OSS Effort Expense Optimization Based on Wiener Process Model and GA

Various open source software are managed by using several bug tracking systems. In particular, the open source software extends to the cloud service and edge computing. Recently, OSF Edge Computing Group is launched by OpenStack. There are big data behind the internet services such as cloud and edge computing. Then, it is important to consider the impact of big data in order to assess the reliability of open source software. Various optimal software release problems have been proposed by specific researchers. In the typical optimal software release problems, the cost parameters are defined as the known parameter. However, it is difficult to decide the cost parameter because of the uncertainty. The purpose of our research is to estimate the effort parameters included in our models. In this paper, we propose an estimation method of effort parameter by using the genetic algorithm. Then, we show the estimation method in section 3. Moreover, we analyze actual data to show numerical examples for the estimation method of effort parameter. As the research results, we found that the OSS managers would be able to comprehend the human resources required before the OSS project in advance by using our method.

Rolling Bearing Remaining Useful Life Prediction Based on Wiener Process

Rolling bearing is the key part of mechanical system.Accurate prediction of bearing life can reduce maintenance costs,improve availability,and prevent catastrophic consequences,aiming at solving the problem of the nonlinear,random and small sample problems faced by rolling bearings in actual operating conditions.In this work,the nonlinearWiener process with random effect and unbiased estimation of unknown parameters is used to predict the remaining useful life of rolling bearings.Firstly,random effects and nonlinear parameters are added to the traditional Wiener process,and a parameter unbiased estimation method is used to estimate the positional parameters of the constructed Wiener model.Finally,the model is validated using a common set of bearing datasets.Experimental results show that compared with the traditional maximum likelihood function estimation method,the parameter unbiased estimation method can effectively improve the accuracy and stability of the parameter estimation results.The model has a good fitting effect,which can accurately predict the remaining useful life of rolling bearing.

Reliability-based selective maintenance for redundant systems with dependent performance characteristics of components

The reliability-based selective maintenance(RSM)decision problem of systems with components that have multiple dependent performance characteristics(PCs)reflecting degradation states is addressed in this paper.A vine-Copulabased reliability evaluation method is proposed to estimate the reliability of system components with multiple PCs.Specifically,the marginal degradation reliability of each PC is built by using the Wiener stochastic process based on the PC’s degradation mechanism.The joint degradation reliability of the component with multiple PCs is established by connecting the marginal reliability of PCs using D-vine.In addition,two RSM decision models are developed to ensure the system accomplishes the next mission.The genetic algorithm(GA)is used to solve the constraint optimization problem of the models.A numerical example illustrates the application of the proposed RSM method.

A Study on Stochastic Differential Equation Using Fractional Power of Operator in the Semigroup Theory

Stochastic differential equation (SDE) is an ordinary differential equation with a stochastic process that can model the unpredictable real-life behavior of any continuous systems. It is the combination of differential equations, probability theory, and stochastic processes. Stochastic differential equations arise in modeling a variety of random dynamic phenomena in physical, biological and social process. The SDE theory is traditionally used in physical science and financial mathematics. Recently, more researchers have been conducted in the application of SDE theory to various areas of engineering. This dissertation is mainly concerned with the existence of mild solutions for impulsive neutral stochastic differential equations with nonlocal conditions in Hilbert spaces. The results are obtained by using fractional powers of operator in the semigroup theory and Sadovskii fixed point theorem.

Remaining useful lifetime prediction for equipment based on nonlinear implicit degradation modeling

Nonlinearity and implicitness are common degradation features of the stochastic degradation equipment for prognostics.These features have an uncertain effect on the remaining useful life(RUL)prediction of the equipment.The current data-driven RUL prediction method has not systematically studied the nonlinear hidden degradation modeling and the RUL distribution function.This paper uses the nonlinear Wiener process to build a dual nonlinear implicit degradation model.Based on the historical measured data of similar equipment,the maximum likelihood estimation algorithm is used to estimate the fixed coefficients and the prior distribution of a random coefficient.Using the on-site measured data of the target equipment,the posterior distribution of a random coefficient and actual degradation state are step-by-step updated based on Bayesian inference and the extended Kalman filtering algorithm.The analytical form of the RUL distribution function is derived based on the first hitting time distribution.Combined with the two case studies,the proposed method is verified to have certain advantages over the existing methods in the accuracy of prediction.

