Inverse Gaussian分布的假设检验

用一种新构造方法，实现了Inverse Gaussian分布的正态化，进而解决了一类长期遗留下来的Inverse Gaussian分布的假设检验问题。

A dynamic condition-based maintenance optimization model for mission-oriented system based on inverse Gaussian degradation process

An effective maintenance policy optimization model can reduce maintenance cost and system operation risk. For mission-oriented systems, the degradation process changes dynamically and is monotonous and irreversible. Meanwhile, the risk of early failure is high. Therefore, this paper proposes a dynamic condition-based maintenance(CBM) optimization model for mission-oriented system based on inverse Gaussian(IG) degradation process. Firstly, the IG process with random drift coefficient is used to describe the degradation process and the relevant probability distributions are obtained. Secondly, the dynamic preventive maintenance threshold(DPMT) function is used to control the early failure risk of the mission-oriented system, and the influence of imperfect preventive maintenance(PM)on the degradation amount and degradation rate is analysed comprehensively. Thirdly, according to the mission availability requirement, the probability formulas of different types of renewal policies are obtained, and the CBM optimization model is constructed. Finally, a numerical example is presented to verify the proposed model. The comparison with the fixed PM threshold model and the sensitivity analysis show the effectiveness and application value of the optimization model.

A Normal Weighted Inverse Gaussian Distribution for Skewed and Heavy-Tailed Data

High frequency financial data is characterized by non-normality: asymmetric, leptokurtic and fat-tailed behaviour. The normal distribution is therefore inadequate in capturing these characteristics. To this end, various flexible distributions have been proposed. It is well known that mixture distributions produce flexible models with good statistical and probabilistic properties. In this work, a finite mixture of two special cases of Generalized Inverse Gaussian distribution has been constructed. Using this finite mixture as a mixing distribution to the Normal Variance Mean Mixture we get a Normal Weighted Inverse Gaussian (NWIG) distribution. The second objective, therefore, is to construct and obtain properties of the NWIG distribution. The maximum likelihood parameter estimates of the proposed model are estimated via EM algorithm and three data sets are used for application. The result shows that the proposed model is flexible and fits the data well.

Inverse Gaussian process-based corrosion growth modeling and its application in the reliability analysis for energy pipelines

This paper describes an inverse Gaussian process-based model to characterize the growth of metal-loss corrosion defects on energy pipelines.The model parameters are evaluated using the Bayesian methodology by combining the inspection data obtained from multiple inspections with the prior distributions.The Markov Chain Monte Carlo(MCMC)simulation techniques are employed to numerically evaluate the posterior marginal distribution of each individual parameter.The measurement errors associated with the ILI tools are considered in the Bayesian inference.The application of the growth model is illustrated using an example involving real inspection data collected from an in-service pipeline in Alberta,Canada.The results indicate that the model in general can predict the growth of corrosion defects reasonably well.Parametric analyses associated with the growth model as well as reliability assessment of the pipeline based on the growth model are also included in the example.The proposed model can be used to facilitate the development and application of reliability-based pipeline corrosion management.

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.