R code for fitting a nonhomogeneous temporal Poisson process model

The following R code demonstrates how to fit a nonhomogeneous Poisson process (NHPP) model to temporal data.

The R code may be used to fit 1) a NHPP model with a loglinear intensity function, with the intensity at time t defined by e^{\gamma_{0} + \gamma_{1}t} , or 2) a NHPP model with a power law intensity function, with the intensity at time t defined by \frac{\beta}{\eta}(\frac{t}{\eta})^{\beta-1}. The latter NHPP model is sometimes referred to as the Crow-AMSAA model.

NHPP loglinear

Continue reading R code for fitting a nonhomogeneous temporal Poisson process model

R code for fitting a loglinear-NHPP model to grouped temporal data

The following R code fits a NonHomogeneous Poisson Process (NHPP) model to grouped temporal data. Grouped temporal data occurs when only the number of recurrences within a given time interval are known.
The R code fits a NHPP model with a loglinear intensity function, where the intensity at time t is given by e^{\gamma_{0} + \gamma_{1}t} .
NHPP loglikelihood Continue reading R code for fitting a loglinear-NHPP model to grouped temporal data

R code for fitting a piecewise NHPP model

The following R code implements a piecewise Weibull NHPP model. In the context of repairable systems a Weibull NHPP model is also known as the Crow-AMSAA model.

Technical details of the piecewise NHPP model are given in: Guo, H., Mettas, A., Sarakakis, G., and Niu, P. (2010), Piecewise NHPP Models with Maximum Likelihood Estimation for Repairable Systems, Reliability and Maintainability Symposium (RAMS), 2010 Proceedings. Continue reading R code for fitting a piecewise NHPP model

R code for fitting the Crow-AMSAA model to grouped data

The Crow-AMSAA model is frequently used for analyzing and assessing reliability growth. In case of grouped data the Crow-AMSAA model parameters have to be estimated by numerical optimization. Grouped data occurs when only the number of failures within a given time period are known.

The Crow-AMSAA model in the R code fits a NonHomogenous Poisson Process (NHPP) having a power law intensity function. See this post for fitting a NHPP model having a loglinear intensity function. Continue reading R code for fitting the Crow-AMSAA model to grouped data