Reliability modeling of the bivariate deteriorating product with both monotonic and non-monotonic degradation paths

Fiber optical gyroscope(FOG)is a highly reliable navigation element,and the degradation trajectories of its two accuracy indexes are monotonic and non-monotonic respectively.In this paper,a flexible accelerated degradation testing(ADT)model is used for analyzing the bivariate dependent degradation process of FOG.The time-varying copulas are employed to consider the dynamic dependency structure between two marginal degradation processes as the Wiener process and the inverse Gaussian process.The statistical inference is implemented by utilizing an inference function for the margins(IFM)approach.It is demonstrated that the proposed method is powerful in modeling the joint distribution with various margins.

REGULARITY OF RANDOM ATTRACTORS FOR A STOCHASTIC DEGENERATE PARABOLIC EQUATIONS DRIVEN BY MULTIPLICATIVE NOISE

We study the regularity of random attractors for a class of degenerate parabolic equations with leading term div(σ(x)▽u) and multiplicative noises. Under some mild conditions on the diffusion variable σ(x) and without any restriction on the upper growth p of nonlinearity, except that p > 2, we show the existences of random attractor in D_0^(1,2)(D_N, σ) (■∈ [2, 2p-2]) space, where D_N is an arbitrary(bounded or unbounded) domain in R^N, N ≥ 2. For this purpose, some abstract results based on the omega-limit compactness are established.

Local Continuity Modulus for Wiener and Infinite Dimensional OU Processes

In this paper, we gave a proof for the local continuity modulus theorem of theWiener process, i. e., lim t→0 sup 0≤s≤t |W（s）|/（2s log log（1/s））1/2=1 a.s.This result was given by Csrg and Revesz （1981）, but the proof gets them nowhere. We alsogave a similar local continuity modulus result for the infinite dimensional OU processes.

Time-varying coupling-induced logical stochastic resonance in a periodically driven coupled bistable system

Coupling-induced logical stochastic resonance(LSR) can be observed in a noise-driven coupled bistable system where the behaviors of system can be interpreted consistently as a specific logic gate in an appropriate noise level. Here constant coupling is extended to time-varying coupling, and then we investigate the effect of time-varying coupling on LSR in a periodically driven coupled bistable system. When coupling intensity oscillates periodically with the same frequency with periodic force or relatively high frequency, the system successfully yields the desired logic output. When coupling intensity oscillates irregularly with phase disturbance, large phase disturbance reduces the area of optimal parameter region of coupling intensity and response speed of logic devices. Although the system behaves as a desired logic gate when the frequency of time-periodic coupling intensity is precisely equal to that of periodic force, the desired logic gate is not robust against tiny frequency difference and phase disturbance. Therefore, periodic coupling intensity with high frequency ratio is an optimal option to obtain a reliable and robust logic operation.

Developed mathematical technique for fractional stochastic point kinetics model in nuclear reactor dynamics

Fractional stochastic kinetics equations have proven to be valuable tools for the point reactor kinetics model, where the nuclear reactions are not fully described by deterministic relations. A fractional stochastic model for the point kinetics system with multi-group of precursors,including the effect of temperature feedback, has been developed and analyzed. A major mathematical and inflexible scheme to the point kinetics model is obtained by merging the fractional and stochastic technique. A novel split-step method including mathematical tools of the Laplace transforms, Mittage–Leffler function, eigenvalues of the coefficient matrix, and its corresponding eigenvectors have been used for the fractional stochastic matrix differential equation. The validity of the proposed technique has been demonstrated via calculations of the mean and standard deviation of neutrons and precursor populations for various reactivities: step, ramp, sinusoidal, and temperature reactivity feedback. The results of the proposed method agree well with the conventional one of the deterministic point kinetics equations.

