Step semi-Markov models and application to manpower management

Barbu, Vlad Stefan; D’Amico, Guglielmo; Manca, Raimondo; Petroni, Filippo

doi:10.1051/ps/2016025

Cited by 2 publications

(2 citation statements)

References 22 publications

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“…Following the procedure proposed in [13] for discrete-time SMPs, the sojourn time X n+1 between two consecutive states J n and J n+1 can be seen as the sum of two different times, say U n+1 and V n+1 , that is X n+1 = U n+1 + V n+1 . Under this setting one can rewrite the semi-Markov condition (1) in the following form…”

Section: System Settingsmentioning

confidence: 99%

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A Continuous-Time Semi-Markov System Governed by Stepwise Transitions

2022

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In this paper, we introduce a class of stochastic processes in continuous time, called step semi-Markov processes. The main idea comes from bringing an additional insight to a classical semi-Markov process: the transition between two states is accomplished through two or several steps. This is an extension of a previous work on discrete-time step semi-Markov processes. After defining the models and the main characteristics of interest, we derive the recursive evolution equations for two-step semi-Markov processes.

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Section: System Settingsmentioning

confidence: 99%

“…The present article extends the discrete-time step semi-Markov processes introduced in [13] to the case of continuous-time semi-Markov processes. It is important to stress from the beginning that the passage from discrete-time case to continuous-time case and vice versa is not obvious at all in such semi-Markov frameworks.…”

Section: Introductionmentioning

confidence: 99%

A Continuous-Time Semi-Markov System Governed by Stepwise Transitions

2022

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Conditional failure occurrence rates for semi-Markov chains

Votsi

2019

Journal of Applied Statistics

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In the present paper, we aim at providing plug-in-type empirical estimators that enable us to quantify the contribution of each operational or/and non-functioning state to the failures of a system described by a semi-Markov model. In the discrete time and finite state space semi-Markov framework, we study different conditional versions of an important reliability measure for random repairable systems, the failure occurrence rate based on counting processes. The aforementioned estimators are characterised by appealing asymptotic properties such as strong consistency and asymptotic normality. We further obtain detailed analytical expressions for the covariance matrices of the random vectors describing the conditional failure occurrence rates. As particular cases we present the failure occurrence rates for hidden (semi-) Markov models. We illustrate our results by means of an academic example based on simulated data. An application to real data is further presented that models sustainable vibration levels in a semi-Markov framework.Semi-Markov models (SMMs) are state-of-the-art models that are widely used in many scientific fields such as reliability and DNA analysis ([3]), seismology ([22]) etc. One of the main distinguising features of SMMs is that contrary to Markov models, they enable us to describe systems that evolve based not only on their last visited state (Markov property) but also on the time elapsed since this state. Due to this feature, popular "memory-full" distributions, such as the Weibull distribution, could be employed to describe sojourn (or interevent) times between successive events. We refer the interested reader to [8] or [12] for an introduction to homogeneous SMMs and to [18,17] for non-homogeneous SMMs, respectively.In the semi-Markov context, many reliability indicators have been introduced, including mean times to failure, hazard rates, availability functions etc. For recent advances in the topic concerning discrete time SMMs, see [1], [3], [5] and [6]. For continuous time SMMs, we address the interested reader to [10] and [11]. For advances in estimation methods of nonparametric semi-Markov models, see [15] and the references therein.Here we focus on the rate of occurrence of failures (ROCOF), which is a fundamental reliability indicator for repairable, random systems subject to multiple failures. Yeh ([23]) was

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Step semi-Markov models and application to manpower management

Cited by 2 publications

References 22 publications

A Continuous-Time Semi-Markov System Governed by Stepwise Transitions

A Continuous-Time Semi-Markov System Governed by Stepwise Transitions

Conditional failure occurrence rates for semi-Markov chains

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