TWO–COMPONENT RESTORABLE TOOL SYSTEM MULTI–PURPOSE MACHINE WITH AN INSTANTLY REFILLED TIME RESERVE

2021 ◽  
Vol 3 ◽  
pp. 40-48
Author(s):  
A.I. PESCHANSKY ◽  
A.O. KHARCHENKO ◽  
S.M. BRATAN
Keyword(s):  
Continuous Phase ◽  
Embedded Markov Chain ◽  
System Availability ◽  
Stationary Time ◽  
Time Between Failures ◽  
Semi Markov Process ◽  
Multipurpose Machine Tool ◽  
Continuous Phase Space ◽  
Parametric Failure ◽  
Time Reserve

The object of the research is the technical system of a multipurpose machine tool, the tools of which can fail and be restored. A failed tool remains functional for some time due to a temporary reserve until a parametric failure occurs, the magnitude of which is random. All random variables describing the system have general distributions. The apparatus for constructing a mathematical model of the described system is a semi–Markov process with a discrete–continuous phase space of states. The stationary distribution of the embedded Markov chain is found explicitly. For systems with parallel connection, series connection with disconnection and without disconnection of elements, the stationary time between failures of the system, the stationary time spent in the state of failure and the stationary system availability factor are found. A numerical example shows the dependence of the stationary characteristics of the system on the size of the time reserve.

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.

The analysis of queues by state-dependent parameters by Markov renewal processes

1971 ◽  
Vol 3 (1) ◽  
pp. 155-175 ◽  
Author(s):  
Manfred Schäl
Keyword(s):  
Limiting Distribution ◽  
Embedded Markov Chain ◽  
Renewal Processes ◽  
Original Process ◽  
Queueing Process ◽  
State Dependent ◽  
Markov Renewal Processes ◽  
Semi Markov Process ◽  
Semi Markov Processes ◽  
The Relationship

In this paper, some results on the asymptotic behavior of Markov renewal processes with auxiliary paths (MRPAP's) proved in other papers ([28], [29]) are applied to queueing theory. This approach to queueing problems may be regarded as an improvement of the method of Fabens [7] based on the theory of semi-Markov processes. The method of Fabens was also illustrated by Lambotte in [18], [32]. In the present paper the ordinary M/G/1 queue is generalized to allow service times to depend on the queue length immediately after the previous departure. Such models preserve the MRPAP-structure of the ordinary M/G/1 system. Recently, the asymptotic behaviour of the embedded Markov chain (MC) of this queueing model was studied by several authors. One aim of this paper is to answer the question of the relationship between the limiting distribution of the embedded MC and the limiting distribution of the original process with continuous time parameter. It turns out that these two limiting distributions coincide. Moreover some properties of the embedded MC and the embedded semi-Markov process are established. The discussion of the M/G/1 queue closes with a study of the rate-of-convergence at which the queueing process attains equilibrium.

scholarly journals Efficiency of molecular machines with continuous phase space

2012 ◽  
Vol 97 (6) ◽  
pp. 60005 ◽  
Author(s):  
N. Golubeva ◽  
A. Imparato ◽  
L. Peliti
Keyword(s):  
Phase Space ◽  
Molecular Machines ◽  
Continuous Phase ◽  
Continuous Phase Space

The analysis of queues by state-dependent parameters by Markov renewal processes

1971 ◽  
Vol 3 (01) ◽  
pp. 155-175
Author(s):  
Manfred Schäl
Keyword(s):  
Limiting Distribution ◽  
Embedded Markov Chain ◽  
Renewal Processes ◽  
Original Process ◽  
Queueing Process ◽  
State Dependent ◽  
Markov Renewal Processes ◽  
Semi Markov Process ◽  
Semi Markov Processes ◽  
The Relationship

In this paper, some results on the asymptotic behavior of Markov renewal processes with auxiliary paths (MRPAP's) proved in other papers ([28], [29]) are applied to queueing theory. This approach to queueing problems may be regarded as an improvement of the method of Fabens [7] based on the theory of semi-Markov processes. The method of Fabens was also illustrated by Lambotte in [18], [32]. In the present paper the ordinary M/G/1 queue is generalized to allow service times to depend on the queue length immediately after the previous departure. Such models preserve the MRPAP-structure of the ordinary M/G/1 system. Recently, the asymptotic behaviour of the embedded Markov chain (MC) of this queueing model was studied by several authors. One aim of this paper is to answer the question of the relationship between the limiting distribution of the embedded MC and the limiting distribution of the original process with continuous time parameter. It turns out that these two limiting distributions coincide. Moreover some properties of the embedded MC and the embedded semi-Markov process are established. The discussion of the M/G/1 queue closes with a study of the rate-of-convergence at which the queueing process attains equilibrium.

Quantum margulis expanders

2008 ◽  
Vol 8 (8&9) ◽  
pp. 722-733
Author(s):  
D. Gross ◽  
J. Eisert
Keyword(s):  
Phase Space ◽  
Probability Distributions ◽  
Continuous Variable ◽  
Continuous Phase ◽  
Classical Counterpart ◽  
Essential Properties ◽  
Quantum Version ◽  
Phase Space Methods ◽  
Continuous Phase Space ◽  
Complete Analogy

We present a simple way to quantize the well-known Margulis expander map. The result is a quantum expander which acts on discrete Wigner functions in the same way the classical Margulis expander acts on probability distributions. The quantum version shares all essential properties of the classical counterpart, e.g., it has the same degree and spectrum. Unlike previous constructions of quantum expanders, our method does not rely on non-Abelian harmonic analysis. Analogues for continuous variable systems are mentioned. Indeed, the construction seems one of the few instances where applications based on discrete and continuous phase space methods can be developed in complete analogy.

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.

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.

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