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.

Indiana University-Purdue University Indianapolis (IUPUI) / Long term no-till (NT) farming can improve the CH4 oxidation capacity of agricultural lands through creation of a favorable soil environment for methanotrophs and diffusive gas transport. However, limited data is available to evaluate the merit of that contention. Although the potential for biological CH4 oxidation may exist in NT soils, restricted diffusion could limit expression of that potential in fine-textured soils. A study was conducted to assess the CH4 oxidation potential and gaseous diffusivity of soils under plow till (PT) and NT for > 50 years. Intact cores and composite soils samples (0-10 and 10-20 cm) were collected from NT and PT plots located at a well-drained site (Wooster silt loam) and at a poorly-drained (Crosby silt loam) site in Ohio. Adjacent deciduous forest soils were also sampled to determine maximum rate expected in undisturbed soils in the region. Regardless of study sites and soil depth, CH4 oxidation rate (measured at near ambient CH4) and oxidation potential (Vmax, measured at elevated CH4) were 3-4 and 1.5 times higher in NT than in PT soils, respectively. Activity in the NT soils approached (66-80 %) that in the forest soils. Half saturation constants (Km) and threshold for CH4 oxidation (Th) were lower in NT (Km: 100.5 µL CH4 L-1; Th: 0.5 µL CH4 L-1) than in PT soils (Km: 134 µL CH4 L-1; Th: 2.8 µL CH4 L-1) suggesting a greater affinity of long-term NT soils for CH4, and a possible shift in methanotrophic community composition. CH4 oxidation rates were lower in intact soil cores compared to sieved soils, suggesting that CH4 oxidation was limited by diffusion, a factor that could lead to lower field-measured CH4 uptake than suggested by biological oxidation capacity measured in the laboratory. Regardless of soil drainage characteristic, long-term NT resulted in significantly higher (2-3 times) CH4 diffusivity (mean: 2.5 x 10-3 cm2 s-1) than PT (1.5 x 10-3 cm2 s-1), probably due to improved soil aggregation and greater macro-pores volume in NT soils. Overall, these results confirm the positive impact of NT on the restoration of the biological (Vmax, Km and Th) and physical (diffusivity) soil attributes essential for CH4 uptake in croplands. Long-term implementation of NT farming can therefore contribute to the mitigation of CH4 emission from agriculture.