Product histogram

It should be noted that the ACT sequence and the standard telomer assay were employed to study oligoselectivity with this template and thus the products analyzed are the same methyl acrylate telomers identified in the previous studies. The ACT reaction of 40 under standard conditions with cyclohexyl iodide and allyltributyltin (2.5 /80V200 "), without the aid of a counter-ion, showed interesting results. The product histogram obtained with 40 after telomer assay is presented in Scheme 8-15. 

The check sheet shown below, which is tool number five, is a simple technique for recording data (47). A check sheet can present the data as a histogram when results are tabulated as a frequency distribution, or a mn chart when the data are plotted vs time. The advantage of this approach to data collection is the abiUty to rapidly accumulate and analy2e data for trends. A check sheet for causes of off-standard polymer production might be as follows ... 

While the F-N curve is a cumulative illustration, the risk profile shows the expected frequency of accidents of a particular category or level of consequence. The diagonal line is a line of constant risk defined such that the product of expected frequency and consequence is a constant at each point along the line. " As the consequences of accidents go up, the expected frequency should go down in order for the risk to remain constant. As the example illustrates, if a portion of the histogram sticks its head up above the line (i.e., a particular type of accident contributes more than its fair share of the risk), then that risk is inconsistent with the risk presented by other accident types. (Note There is no requirement that you use a line of constant risk other more appropriate risk criteria for your application can be easily defined and displayed on the graph.)... 

Fig. 9-8 Histogram of dissolved solids of samples from the Orinoco and Amazon River basins and corresponding denudation rates for morpho-tectonic regions in the humid tropics of South America (Stal-lard, 1985). The approximate denudation scale is calculated as the product of dissolved solids concentrations, mean armual runoff (1 m/yr), and a correction factor to account for large ratios of suspended load in rivers that drain mountain belts and for the greater than average annual precipitation in the lowlands close to the equator. The correction factor was treated as a linear function of dissolved solids and ranged from 2 for the most dilute rivers (dissolved solids less than lOmg/L) to 4 for the most concentrated rivers (dissolved solids more than 1000 mg/L). Bedrock density is assumed to be 2.65 g/cm. (Reproduced with permission from R. F. Stallard (1988). Weathering and erosion in the humid tropics. In A. Lerman and M. Meybeck, Physical and Chemical Weathering in Geochemical Cycles," pp. 225-246, Kluwer Academic Publishers, Dordrecht, The Netherlands.)...

Figure 1.8. Schematic frequency distributions for some independent (reaction input or control) resp. dependent (reaction output) variables to show how non-Gaussian distributions can obtain for a large population of reactions (i.e., all batches of one product in 5 years), while approximate normal distributions are found for repeat measurements on one single batch. For example, the gray areas correspond to the process parameters for a given run, while the histograms give the distribution of repeat determinations on one (several) sample(s) from this run. Because of the huge costs associated with individual production batches, the number of data points measured under closely controlled conditions, i.e., validation runs, is miniscule. Distributions must be estimated from historical data, which typically suffers from ever-changing parameter combinations, such as reagent batches, operators, impurity profiles, etc.

Figure 1.30. A histogram of raw weights from Figure 1.29 and the distribution of residuals that resulted after subtraction of a shifted box-car average are superimposed. The CP-curve, plotted with the (NPS) option in HISTO, is for the raw weights the corresponding curve for the residuals would be about twice as steep. The asymmetry of the raw-weight distribution is evident both in the histogram and the lack of linearity of the CP-curve it is due to many subpopulations of product being lumped into one batch. Every time a mechanic makes an adjustment on a knife, a new subpopulation is created. The residuals appear to be normally distributed, however.

The activity of all catalysts were evaluated for the CO hydrogenation reaction. The histogram shown in Fig. 8 reveals that the bimetallic Co-Mo nitride system has appreciable hydrogenation activity with exception of samples 2 and 4. This apparent anomaly was probably due to the relatively high heat of adsorption for these two catalysts, which offered strong CO chemisorption but with imfavourable product release. 

Fig. 3.1. Histogram showing the change in volume of volcanic products during the Neogene and Quaternary periods. The far-right part shows a very small amount for the Paleogene Period (Sugimura et al., 1963).

Fig. 7 Histogram showing the products PG and PGgg> formed after charge injection into G, water trapping of the guanine radical cations and subsequent strand cleavage...

Figure 3. Product energy distributions for the Cl" CHaBr - CICH3 + Br reaction histogram, trajectory result 6 dashed line, experiment 29 and solid line, prediction of OTS/PST. The trajectory results are scaled to match the experimental exothermicity.

For each wind speed value (v) from the cut-in (ci) to the cut-out (co) phase of the WTG, the product of its corresponding power output (Pv) multiplied by the time Hv (in hours) during which value v appears in a year is calculated. The sum of these products gives the annual energy production (WEY). Wind speed values are referred to the hub height of the turbine. The power output values, which compose the power curve of a WTG, are provided by the turbine manufacturer. Hv values are calculated from the annual distribution (or the histogram) of the wind speed values. 

The shade of a product is another parameter which is influenced by the particle size (Sec. 1.6.1.2). This is easy to see by comparing the reflection curves of two Pigment Yellow 83 white reductions in an alkyd-melamine resin system. The electron photomicrographs in Fig. 65 and the particle size distribution histograms in Fig. 66 represent these samples. At equal pigment concentration, curve 1 of the two remission curves in Fig. 67 reflects the behavior of the pigment with the smaller... 

Carlos and Latif both fluidised glass particles in dimethyl phthalate. Data on the movement of the tracer particle, in the form of spatial co-ordinates as a function of time, were used as direct input to a computer programmed to calculate vertical, radial, tangential and radial velocities of the particle as a function of location. When plotted as a histogram, the total velocity distribution was found to be of the same form as that predicted by the kinetic theory for the molecules in a gas. A typical result is shown in Figure 6.11(41 Effective diffusion or mixing coefficients for the particles were then calculated from the product of the mean velocity and mean free path of the particles, using the simple kinetic theory. 

The Bayesian analysis of BACLASS (a program of ARTHUR), where the decision function is obtained from the product of the marginal PDs computed by the smootted (symmetrical or skewed) histograms, may apparently be used with skewed distributions, without preliminary transformations of the original variables. 

Figure 16 shows the histogram of the data in relation to the specifications. The x and s charts in Figure 11 show that the process is in statistical control. However, since Cp < Cpk, the process is not centered. With a Cpk value of 0.579, it is expected to have 53,711 nonconforming Pet Tabs manufactured out of one million parts in this production line. 

Power generation—phasing. A histogram of power-consumption requirements includes drilling, personuel support, reservoir support, and production (Fig. 3). It should be constructed early because it is a key documeet used to determine the total platters power configuration and type of drivers. 

After a careful look at the power consumption histogram and discussion with both the production facilities and drilling personnel of the operating company, a new configuration was designed (Table 3—Optimization). 

Statistical process control (SPC), also called statistical quality control and process validation (PV), represents two sides of the same coin. SPC comprises the various mathematical tools (histogram, scatter diagram run chart, and control chart) used to monitor a manufacturing process and to keep it within in-process and final product specification limits. Lord Kelvin once said, When you can measure what you are speaking about and express it in numbers, then you know something about it. Such a thought provides the necessary link between the two concepts. Thus, SPC represents the tools to be used, while PV represents the procedural environment in which those tools are used. 

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