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No description available.

In Statistical Process Control, it is usually assumed that observations taken from the process at different times are independent with a constant mean and with variation due only to measurement error. In many processes this assumption of independence is not satisfied. The lack of independence of observations taken at different times may have a significant effect on the properties of a process monitoring technique. A first order autoregressive process which is observed subject to measurement error is considered. Integral equation, Markov chain and simulation approaches are used to evaluate the average run length (ARL) of exponentially weighted moving average (EWMA) and one-sided cumulative sum (CUSUM) control charts used to monitor the process. The effects of correlation and measurement error on the ARL's of the control charts are studied for a process which is in control and for a process which has undergone a shift in mean level away from the target value. Methods of estimation of the parameters of the process are examined, and tables are given to assist in the design of EWMA and CUSUM control charts for AR(1) processes. Examples of designing an EWMA and a CUSUM chart for an AR(1) process are presented. / Ph. D.

Hydrological observations are characterised by wet and dry cycles, a characteristic that is termed hydrological persistence. Interactions between global climate phenomena and the hydrological cycle result in rainfall and streamflow data clustering into wetter and drier states. These states have implications for the management and planning of water resources. Statistical tests constructed from the theory of wet and dry spells indicate that evidence for persistence in monthly observations is more compelling than at an annual scale. This thesis demonstrates that examination of monthly data yields spatially - consistent patterns of persistence across a range of hydrological variables. It is imperative that time series models for rainfall and streamflow replicate the observed fluctuations between the climate regimes. Monthly time series are generally represented with linear models such as ARMA variants ; however simulations from such models may underestimate the magnitude and frequency of persistence. A different approach to modelling these data is to incorporate shifting levels in the broader climate with a tendency to persist within these regimes. Hidden Markov models ( HMMs ) provide a strong conceptual basis for describing hydrological persistence, and are shown to provide accurate descriptions of fluctuating climate states. These models are calibrated here with a full Bayesian approach to quantify parameter uncertainty. A range of novel variations to standard HMMs are introduced, in particular Autoregressive HMMs and hidden semi - Markov models which have rarely been used to model monthly rainfall totals. The former model combines temporal persistence within observations with fluctuations between persistent climate states, and is particularly appropriate for modelling streamflow time series. The latter model extends the modelling capability of HMMs by fitting explicit probability distributions for state durations. These models have received little attention for modelling persistence at monthly scale. A non - parametric ( NP ) HMM, which overcomes the major shortcomings of standard parametric HMMs, is also described. Through removing the requirement to assume parametric forms of conditional distributions prior to model calibration, the innovative NP HMM framework provides an improved estimation of persistence in discrete and continuous data that remains unaffected by incorrect parametric assumptions about the state distributions. Spatially - consistent persistence is identified across Australia with the NP HMM, showing a tendency toward stronger persistence in low-rainfall regions. Coherent signatures of persistence are also identified across time series of total monthly rainfall, numbers of rain - days each month, and the intensities of the most extreme rain events recorded each month over various short durations, illustrating that persistent climate states modulate both the numbers of rain events and the amount of moisture contained within these events. These results provide a new interpretation of the climatic interactions that underlie hydrological persistence. The value of HMMs to water resource management is illustrated with the accurate simulation of a range of hydrologic data, which in each case preserves statistics and spell properties over a range of aggregations. Catchment - scale rainfall for the Warragamba Reservoir is simulated accurately with HMMs, and rainfall - runoff transformations from these simulations provide reservoir inflows of lower drought risk than provided from ARMA models. / Thesis (Ph.D.)--School of Civil and Environmental Engineering, 2006.

