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.

A multivariate reward process defined on a semi-Markov process and its first-passage-time distributions

1991 ◽  
Vol 28 (2) ◽  
pp. 360-373 ◽  
Author(s):  
Yasushi Masuda ◽  
Ushio Sumita
Keyword(s):  
Asymptotic Behavior ◽  
Markov Process ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Renewal Equations ◽  
Supplementary Variables ◽  
Semi Markov Process ◽  
Reward Process

A multivariate reward process defined on a semi-Markov process is studied. Transform results for the distributions of the multivariate reward and related processes are derived through the method of supplementary variables and the Markov renewal equations. These transform results enable the asymptotic behavior to be analyzed. A class of first-passage time distributions of the multivariate reward processes is also investigated.

A multivariate reward process defined on a semi-Markov process and its first-passage-time distributions

1991 ◽  
Vol 28 (02) ◽  
pp. 360-373 ◽  
Author(s):  
Yasushi Masuda ◽  
Ushio Sumita
Keyword(s):  
Asymptotic Behavior ◽  
Markov Process ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Renewal Equations ◽  
Supplementary Variables ◽  
Semi Markov Process ◽  
Reward Process

A multivariate reward process defined on a semi-Markov process is studied. Transform results for the distributions of the multivariate reward and related processes are derived through the method of supplementary variables and the Markov renewal equations. These transform results enable the asymptotic behavior to be analyzed. A class of first-passage time distributions of the multivariate reward processes is also investigated.

scholarly journals Distributional Properties of Fluid Queues Busy Period and First Passage Times

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1988
Author(s):  
Zbigniew Palmowski
Keyword(s):  
Markov Process ◽  
Busy Period ◽  
First Passage Time ◽  
Passage Time ◽  
Fluid Queue ◽  
First Passage ◽  
Fluid Queues ◽  
Distributional Properties ◽  
Finite State ◽  
Passage Times

In this paper, I analyze the distributional properties of the busy period in an on-off fluid queue and the first passage time in a fluid queue driven by a finite state Markov process. In particular, I show that the first passage time has a IFR distribution and the busy period in the Anick-Mitra-Sondhi model has a DFR distribution.

scholarly journals First excess levels of vector processes

1994 ◽  
Vol 7 (3) ◽  
pp. 457-464 ◽  
Author(s):  
Jewgeni H. Dshalalow
Keyword(s):  
Point Process ◽  
Renewal Process ◽  
Stochastic Models ◽  
First Passage Time ◽  
Passage Time ◽  
Two Dimensional ◽  
First Passage ◽  
Compound Process ◽  
First Time

This paper analyzes the behavior of a point process marked by a two-dimensional renewal process with dependent components about some fixed (two-dimensional) level. The compound process evolves until one of its marks hits (i.e. reaches or exceeds) its associated level for the first time. The author targets a joint transformation of the first excess level, first passage time, and the index of the point process which labels the first passage time. The cases when both marks are either discrete or continuous or mixed are treated. For each of them, an explicit and compact formula is derived. Various applications to stochastic models are discussed.

Bunching in a semi-Markov process

1970 ◽  
Vol 7 (1) ◽  
pp. 175-182 ◽  
Author(s):  
A. G. Hawkes
Keyword(s):  
Markov Process ◽  
Renewal Process ◽  
Constant Time ◽  
Time Interval ◽  
Type Ii ◽  
Successive Pair ◽  
Semi Markov Process

In the type II counter with constant deadtime, particles which arrive within some constant time τ following another particle are unrecorded. We can think of this process as an alternating sequence of gaps and bunches of events. Gaps have duration > τ, while the intervals between any successive pair of events within a bunch are all ≦ τ. Counter theory is usually concerned with the distribution of intervals between recorded events (i.e., the first event of each bunch) and the distribution of the number of recorded events in a given time interval. In the case where the events form a renewal process this has been studied intensively by Pyke [2], Smith [5] and Takács [6].

Bunching in a semi-Markov process

1970 ◽  
Vol 7 (01) ◽  
pp. 175-182 ◽  
Author(s):  
A. G. Hawkes
Keyword(s):  
Markov Process ◽  
Renewal Process ◽  
Constant Time ◽  
Time Interval ◽  
Type Ii ◽  
Successive Pair ◽  
Semi Markov Process

In the type II counter with constant deadtime, particles which arrive within some constant time τ following another particle are unrecorded. We can think of this process as an alternating sequence of gaps and bunches of events. Gaps have duration > τ, while the intervals between any successive pair of events within a bunch are all ≦ τ. Counter theory is usually concerned with the distribution of intervals between recorded events (i.e., the first event of each bunch) and the distribution of the number of recorded events in a given time interval. In the case where the events form a renewal process this has been studied intensively by Pyke [2], Smith [5] and Takács [6].

Ageing first-passage times of Markov processes: a matrix approach

1997 ◽  
Vol 34 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Haijun Li ◽  
Moshe Shaked
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
First Passage Time ◽  
Passage Time ◽  
Critical Value ◽  
First Passage Times ◽  
Matrix Approach ◽  
First Passage ◽  
Passage Times

Using a matrix approach we discuss the first-passage time of a Markov process to exceed a given threshold or for the maximal increment of this process to pass a certain critical value. Conditions under which this first-passage time possesses various ageing properties are studied. Some results previously obtained by Li and Shaked (1995) are extended.

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.

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