scholarly journals Lifetime Estimation for Multi-Phase Deteriorating Process with Random Abrupt Jumps

Sensors ◽  
2019 ◽  
Vol 19 (6) ◽  
pp. 1472 ◽  
Author(s):  
Jianxun Zhang ◽  
Xiaosheng Si ◽  
Dangbo Du ◽  
Chen Hu ◽  
Changhua Hu
Keyword(s):  
First Passage Time ◽  
Random Effect ◽  
Model Identification ◽  
Degradation Process ◽  
Passage Time ◽  
Closed Form Expression ◽  
Lifetime Estimation ◽  
Two Phase ◽  
Deteriorating Process ◽  
Multi Phase

Owing to operating condition changing, physical mutation, and sudden shocks, degradation trajectories usually exhibit multi-phase features, and the abrupt jump often appears at the changing time, which makes the traditional methods of lifetime estimation unavailable. In this paper, we mainly focus on how to estimate the lifetime of the multi-phase degradation process with abrupt jumps at the change points under the concept of the first passage time (FPT). Firstly, a multi-phase degradation model with jumps based on the Wiener process is formulated to describe the multi-phase degradation pattern. Then, we attain the lifetime’s closed-form expression for the two-phase model with fixed jump relying on the distribution of the degradation state at the change point. Furthermore, we continue to investigate the lifetime estimation of the degradation process with random effect caused by unit-to-unit variability and the multi-phase degradation process. We extend the results of the two-phase case with fixed parameters to these two cases. For better implementation, a model identification method with off-line and on-line parts based on Expectation Maximization (EM) algorithm and Bayesian rule is proposed. Finally, a numerical case study and a practical example of gyro are provided for illustration.

scholarly journals A hybrid approach for modelling multidimensional degradation processes

2021 ◽  
Vol 1207 (1) ◽  
pp. 012023
Author(s):  
Renyan Jiang ◽  
Binbin Xiong
Keyword(s):  
Model Selection ◽  
Residual Life ◽  
Hybrid Approach ◽  
Degradation Process ◽  
Closed Form Expression ◽  
Second Phase ◽  
Two Phase ◽  
Degradation Model ◽  
One Dimensional ◽  
Degradation Processes

Abstract Degradation processes are often multidimensional. Modeling such degradation processes needs to address two key issues: indicator fusion and degradation model selection; and they have been separately addressed in the literature. This paper proposes a hybrid approach to jointly address these two issues. The proposed approach first fuses multiple degradation indicators into a composite degradation indicator. This fusion step involves data normalization, aggregation model selection and determination of indicator weights. After the fusion step, the problem becomes one-dimensional, and the existing method to select the degradation model for a one-dimensional degradation process can be applied. The resulting model obtained from the proposed approach can be a two-phase model; and the model for the second phase has a closed-form expression. This considerably facilitates residual life prediction. A real-world example is included to illustrate the proposed approach and its appropriateness.

Certain functionals of squared telegraph processes

2019 ◽  
Vol 20 (01) ◽  
pp. 2050005 ◽  
Author(s):  
Barbara Martinucci ◽  
Alessandra Meoli
Keyword(s):  
Hypergeometric Functions ◽  
First Passage Time ◽  
Moment Generating Function ◽  
Passage Time ◽  
Probability Density Functions ◽  
Closed Form Expression ◽  
Form Expression ◽  
Telegraph Process ◽  
The Moment ◽  
Derivatives Of

We investigate the stochastic process defined as the square of the (integrated) symmetric telegraph process. Specifically, we obtain its probability law and a closed form expression of the moment generating function. Some results on the first-passage time through a fixed positive level are also provided. Moreover, we analyze some functionals [Formula: see text] of two independent squared telegraph processes, both in the case [Formula: see text] and [Formula: see text]. Starting from this study, we provide some results on the probability density functions of the two-dimensional radial telegraph process and of the product of two independent symmetric telegraph processes. Some of the expressions obtained are given in terms of new results about derivatives of hypergeometric functions with respect to parameters.

scholarly journals On first-passage-time and transition densities for strongly symmetric diffusion processes

1997 ◽  
Vol 145 ◽  
pp. 143-161 ◽  
Author(s):  
A. Di Crescenzo ◽  
V. Giorno ◽  
A. G. Nobile ◽  
L. M. Ricciardi
Keyword(s):  
Diffusion Process ◽  
Closed Form ◽  
Diffusion Processes ◽  
First Passage Time ◽  
Passage Time ◽  
Time Dependent ◽  
Closed Form Expression ◽  
First Passage ◽  
One Dimensional ◽  
Transition Functions

One dimensional diffusion processes have been increasingly invoked to model a variety of biological, physical and engineering systems subject to random fluctuations (cf., for instance, Blake, I. F. and Lindsey, W. C. [2], Abrahams, J. [1], Giorno, V. et al [10] and references therein). However, usually the knowledge of the ‘free’ transition probability density function (pdf) is not sufficient; one is thus led to the more complicated task of determining transition functions in the presence of preassigned absorbing boundaries, or first-passage-time densities for time-dependent boundaries (see, for instance, Daniels, H. E. [6], [7], Giorno, V. et al. [10]). Such densities are known analytically only in some special instances so that numerical methods have to be implemented in general (cf., for instance, Buono-core, A. et al [3], [4], Giorno, V. et al [11]). The analytical approach becomes particularly effective when the diffusion process exhibits some special features, such as the symmetry of its transition pdf. For instance, in [10] special symmetry conditions on the transition pdf of one-dimensional time-homogeneous diffusion process with natural boundaries are investigated to derive closed form results concerning the transition pdf’s and the first-passage-time pdf for particular time-dependent boundaries. On the other hand, by using the method of images, in [6] Daniels has obtained a closed form expression for the transition pdf of the standard Wiener process in the presence of a particular time-dependent absorbing boundary. It is interesting to remark that such density cannot be obtained via the methods described in [10], even though the considered process exhibits the kind of symmetry discussed therein.

