The objective of this project is to determine whether utilizing an EM Algorithm to fit a Gaussian mixed model distribution model provides needed accuracy in identifying the number of defective parts per million when the overall population is made up of multiple independent runs or lots. The other option is approximating using standard software tools and common known techniques available to a process, industrial or quality engineer. These tools and techniques provide methods utilizing familiar distributions and statistical process control methods widely understood. This paper compares these common methods with an EM Algorithm programmed in R using a dataset of actual measurements for length of manufactured product. / text

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As the public and policy makers continue to become more concerned with climate change, researchers continue to seek to understand and explain energy and greenhouse gas (GHG) emissions trends and their drivers. Living and existing in different areas is associated with different impacts, so growth in different areas, as well as the movement of people to and from those areas will affect energy use and emissions over US, individual states, and counties. First the emissions implications of state to state mobility on household energy and GHG emissions are explored. 3 million households move across state lines annually, and generally move from the North East to the South and West. Migrating households often move to states with different climates, and thus heating and cooling and needs, different fuel mixes, and different regional electricity grids which leads them to experience changes in household emissions as a result of their move. Under current migration trends, the emissions increases of households moving from the Northeast to the South and Southwest are balanced by the emissions decreases of households moving to California and the Pacific Northwest. The net sum of emissions changes for migrating households is slightly positive but near zero; however, that net zero sum represents the balance of many emission changes. Summing emissions changes over individual states and regions show the regional differences in household emissions. Next, a similar analysis is conducted for the 120,000 households that annually move between counties in Pennsylvania. From 2006–2010, the emissions changes experienced by those households balanced to near zero values, similar to the state analysis. The emissions increases from households moving to metropolitan fringe and suburban counties were countered by the emissions decreases from households moving to low emission urban centers, even though urban centers experienced net negative migration. While emission changes experienced by households were dominated by differences in emissions from residential energy use, emission changes for household moving within Pennsylvania were dominated by differences from transportation emissions. Finally, this thesis explores the long term effects of growth and decline at the metropolitan level by estimating fossil based CO2 emissions from1900−2000 for Allegheny County, Pennsylvania. From 1970 to 2000, Allegheny County experienced a 30% decrease in total emissions and energy use from peak values, primarily because of a decline in industrial activity! (40% decrease in value added) and the loss of a quarter of its population. Allegheny County’s history suggests that the scale of change needed to achieve local emissions reductions may be significant; given years of major technological, economic, and demographic changes, per capita emissions in 1940 were nearly the same in 2000. Most local governments are planning emissions reductions rates that exceed 1% per year, which deviate significantly from historical trends. These results suggest additional resources and improved planning paradigms are likely necessary to achieve significant emissions reductions, especially for areas where emissions are still increasing. This work shows that overtime, growth and decline within a! region drives its evolving GHG footprint. Population decline within region may lead to emission reductions, as seen in the Allegheny County, but those reductions are more accurately described as displaced emissions due to population redistribution. From 2005-2010, the mobility of the US population between states, regions and counties was responsible for many household emissions changes that balance annually over the entire US. The near zero sum represents the v precarious emissions balance of two kinds of household moves. First, moves resulting in moderate emissions increases either as a result of households moving to higher carbon regions, like the South or South West, or as a result of households moving higher carbon suburban counties within states. Second, moves resulting in significant emissions decreases! As a result of households moving to low carbon regions or low carbon urban centers. Planning for continued low carbon growth in low carbon regions or cities experiencing high growth rates driven by migration, like California or Philadelphia, is essential in order to offset the moderate emissions increases experienced by households moving to high carbon regions or suburban areas.