Time Discretized Variational Iteration Method for the Stochastic Volatility Process with Jumps

A model for both stochastic jumps and volatility for equity returns in the area of option pricing is the stochastic volatility process with jumps (SVPJ). A major advantage of this model lies in the area of mean reversion and volatility clustering between returns and volatility with uphill movements in price asserts. Thus, in this article, we propose to solve the SVPJ model numerically through a discretized variational iteration method (DVIM) to obtain sample paths for the state variable and variance process at various timesteps and replications in order to estimate the expected jump times at various iterates resulting from executing the DVIM as n increases. These jumps help in estimating the degree of randomness in the financial market. It was observed that the average computed expected jump times for the state variable and variance process is moderated by the parameters (variance process through mean reversion), Θ (long-run mean of the variance process), σ (volatility variance process) and λ (constant intensity of the Poisson process) at each iterate. For instance, when = 0.0, Θ = 0.0, σ = 0.0 and λ = 1.0, the state variable cluttered maximally compared to the variance process with less volatility cluttering with an average computed expected jump times of 52.40607869 as n increases in the DVIM scheme. Similarly, when = 3.99, Θ = 0.014, σ = 0.27 and λ = 0.11, the stochastic jumps for the state variable are less cluttered compared to the variance process with maximum volatility cluttering as n increases in the DVIM scheme. In terms of option pricing, the value 52.40607869 suggest a better bargain compared to the value 20.40344029 due to the fact that it yields less volatility rate. MAPLE 18 software was used for all computations in this research.

AN EFFICIENT FINITE DIFFERENCE METHOD FOR STOCHASTIC LINEAR SECOND-ORDER BOUNDARY-VALUE PROBLEMS DRIVEN BY ADDITIVE WHITE NOISES

In this paper,we develop and analyze a finite difference method for linear second-order stochastic boundary-value problems(SBVPs)driven by additive white noises.First we regularize the noise by the Wong-Zakai approximation and introduce a sequence of linear second-order SBVPs.We prove that the solution of the SBVP with regularized noise converges to the solution of the original SBVP with convergence order O(h)in the meansquare sense.To obtain a numerical solution,we apply the finite difference method to the stochastic BVP whose noise is piecewise constant approximation of the original noise.The approximate SBVP with regularized noise is shown to have better regularity than the original problem,which facilitates the convergence proof for the proposed scheme.Convergence analysis is presented based on the standard finite difference method for deterministic problems.More specifically,we prove that the finite difference solution converges at O(h)in the mean-square sense,when the second-order accurate three-point formulas to approximate the first and second derivatives are used.Finally,we present several numerical examples to validate the efficiency and accuracy of the proposed scheme.

Objective Bayesian analysis for the accelerated degradation model usingWiener process with measurement errors

The Wiener process as a degradation model plays an important role in the degradation analysis.In this paper, we propose an objective Bayesian analysis for an acceleration degradation Wienermodel which is subjected to measurement errors. The Jeffreys prior and reference priors underdifferent group orderings are first derived, the propriety of the posteriors is then validated. It isshown that two of the reference priors can yield proper posteriors while the others cannot. A simulation study is carried out to investigate the frequentist performance of the approach comparedto the maximum likelihood method. Finally, the approach is applied to analyse a real data.

Step-stress accelerated degradation test planning based on Wiener processwith correlation

To assess the lifetime distribution of highly reliable or expensive product,one of the most commonly used strategies is to construct step-stress accelerated degradation test(SSADT)which can curtail the test duration and reduce the test cost.In reality,it is not unusual for a unit with a higher degradation rate which exhibits a more volatile degradation path.Recently,Ye,Chen,and Shen[(2015).A new class of Wiener process models for degradation analysis.Reliability Engineering and System Safety,139,58–67]proposed a Wiener process to capture the positive correlation between the drift rate and the volatility.In this paper,an optimal SSADT plan is developed under the assumption that the underlying degradation path follows the Wiener process with correlation.Firstly,the stochastic diffusion process is introduced to model a typical SSADT problem.Then the design variables,including the sample size,the measurement frequency and the numbers of measurements under each stress level,are optimised by minimising the asymptotic variance of the estimated p-percentile of the product’s lifetime distribution subject to the total experimental cost not exceeding a pre-specified budget.Finally,a numerical example is presented to illustrate the proposed method.

