Variation statistics

End-of-pipe measures continue to be vitally important. The largest PSM and ESH management costs are accident and incident related. If you reduce the costs of managing PSM and ESH, yet accident and incident rates rise beyond any normal statistical variation, the new system is costing the company more. Near misses are a leading indicator for accidents and incidents and should not be neglected. 

One major oil and chemical company has collected data on the cost of accidents, the equipment involved and the cause of the failure for more than 50 years. These data are analyzed annually to help decide where to focus efforts to reduce losses and/or to modify design standards to prevent recurrence. This analysis also identifies failures of the PSM and ESH management system. These can be compared with the cost of delivering the systems and adjustments made to expenditures to improve the cost/benefit balance. Any such changes must be carefully considered as normal statistical variation may cause you to take unjustified action. 

Another difference between the wireline logs and the MWD logs is the logging speed. With a wireline, the sonde is pulled out at a speed of 500 to 2,000 ft/min (150 to 600 m/min). The time constant used to optimize the effect of the statistical variations of the radioactivity emission, varied from 2 to 6 s. Consequently, the log values are somewhat distorted and inaccurate. 

Individual ability to tolerate radiation damage varies, so a statistical variation exists in the relationship between dose level and health effects. Also, there are effective treatments, such as blood transfusions, for some radiation effects. The statistical patterns of human response to radiation are summarized in Table 22-5. Doses of over 600 rem are almost always fatal. 

In Nature, however, we always have a contiiinous distribution of particles. This means that we have all sizes, even those of fractional parentage, i.e.-18.56n, 18.57p, 18.58 p, etc. (supposing that we can measure 0.01 p differences). The reason for this is that the mecheuiisms for particle formation, i.e.- precipitation, embryo and nucleation growth, Ostwald ripening, and sintering, are random processes. Thus, while we may speak of the "statistical variation of diameters", and while we use whole numbers for the particle diameters, the actuality is that the diameters are fractional in nature. Very few particle-size" specialists seem to recognize this fact. Since the processes are random in nature, we can use statistics to describe the... 

Historical data on the indicator. Existing information on the statistical variation, bias, and other interpretational attributes of potential biological indicators should be examined and considered in the design of a sampling program for assessing trends in mercury bioaccumulation. 

The advantage of the PSD calculation method outlined in this subsection is that only one additional differential equation need be integrated, a fact which considerably simplifies matters and saves in computation time. A drawback of the present approach (and also of the other approaches of Table II) is that the statistical variation of the distribution arising from the variation of the number of radicals per particle in a class of a certain size is missing. The PSD s thus calculated indicate the average particle diameter growth of each particle. 

Collapse when statistical variations cause one of the important components of the cycle to die off, the complete cycle collapses. 

A closer look at the data shows the lifetime distributions are comparatively broad, about 0.25 ns for both distributions. This is in fact much broader than what one would expect from photon statistics alone. Based on realistic / -values (1.2-1.5) lifetime images recorded with this many counts are expected to yield distributions with widths on the order of 0.1 ns. The broadening is therefore not because of photon statistics. Variations in the microenvironment of the GFP are the most likely source of the lifetime heterogeneities. Importantly, such sensitivity for local microenvironment may be the source of apparent FRET signals. In this particular FRET-FLIM experiment, we found that the presence of CTB itself without the acceptor dye already introduced a noticeable shift of the donor lifetime. Therefore, in this experiment the donor-only lifetime image was recorded after unlabeled CTB was added to the cells. The low FRET efficiency and broadened lifetime distribution call for careful control experiments and repeatability checks. 

This is where we see the convergence of Statistics and Chemometrics. The cross-product matrix, which appears so often in Chemometric calculations and is so casually used in Chemometrics, thus has a very close and fundamental connection to what is one of the most basic operations of Statistics, much though some Chemometricians try to deny any connection. That relationship is that the sums of squares and cross-products in the (as per the Chemometric development of equation 70-10) cross-product matrix equals the sum of squares of the original data (as per the Statistics of equation 70-20). These relationships are not approximations, and not within statistical variation , but, as we have shown, are mathematically (algebraically) exact quantities. 

