In traditional quality control charts, fixed sampling interval (FSI) schemes are used where the time between samples has fixed intervals. More efficient methods called variable sampling interval (VSI) schemes have been developed where one takes the next observation sooner than usual if there is an indication that the process is operating off the target value. Another traditional assumption behind most statistical process control charts is that the sequential observations are independent. However, there are many situations where the sequential observations should not to be treated as independent. Rather, a time series model, in particular the first order autoregressive (AR (1)) model, is appropriate. A Markov chain representation is used to study the properties of the FSI and VSI Shewhart X control charts. First, the results show that if the process variance is properly estimated and if traditional control limits are used in the FSI control charts, then the detection time is shorter when the consecutive observations are negatively correlated than when they are positively correlated. If they are positively correlated, then the false alarm rate decreases as the correlation between consecutive observations increases. On the other hand, the detection time increases as the correlation increases. In VSI control charts with traditional control limits, if the process mean is on or near the target, then the average time to signal (A TS) and average number of samples to signal (ANSS) tend to decrease as the correlation increases until the correlation becomes rather moderate. Then, for more highly correlated data, the A TS and ANSS tend to increase as the correlation increases. Next, the results show that, even under the AR (1) process, the VSI chart is more efficient than the FSI chart in terms of ATS. In contrast, the VSI chart is less efficient than the FSI chart in terms of ANSS. The efficiency (inefficiency) of ATS (ANSS) tends to decrease (increase) as the correlation between the consecutive observations becomes stronger. Steady state ATS (A TS·) and steady state ANSS (ANSSO) under the AR (1) process show the same trend as the 'regular' ATS and 'regular' ANSS except when the deviation is very large. If the deviation is very large, then the VSI control chart does not seem to be more efficient than the FSI control chart in terms of steady state ATS. If we have an AR (2) process, then for any given value of tP2 a PSI control chart has a shorter detection time when tPl is negative than when tPl is positive. In a FSI control chart, the effect of positive </>2 in addition to positive tPl is that the false alarm rate decreases even further and the detection time is even longer. / Ph. D.

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<p> The sulfur cycle is perhaps one of earth's most important cycles. Biologically sulfur is the main constituent needed to form building blocks such as amino acids. Ecologically, it can devastate forests, lakes and ecosystems in one of it's many forms. Industrially (and perhaps naturally) it is the source of our acid rain problem. </p> <p> An estimation of sulfide fluxes emitted into the atmosphere is extremely variant due to the lack of efficient means of measuring these fluxes. Several simplistic measuring devices have been employed to estimate the oceanic, continental and atmospheric fluxes. Problems have arisen due to the non-uniform distribution of sulfur sources such as industries, volcanoes and marshlands. </p> <p> In the specific case estimates of fluxes have of organic volatile been deduced and not sulfides, actually measured to any great extent. The fundamental reason for this being the lack of an efficient means of recording data in the field to support the flux estimates. </p> <p> This study has attempted to secure the efficiency of adsorption tubes used to sample in situ freshwater sulfide fluxes. Optimal preparation involved using Molecular Sieve SA (60/80 mesh) contained and activated in pyrex glass tubing (6mm. o.d.). Proper activation occurred at 300C for 8 hours under a constant helium flow. </p> <p> Adsorption of sulfides was by helium induced release of gases at room/atmospheric temperatures. After 15 minutes, the adsorption tube was recapped and stored at (-8C) for no more than 7 days. At this time, the tubes were analyzed. </p> <p> Analysis was by GC/HECD in the laboratory. A custom made heat desorber (at 270C), in conjunction with liquid nitrogen and hot water sufficiently trapped the released sulfides from the adsorption tube. Calibrated data obtained in the laboratory provided for proper analytical interpretations of the flux of sulfides emitted from the sample. </p> / Thesis / Bachelor of Science (BSc)

Ewens sampling formula is the sampling distribution for a population assumed to follow a one parameter Poisson-Dirichlet distribution, where the parameter is fixed. In this project this assumption will be loosened and we will look at the parameter as a function of the sample size. This will result in sampling from a family of Poisson-Dirichlet distributions. Estimators for this new construction will be tested using two different simulation methods. / Thesis / Master of Science (MSc)

<p> The role of verbal hypotheses in concept identification was explored by manipulating three variables affecting the relation between verbalized rules and classification performance. (i) Verbalizing rules before and after classification changed subjects' cue-sampling strategies and the control of verbal hypotheses over sorting performance. (ii) The difficulty of stimulus description affected how subjects utilized verbal hypotheses, and whether verbalized rules completely specified the cues used for classification. (iii) The number of irrelevant attributes changed the relative efficiency of stimulus-learning over rule-learning for concept identification.</p> <p> These investigations demonstrate effective techniques for varying and evaluating the importance of verbal rules for classification; and suggest that subjects' prior verbal habits markedly affect the degree of reliance placed on verbal hypotheses in concept attainment.</p> / Thesis / Doctor of Philosophy (PhD)

Although sampling techniques have been used effectively in education research and practice it is not clear how stratified random sampling techniques apply to high-stakes testing in the current educational environment. The present study focused on representative sampling as a possible means for reducing the quantity of state-administered tests in Texas public education. The purpose of this study was two-fold: (1) to determine if stratified random sampling is a viable option for reducing the number of students participating in Texas state assessments, and (2) to determine which sampling rate provides consistent estimates of the actual test results among the population of students. The study examined students’ scaled scores, percent of students passing, and student growth over a three-year period on state-mandated assessments in reading, mathematics, science, and social studies. Four sampling rates were considered (10%, 15%, 20%, & 25%) when analyzing student performance across demographic variables, including population estimates by socioeconomic status, limited English proficiency, and placement in special education classes. The data set for this study included five school districts and 68,641 students. Factorial ANOVAs were used initially to examine the effects of sampling rate on bias in reading and mathematics scores and bias in percentage of students passing these tests. Also 95% confidence intervals (CIs) and effect sizes for each model were examined to aid in the interpretation of the results. The results showed main effects for sampling rate and campus as well as a two-way interaction between these variables. The results indicated that a 20% sampling rate would closely approximate the parameter values regarding the mean TAKS reading and mathematics scale scores and the percentage of students passing these assessments. However, as population size decreases, sampling rate may have to be increased. For example, in populations with 30 or fewer students in a subgroup it is recommended that all students be included in the testing program. This study situated in one state contributes to the growing body of research being conducted on an international basis in sample-based educational assessments.

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