Hydrological observations are characterised by wet and dry cycles, a characteristic that is termed hydrological persistence. Interactions between global climate phenomena and the hydrological cycle result in rainfall and streamflow data clustering into wetter and drier states. These states have implications for the management and planning of water resources. Statistical tests constructed from the theory of wet and dry spells indicate that evidence for persistence in monthly observations is more compelling than at an annual scale. This thesis demonstrates that examination of monthly data yields spatially - consistent patterns of persistence across a range of hydrological variables. It is imperative that time series models for rainfall and streamflow replicate the observed fluctuations between the climate regimes. Monthly time series are generally represented with linear models such as ARMA variants ; however simulations from such models may underestimate the magnitude and frequency of persistence. A different approach to modelling these data is to incorporate shifting levels in the broader climate with a tendency to persist within these regimes. Hidden Markov models ( HMMs ) provide a strong conceptual basis for describing hydrological persistence, and are shown to provide accurate descriptions of fluctuating climate states. These models are calibrated here with a full Bayesian approach to quantify parameter uncertainty. A range of novel variations to standard HMMs are introduced, in particular Autoregressive HMMs and hidden semi - Markov models which have rarely been used to model monthly rainfall totals. The former model combines temporal persistence within observations with fluctuations between persistent climate states, and is particularly appropriate for modelling streamflow time series. The latter model extends the modelling capability of HMMs by fitting explicit probability distributions for state durations. These models have received little attention for modelling persistence at monthly scale. A non - parametric ( NP ) HMM, which overcomes the major shortcomings of standard parametric HMMs, is also described. Through removing the requirement to assume parametric forms of conditional distributions prior to model calibration, the innovative NP HMM framework provides an improved estimation of persistence in discrete and continuous data that remains unaffected by incorrect parametric assumptions about the state distributions. Spatially - consistent persistence is identified across Australia with the NP HMM, showing a tendency toward stronger persistence in low-rainfall regions. Coherent signatures of persistence are also identified across time series of total monthly rainfall, numbers of rain - days each month, and the intensities of the most extreme rain events recorded each month over various short durations, illustrating that persistent climate states modulate both the numbers of rain events and the amount of moisture contained within these events. These results provide a new interpretation of the climatic interactions that underlie hydrological persistence. The value of HMMs to water resource management is illustrated with the accurate simulation of a range of hydrologic data, which in each case preserves statistics and spell properties over a range of aggregations. Catchment - scale rainfall for the Warragamba Reservoir is simulated accurately with HMMs, and rainfall - runoff transformations from these simulations provide reservoir inflows of lower drought risk than provided from ARMA models. / Thesis (Ph.D.)--School of Civil and Environmental Engineering, 2006.

published_or_final_version / Computer Science and Information Systems / Doctoral / Doctor of Philosophy

published_or_final_version / abstract / Statistics and Actuarial Science / Master / Master of Philosophy

Approved for public release; distribution is unlimited / This thesis developed a deterministic Markov state model to provide the U.S. Navy Nurse Corps a tool to more accurately forecast recruiting goals and future years force structure. Nurse Corps data was provided by the Nurse Corps Community Manager's office covering fiscal years 1990 to 2003. The probabilities used in the Markov model were derived from the fiscal year data. Transitions used in this model were stay at present grade, move up one grade or exit the system. Backward movement was not allowed and individuals could only move up one grade per year. The model was limited to eleven years and focused primarily on the ranks of O-1 to O-3. O-4's and O-5's that appeared in the data were allowed to flow through the system. Logistic regression was then used to investigate the probability of "staying" in the Nurse Corps to certain career decision points. Nurse Corps cohort data files for fiscal years 90 through 94 were merged for analysis, as was cohort data for fiscal year 96 through 98. Results of the markov model show that the O-1's and O-2's reach a steady state at the eight-year mark while the O-3's reach a steady state at the seventeen-year mark (based on provided data). The steady state values are compared to actual Nurse Corps goals. Results of the logistic regression show that Recalls, Medical Enlisted Commissioning Program and Nurse Candidate Program were all significant at increasing the probability of staying in the Nurse Corps. Males were more likely than females to stay in the Nurse Corps and changes in education levels decreased the probability of staying in the Nurse Corps. / Lieutenant, United States Navy