Comment on “The nonhomogeneous Poisson process—a model for the reliability of complex repairable systems”

1990 ◽  
Vol 30 (4) ◽  
pp. 807-808 ◽  
Author(s):  
H. Ascher
Keyword(s):  
Poisson Process ◽  
Nonhomogeneous Poisson Process ◽  
Repairable Systems

scholarly journals A Reliability Growth Process Model with Time-Varying Covariates and Its Application

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 905
Author(s):  
Xin-Yu Tian ◽  
Xincheng Shi ◽  
Cheng Peng ◽  
Xiao-Jian Yi
Keyword(s):  
Poisson Process ◽  
Process Model ◽  
Growth Process ◽  
Nonhomogeneous Poisson Process ◽  
Reliability Growth ◽  
Time Varying ◽  
Repairable Systems ◽  
Martingale Theory ◽  
Amsaa Model ◽  
Time Varying Covariates

The nonhomogeneous Poisson process model with power law intensity, also known as the Army Materiel Systems Analysis Activity (AMSAA) model, is commonly used to model the reliability growth process of many repairable systems. In practice, it is necessary to test the reliability of the product under different operational environments. In this paper we introduce an AMSAA-based model considering the covariate effects to measure the influence of the time-varying environmental condition. The parameter estimation of the model is typically performed using maximum likelihood on the failure data. The statistical properties of the estimation in the model are comprehensively derived by the martingale theory. Further inferences including confidence interval estimation and hypothesis tests are designed for the model. The performance and properties of the method are verified in a simulation study, compared with the classical AMSAA model. A case study is used to illustrate the practical use of the model. The proposed approach can be adapted for a wide class of nonhomogeneous Poisson process based models.

scholarly journals Bayesian modeling and prediction of accrual in multi-regional clinical trials

2014 ◽  
Vol 26 (2) ◽  
pp. 752-765 ◽  
Author(s):  
Yi Deng ◽  
Xiaoxi Zhang ◽  
Qi Long
Keyword(s):  
Clinical Trials ◽  
Poisson Process ◽  
Process Model ◽  
Nonhomogeneous Poisson Process ◽  
Modeling And Prediction ◽  
Accuracy And Precision ◽  
Start Up ◽  
Accrual Rate ◽  
Model Region ◽  
Over Time

In multi-regional trials, the underlying overall and region-specific accrual rates often do not hold constant over time and different regions could have different start-up times, which combined with initial jump in accrual within each region often leads to a discontinuous overall accrual rate, and these issues associated with multi-regional trials have not been adequately investigated. In this paper, we clarify the implication of the multi-regional nature on modeling and prediction of accrual in clinical trials and investigate a Bayesian approach for accrual modeling and prediction, which models region-specific accrual using a nonhomogeneous Poisson process and allows the underlying Poisson rate in each region to vary over time. The proposed approach can accommodate staggered start-up times and different initial accrual rates across regions/centers. Our numerical studies show that the proposed method improves accuracy and precision of accrual prediction compared to existing methods including the nonhomogeneous Poisson process model that does not model region-specific accrual.

Optimal Advertizing Policy for Selling a Single Asset

1991 ◽  
Vol 5 (1) ◽  
pp. 89-100 ◽  
Author(s):  
David Assaf ◽  
Benny Levikson
Keyword(s):  
Poisson Process ◽  
Nonhomogeneous Poisson Process ◽  
Independent And Identically Distributed

Suppose we have a single asset that we would like to sell. As time goes by, independent and identically distributed offers with a common known distribution F are given to us. At any given moment, we may either accept the current offer or reject it, thereby losing it forever. The rate at which offers arrive follows a nonhomogeneous Poisson process whose instantaneous intensity is under our control, using advertizing in a manner to be described. Our objective is, roughly, that of maximizing the total discounted expected reward composed of the offer we decide to accept, minus the total advertizing costs.

Operator-based intensity functions for the nonhomogeneous Poisson process

2016 ◽  
Vol 25 (2) ◽  
pp. 79-98 ◽  
Author(s):  
S. K. Bar-Lev ◽  
D. Bshouty ◽  
F. A. van der Duyn Schouten
Keyword(s):  
Poisson Process ◽  
Nonhomogeneous Poisson Process ◽  
Intensity Functions
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