The procedures discussed so far take as fundamental variables the species concentration and specific rates, the latter obtained from homogeneous experiments. Such procedures are called deterministic—that is, admitting no fluctuation in the number of reactant species—as opposed to stochastic methods where statistical variation is built in. 

Ks Factor for statistical variation in test results (see para. IP-3.8.4) ... 

Statistical variation - mercury inventories in cells are so large, and emissions so small, that the calculations involving very small differences between very large numbers are inevitably subject to statistical error. 

The homologues of the methylated non-ionic EO/PO surfactant blend were ionised as [M + NH4]+ ions. A mixture of these isomeric compounds, which could not be defined by their structure because separation was impossible, was ionised with its [M + NH4]+ ion at m/z 568. The mixture of different ions hidden behind this defined m/z ratio was submitted to fragmentation by the application of APCI—FIA—MS— MS(+). The product ion spectrum of the selected isomer as shown with its structure in Fig. 2.9.23 is presented together with the interpretation of the fragmentation behaviour of the isomer. One of the main difficulties that complicated the determination of the structure was that one EO unit in the ethoxylate chain in combination with an additional methylene group in the alkyl chain is equivalent to one PO unit in the ethoxylate chain (cf. table of structural combinations). The overview spectrum of the blend was complex because of this variation in homologues and isomers. The product ion spectrum was also complex, because product ions obtained by FIA from isomers with different EO/PO sequences could be observed complicating the spectrum. The statistical variations of the EO and PO units in the ethoxylate chain of the parent ions of isomers with m/z 568 under CID... 

On development, the grains of the L4 emulsion swell to about 0.25 /un. However, the granularity observed on the topograph when viewed under the microscope is not a result of the grain of the film but is statistical shot noise , arising from the statistical variation in the number of developed grains per unit area. This... 

Thus, accurate determination of the specific activities SAa and SAa immediately provides the value of the unknown Ax. Note Whenever Axisotope dilution method suffers from any statistical variation in the measurements of quantities that are nearly identical. Should this prove to be true for your measurements, use a lesser amount of isotopic probe, so that Ax A. 

As a consequence of random variations in the propagation characteristics of individual charge carriers, an initially discrete packet of carriers will necessary broaden out in profile as it drifts across a specimen. For the carriers that move exclusively in extended states, this dispersion results from statistical variations in scattering processes and may be described in terms of a diffusion coefficient D, which is related to the carrier mobility via Einstein relation... 

The composition of the copolymer was determined by either NMR analysis at 90 MHz according to the equations derived by Mochel (21) or by infrared. (22) The agreement of these methods was 2% when applied to copolymer taken to 100% conversion. The reactivity ratios were calculated according to the Mayo-Lewis Plot (13,15), the Fineman-Ross Method (14), or by the Kelen-Tudos equation.(16,17,18) The statistical variations recently noted by 0 Driscoll (23), were also considered. 

The accuracy index, the untransformed average bias and the statistical variation in... 

This expression will predict the movement of a solute whose adsorption is in equilibrium with the surrounding strata. This equilibrium chromatographic motion will result in the migration of a band of activity whose concentration profile is gaussian and whose deviation will be a function of the hydrodynamic dispersion, T (due to statistical variations in path length) and absorptive dispersion T (due to statistical variations in the absorption and desorption process). While these dispersions are interactive and do not sum in a simple fashion they both depend on path length. 

Pretending each paper clip is a legonium atom, toss all of them onto aflat surface. Remove all the atoms in the leg-up orientation and write down the number remaining in the row numbered 1 of the data table, for trial 1. Continue until all the legonium atoms have been removed.This completes one trial, and so you need to run four more because there will be a lot of statistical variation. Count the number of throws required to remove all atoms in each trial and calculate an average. 

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