Reverse Auction Bidding (RAB) is a recently developed procurement method that can be used by the construction industry. The technique is different from a traditional auction system, since RAB system uses a bidding activity method that is completed anonymously by pre-qualified bidders during a fixed auction time. The basic premise for the auction is that the current best auction price is available for viewing during the whole auction process by both bidders and owner. The apparent incentive is for noncompetitive bidders to lower the price. There are however controlling factor beyond the reach of owners, such as market demand, lending restrictions, stakeholder expectations and risk tolerance levels, that impact on price levels. However, owners continue to attempt to drive down prices using this technique. A study into the mechanics of RAB was launched at Texas A&M University in 2004. This ongoing study of RAB continues to this time with eighteen case studies. This nineteenth study looks at the time series bid data from some of the prior work. Nine case studies were selected from the previous case studies. These nine studies provided untainted data with 6674 RAB bid arrivals by prior investigator actions. This study concerns the statistical process of bid arrivals with time. The hypothesis to be tested is that the RAB bid arrivals timing can be modeled with a statistical process. The analysis reviewed the fit for several types of distribution, including Gaussian and Poissionian. The best fit was modeled by non-homogeneous Poisson process (NHPP). The first conclusion from the analysis is that RAB bid arrivals follows a Poisson process, termed non-homogeneous Poisson process (NHPP). The second conclusion is that the controlling Poissionian process has a square root factor. The NHPP model for RAB provides a tool for future studies of RAB in real time. Future work is suggested on the inter-time periods for the bidding.

Recurrent events are very common in a wide range of scientific disciplines. The majority of statistical models developed to characterise recurrent events are derived from either reliability theory or survival analysis. This thesis concentrates on applications that arise from reliability, which in general involve the study about components or devices where the recurring event is failure. Specifically, interest lies in repairable components that experience a number of failures during their lifetime. The goal is to develop statistical models in order to gain a good understanding about the driving force behind the failures. A particular counting process is adopted, the non-homogenous Poisson process (NHPP), where the rate of occurrence (failure rate) depends on time. The primary application considered in the thesis is the prediction of underground water pipe bursts although the methods described have more general scope. First, a Bayesian mixed effects NHPP model is developed and applied to a network of water pipes using MCMC. The model is then extended to a mixture of NHPPs. Further, a special mixture case, the zero-inflated NHPP model is developed to cope with data involving a large number of pipes that have never failed. The zero-inflated model is applied to the same pipe network. Quite often, data involving recurrent failures over time, are aggregated where for instance the times of failures are unknown and only the total number of failures are available. Aggregated versions of the NHPP model and its zero-inflated version are developed to accommodate aggregated data and these are applied to the aggregated version of the earlier data set. Complex devices in random environments often exhibit what may be termed as state changes in their behaviour. These state changes may be caused by unobserved and possibly non-stationary processes such as severe weather changes. A hidden semi-Markov NHPP model is formulated, which is a NHPP process modulated by an unobserved semi-Markov process. An algorithm is developed to evaluate the likelihood of this model and a Metropolis-Hastings sampler is constructed for parameter estimation. Simulation studies are performed to test implementation and finally an illustrative application of the model is presented. The thesis concludes with a general discussion and a list of possible generalisations and extensions as well as possible applications other than the ones considered.

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