homogeneous poisson process
Recently Published Documents

Machine reliability in cellular manufacturing is a challenging engineering problem in the formation and design of manufacturing cells. The heterogeneity of feedstock quality is also common in manufacturing industry. However, so far, no work has been done to investigate the performance of diversely configurated manufacturing cells under the heterogeneous feedstocks. In this paper, considering the actual engineering condition, the uniformly random arrival and the clustered arrival of low-quality feedstocks are proposed and modeled by the homogeneous Poisson process and Hawkes process, respectively. Also, to study the mixed reliability of a machine under the impact of heterogeneous feedstocks, a mixed failure-rate model is constructed by the mixture of exponential and Weibull distributions, and the processing quality is modeled by a non-homogeneous Poisson process with a dynamic intensity function. Then, we achieve a contrastive analysis for operational reliability and quality loss of manufacturing cells with basic serial and parallel configurations under the impact of heterogeneous feedstocks. At last, the designed simulation illustrates the effectiveness of our proposed models, and some results are concluded to provide some guidelines for the design of manufacturing cells.

Accurate long-term risk and resilience assessment of bridges are of paramount importance to aid rational decision-making under seismic hazards. There exist time-varying features within both earthquakes and structural deterioration. It has been found that the occurrence of large earthquakes is dependent on time due to energy accumulation, whereas the widely adopted homogeneous Poisson process assumes the time-independent occurrence of hazards. Besides, bridges can deteriorate over time due to environmental exposure, resulting in increased seismic vulnerability. The time-varying characteristics associated with both earthquakes and deterioration, which cause compound effects to structures, should be incorporated in long-term seismic risk and resilience assessment. In this paper, an approach for assessing the long-term resilience of bridges incorporating time-varying characteristics of earthquakes and deterioration is proposed. The Brownian Passage Time (BPT) model capturing energy accumulation and release is used to model time-varying characteristics of earthquakes. The bridge seismic vulnerability is computed in a time-variant manner considering deterioration. Subsequently, long-term bridge resilience is computed by considering earthquakes and deterioration occurring during the entire service life of bridges. The proposed approach is illustrated on a highway bridge under time-dependent seismic hazard and structural deterioration.

In this paper, we consider a history-dependent mixed shock model which is a combination of the history-dependent extreme shock model and the history-dependent $\delta$ -shock model. We assume that shocks occur according to the generalized Pólya process that contains the homogeneous Poisson process, the non-homogeneous Poisson process and the Pólya process as the particular cases. For the defined survival model, we derive the corresponding survival function, the mean lifetime and the failure rate. Further, we study the asymptotic and monotonicity properties of the failure rate. Finally, some applications of the proposed model have also been included with relevant numerical examples.

The COVID-19 pandemic has highlighted the need for finding mathematical models to forecast the evolution of the contagious disease and evaluate the success of particular policies in reducing infections. In this work, we perform Bayesian inference for a non-homogeneous Poisson process with an intensity function based on the Gompertz curve. We discuss the prior distribution of the parameter and we generate samples from the posterior distribution by using Markov Chain Monte Carlo (MCMC) methods. Finally, we illustrate our method analyzing real data associated with COVID-19 in a specific region located at the south of Spain.

The purpose of this paper is to present the results of the application of various models to estimate the reliability of environmental test chambers, especially, the methodology proposed by the International Electrotechnical Commission (IEC), using the Homogeneous Poisson process (HPP) and Non-Homogeneous Poisson process (NHPP) models, is adopted first, and then, a non-monotonic trend test and bathtub curve intensity function not covered by IEC are used, and supplementary analysis is used to characterize the resulting failure intensity. For the first time, the stochastic process model was applied to evaluate the reliability of 20 environmental test chambers. The results show that the IEC standards process is suitable for the reliability evaluation of a single chamber, and 16 chambers conform to the HPP model and 4 chambers conform to the NHPP model. However, there is the power-law model (PLP) rejection cases among the overall description of multiple chambers by the IEC model. The rejected cases were analyzed again by using a non-monotonic trend test and constructing a double Weibull process tub curve strength function, and the 3-stage time interval of the bathtub curve failure is obtained, which is in line with the actual operation data. The Ward clustering method is used for the mean time between failures of 20 chambers, resulting in 4 types of chamber groups with different reliability values (71,52,100,130 days), which is of great significance for studying the reliability of the environmental test chamber and carrying out customized maintenance.