Remaining Useful Life Prediction Method for Multi-Component System Considering Maintenance:Subsea Christmas Tree System as A Case Study

Maintenance is an important technical measure to maintain and restore the performance status of equipment and ensure the safety of the production process in industrial production,and is an indispensable part of prediction and health management.However,most of the existing remaining useful life(RUL)prediction methods assume that there is no maintenance or only perfect maintenance during the whole life cycle;thus,the predicted RUL value of the system is obviously lower than its actual operating value.The complex environment of the system further increases the difficulty of maintenance,and its maintenance nodes and maintenance degree are limited by the construction period and working conditions,which increases the difficulty of RUL prediction.An RUL prediction method for a multi-omponent system based on the Wiener process considering maintenance is proposed.The performance degradation model of components is established by a dynamic Bayesian network as the initial model,which solves the uncertainty of insufficient data problems.Based on the experience of experts,the degree of degradation is divided according to Poisson process simulation random failure,and different maintenance strategies are used to estimate a variety of condition maintenance factors.An example of a subsea tree system is given to verify the effectiveness of the proposed method.

Asymptotic expansions in the central limit theorem for a branching Wiener process

We consider a branching Wiener process in R^(d),in which particles reproduce as a super-critical Galton-Watson process and disperse according to a Wiener process.For B⊂R^(d),let Z_(n)(B) be the number of particles of generation n located in B.The study of the central limit theorem and related results about the counting measure Z_(n)(·)is important because such results give good descriptions of the con guration of the branching Wiener process at time n.In earlier works,the exact convergence rate in the central limit theorem and the asymptotic expansion until the third order have been given.Here,we establish the asymptotic expansion of any order in the central limit theorem under a moment condition of the form EX(logX)^(1+λ)<∞.

Multiscale Analysis of Semilinear Damped Stochastic Wave Equations

In this paper we proceed with the multiscale analysis of semilinear damped stochastic wave motions. The analysis is made by combining the well-known sigma convergence method with its stochastic counterpart, associated to some compactness results such as the Prokhorov and Skorokhod theorems. We derive the equivalent model, which is of the same type as the micro-model. One of the novelties of the work is that the corrector problem is solved in the classical sense of distributions,thereby allowing numerical computations of the homogenized coefficients.

Reliability Evaluation of Two-Phase Degradation Process with a Fuzzy Change-Point

For some products,degradation mechanisms change during testing,and therefore,their degradation patterns vary at different points in time;these points are called change-points.Owing to the limitation of measurement costs,time intervals for degradation measurements are usually very long,and thus,the value of change-points cannot be determined.Conventionally,a certain degradation measurement is selected as the change-point in a two-phase degradation process.According to the tendency of the two-phase degradation process,the change-point is probably located in the interval between two neighboring degradation measurements,and it is a fuzzy variable.The imprecision of the change-point may lead to the incorrect product’s reliability evaluation results.In this paper,based on the fuzzy theory,a two-phase degradation model with a fuzzy change-point and a statistical analysis method are proposed.First,a two-phase Wiener degradation model is developed according to the membership function of the change-point.Second,the reliability evaluation is carried out using maximum likelihood estimation and a fuzzy simulation approach.Finally,the proposed methodology is verified via a case study.The results of the study show that the proposed methodology can achieve more believable reliability evaluation results compared with those of the conventional approach.

Sequential degradation-based burn-in test with multiple periodic inspections

Bum-in has been proven effective in identifying and removing defective products before they are delivered to customers.Most existing bum-in models adopt a one-shot scheme,which may not be sufficient enough for identification.Borrowing the idea from sequential inspections for remaining useful life prediction and accelerated lifetime test,this study proposes a sequential degradation-based bum-in model with multiple periodic inspections.At each inspection epoch,the posterior probability that a product belongs to a normal one is updated with the inspected degradation level.Based on the degradation level and the updated posterior probability,a product can be disposed,put into field use,or kept in the test till the next inspection epoch.We cast the problem into a partially observed Markov decision process to minimize the expected total bum-in cost of a product,and derive some interesting structures of the optimal policy.Then,algorithms are provided to find the joint optimal inspection period and number of inspections in steps.A numerical study is also provided to illustrate the effectiveness of our proposed model.