scholarly journals First-Passage Time Model Driven by Lévy Process for Pricing CoCos

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Xiaoshan Su ◽  
Manying Bai
Keyword(s):  
Closed Form ◽  
Lévy Process ◽  
First Passage Time ◽  
Passage Time ◽  
Levy Process ◽  
Closed Form Expression ◽  
Lévy Measure ◽  
First Passage ◽  
Time Model ◽  
Time Problem

Contingent convertible bonds (CoCos) are typical form of contingent capital that converts into equity of issuing firm or writes down if a prespecified trigger occurs. This paper proposes a general Lévy framework for pricing CoCos. The Lévy framework indicates that the difficulty in giving closed-form expression for CoCos price is the possible introduction of the Lévy process whose first-passage time problem has not been solved. According to characteristics of new Lévy measure after the measure transform, three specific Lévy models driven by drifted Brownian motion, spectrally negative Lévy process, and double exponential jump diffusion process are proposed to give the solution keeping the form of the driving process unchanged under the measure transform. These three Lévy models provide closed-form expressions for CoCos price while the latter two possess them up to Laplace transform, whose pricing results are given by combining with numerical Fourier inversion and Laplace inversion. Numerical results show that negative jumps have large influence on CoCos pricing and the Black-Scholes model would overestimate CoCos price by simply compressing jumps information into volatility while the other two models would give more accurate CoCos price by taking jump risk into consideration.

ON DEGRADATION-BASED REMAINING LIFETIME

2021 ◽  
pp. 1-12
Author(s):  
Maxim Finkelstein ◽  
Ji Hwan Cha
Keyword(s):  
Stochastic Processes ◽  
Regime Switching ◽  
First Passage Time ◽  
Degradation Process ◽  
Passage Time ◽  
Coherent System ◽  
Stochastic Comparisons ◽  
First Passage ◽  
Virtual Age ◽  
Predetermined Level

The new reliability notion describing the remaining lifetime is introduced for items with monotonically increasing degradation. We consider the remaining lifetime of an item (to be called, the predicted remaining lifetime) after its degradation reaches the predetermined level. The prediction is executed at inception of an item into operation. For the nonhomogeneous stochastic processes of degradation, this characteristic depends on the random first passage time of a degradation process. Some properties of the predicted remaining lifetime and the corresponding stochastic comparisons are discussed for items from homogeneous and heterogeneous populations, and a generalization to the case of the n-component coherent system is outlined. The problem of regime switching is described, and the new notion of the corresponding virtual age after the switching is proposed.

First passage time for the state of exact chemical equilibrium

1980 ◽  
Vol 45 (3) ◽  
pp. 777-782 ◽  
Author(s):  
Milan Šolc
Keyword(s):  
Chemical Equilibrium ◽  
First Passage Time ◽  
Passage Time ◽  
The State ◽  
Recurrence Time ◽  
First Passage ◽  
First Order ◽  
The Mean ◽  
Passage Times ◽  
Number Of Particles

The establishment of chemical equilibrium in a system with a reversible first order reaction is characterized in terms of the distribution of first passage times for the state of exact chemical equilibrium. The mean first passage time of this state is a linear function of the logarithm of the total number of particles in the system. The equilibrium fluctuations of composition in the system are characterized by the distribution of the recurrence times for the state of exact chemical equilibrium. The mean recurrence time is inversely proportional to the square root of the total number of particles in the system.

scholarly journals Credit Gap Risk in a First Passage Time Model with Jumps

2009 ◽  
Author(s):  
Natalie Packham ◽  
Lutz Schloegl ◽  
Wolfgang M. Schmidt
Keyword(s):  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Time Model ◽  
Gap Risk ◽  
Credit Gap

scholarly journals Two-phase CFD simulation of the monodyspersed suspension hydraulic behaviour in the tank apparatus from a circulatory pipe

2008 ◽  
Vol 10 (1) ◽  
pp. 22-27 ◽  
Author(s):  
Roch Plewik ◽  
Piotr Synowiec ◽  
Janusz Wójcik
Keyword(s):  
Cfd Simulation ◽  
Fluidised Bed ◽  
Cfd Simulations ◽  
Two Phase ◽  
Hydraulic Behaviour ◽  
Hydraulic Conditions ◽  
The One ◽  
Cfd Method ◽  
Multi Phase ◽  
The Ideal

Two-phase CFD simulation of the monodyspersed suspension hydraulic behaviour in the tank apparatus from a circulatory pipe The hydrodynamics in fluidized-bed crystallizers is studied by CFD method. The simulations were performed by a commercial packet of computational fluid dynamics Fluent 6.x. For the one-phase modelling (15), a standard k-ε model was applied. In the case of the two-phase flows the Eulerian multi-phase model with a standard k-ε method, aided by the k-ε dispersed model for viscosity, has been used respectively. The collected data put a new light on the suspension flow behaviour in the annular zone of the fluidised bed crystallizer. From the presented here CFD simulations, it clearly issues that the real hydraulic conditions in the fluidised bed crystallizers are far from the ideal ones.

Sign in / Sign up

Export Citation Format

Share Document