A limit theorem for semi-Markov processes

1974 ◽  
Vol 11 (3) ◽  
pp. 521-528 ◽  
Author(s):  
Domokos Szász
Keyword(s):  
Limit Theorem ◽  
Small Parameter ◽  
Markov Processes ◽  
Reliability Theory ◽  
Absorbing State ◽  
Essential State ◽  
Semi Markov Processes

A limit theorem is proved for semi-Markov processes, which depend on a small parameter, tending to 0, in the case when the processes have an absorbing state and some asymptotically non-essential states and one asymptotically essential state. The application of the theorem is illustrated by an example from reliability theory.

A limit theorem for semi-Markov processes

1974 ◽  
Vol 11 (03) ◽  
pp. 521-528
Author(s):  
Domokos Szász
Keyword(s):  
Limit Theorem ◽  
Small Parameter ◽  
Markov Processes ◽  
Reliability Theory ◽  
Absorbing State ◽  
Essential State ◽  
Semi Markov Processes

A limit theorem is proved for semi-Markov processes, which depend on a small parameter, tending to 0, in the case when the processes have an absorbing state and some asymptotically non-essential states and one asymptotically essential state. The application of the theorem is illustrated by an example from reliability theory.

scholarly journals A Multistate Model of Reliability of Farming Machinery

2018 ◽  
Vol 10 ◽  
pp. 02005
Author(s):  
Karol Durczak ◽  
Piotr Jurek ◽  
Jan Beba ◽  
Adam Ekielski ◽  
Tomasz Żelaziński
Keyword(s):  
Stochastic Model ◽  
Detailed Analysis ◽  
Markov Processes ◽  
Reliability Theory ◽  
Reliability Model ◽  
Multistate Model ◽  
Intermediate States ◽  
The Moment ◽  
Semi Markov Processes

The article describes a multistate model of reliability of farming machinery as a deductive stochastic model of the process of changes in the technical conditions observed during operation. These conditions determine the capacity of machinery to fulfil functions, simultaneously keeping safety and maintaining acceptable costs of possible repairs. The theory of semi-Markov processes was used to solve the problem. After detailed analysis of the symptoms of damage to exemplary groups of farming machinery (rotary mowers, rotary harrows and harvesting presses) we obligatorily and arbitrarily proposed an optimal four-state reliability model to describe changes in technical conditions. In contrast to the classic reliability theory, which allows only two states of technical usability (either a machine is fit to function or not), we also allowed intermediate states, because not all types of damage affect the functionality of machinery. This approach increases the probability of technical usability of machinery and rationally delays the moment of premature repair.

A limit theorem for semi-Markov processes

Cybernetics ◽  
1972 ◽  
Vol 5 (4) ◽  
pp. 524-526 ◽  
Author(s):  
V. S. Korolyuk ◽  
L. I. Polishchuk ◽  
A. A. Tomusyak
Keyword(s):  
Limit Theorem ◽  
Markov Processes ◽  
Semi Markov Processes

Additional quasi-stationary distributions for semi-Markov processes

1972 ◽  
Vol 9 (3) ◽  
pp. 671-676 ◽  
Author(s):  
David C. Flaspohler ◽  
Paul T. Holmes
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Sufficient Conditions ◽  
Initial State ◽  
Stationary Distributions ◽  
Absorbing State ◽  
Semi Markov Process ◽  
Image Position ◽  
Semi Markov Processes

Consider a semi-Markov process X(t) defined on a subset of the non-negative integers with zero as an absorbing state and the non-zero states forming an irreducible class with exit to zero being possible. Conditions are given for the existence of the limits: where Xj(t) is the amount of time prior to time t spent in state j.The limits (which are independent of the initial state) are evaluated when the sufficient conditions are satisfied.

Additional quasi-stationary distributions for semi-Markov processes

1972 ◽  
Vol 9 (03) ◽  
pp. 671-676 ◽  
Author(s):  
David C. Flaspohler ◽  
Paul T. Holmes
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Sufficient Conditions ◽  
Initial State ◽  
Stationary Distributions ◽  
Absorbing State ◽  
Semi Markov Process ◽  
Image Position ◽  
Semi Markov Processes

Consider a semi-Markov process X(t) defined on a subset of the non-negative integers with zero as an absorbing state and the non-zero states forming an irreducible class with exit to zero being possible. Conditions are given for the existence of the limits: where Xj (t) is the amount of time prior to time t spent in state j. The limits (which are independent of the initial state) are evaluated when the sufficient conditions are satisfied.

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