◽  
Lifetime Distributions ◽  
State Dependent ◽  
Semi Markov Process ◽  
Semi Markov Processes ◽  
Infinite State ◽  
State Case ◽  
Residual Lifetimes

A generalized semi-Markov process with speeds describes the fluctuation, in time, of the state of a certain general system involving, at any given time, one or more living components, whose residual lifetimes are being reduced at state-dependent speeds. Conditions are given for the stationary state distribution, when it exists, to depend only on the means of some of the lifetime distributions, not their exact shapes. This generalizes results of König and Jansen, particularly to the infinite-state case.

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.

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