Deviations measurement

In connection with Eq. (1.4), we noted that the standard deviation measures the spread of a distribution now we see that the ratio M /M also measures this polydispersity. The relationship between these two different measures of polydispersity is easily shown. Equation (1.14) may be written as... 

Tab. 4.2 Relative standard deviations measured in homogeneity tests of a candidate CRM PCBs in mussels (BCR 682) (de Boer et al. 2000)...

Both qualitative observations and quantitative measurements cannot be reproduced with absolute reliability. By reason of inevitable deviations, measured results vary within certain intervals and observations, mostly in form of decision tests, may fail. The reliability of analytical tests depends on the sample or the process to be controlled and the amount of the analyte, as well as on the analytical method applied and on the economical expenditure available. 

Kristoffersen, T.K. (2005) Deviation measures in linear two-stage stochastic programming. Mathematical Methods of Operations Research, 62, 255. 

In the response surface strategy that was discussed in Section 2.3 standard response surface techniques are used to generate two response surface models, one for the mean response and one for the standard deviation of the response (or some function of the standard deviation). The standard deviation measures the stability of the response to the environmental variation. Standard analysis can reveal which factors affect the mean only, which only affect the variability, and which affect both the mean and the variability. The researcher can then apply optimization methods or construct contour plots of the mean and standard deviation response surfaces to determine settings of the design variables that will give a mean response that is close to the target with minimum variation. 

Figure 9 (A) Relative standard deviation measured for axially segregated blends of different cohesion in a 1-quart V-blender. As cohesion increases, blending becomes slower. (B) Relative standard deviation measured for axially segregated blends of different cohesion in a 28-quart V-blender. In a large vessel, the effects of cohesion become unimportant.

Calculate the angle of deviation measured with respect to the direction of the incident radiation which collects the emission line LJ of bromine (A = 8.126 A) of a sample of sodium bromide (it may be considered that the observations recorded are of first order reflection). 

The mean gives the center of the distribution. The standard deviation measures the width of the distribution. 

The standard deviation measures the width of the Gaussian curve. The larger the value of cr, the broader the curve. In any Gaussian curve, 68.3% of the area is in the range from p — la to p + la. That is, more than two-thirds of the measurements are expected to lie within one standard deviation of the mean. Also, 95.5% of the area lies within p 2a. and 99.7% of the area lies within p 3a. Suppose that you use two different techniques to measure sulfur in coal Method A has a standard deviation of 0.4%, and method B has a standard deviation of 1.1%. You can expect that approximately two-thirds of measurements from method A will lie within 0.4% of the mean. For method B, two-thirds will lie within 1.1% of the mean. 

The deviation of the correction factor from unity measured with spectrometers with PGT 386 amplifiers is comparable with the deviations measured in [5], There the authors reported a deviation of the peak count rate of approximately 2% at 1400 keV and 0.5% at 122 keV at a total count rate of 9000 s1. The measurement with the Ortec 573 amplifier yielded superior results. At the accuracy achieved, the deviation was not measurable up to 10000 s1 with this amplifier. The difference in the performance of the measurements with different amplifiers originates, most probably, in the fact that the Ortec amplifier is of newer design. 

The data in this example represent an investigation of ammonia production in the presence of a particular catalyst. The measured yield in percent is shown in the far right column of Table 8.10. Suppose we wish to achieve a prediction error less than fi = 1.5% in an example, where the standard deviation (measurement error) is y.2 = 1.05 estimated with 11 measurements, i.e., with degrees of freedom v= 10. The critical value of Student s /-statistic is found to be t10A95 = 2.228. At IV = 16 experiments, we check to see if the desired level of accuracy is achieved and obtain Kj-a Jd = 2.228 0.438 x 1.05 =1.51 > 1.5. At N= 16 experiments, weobtain tvl aJd =1.48 < 1.5 therefore, we can stop at N = 17 and be assured that, 95% of the time, we will achieve a prediction error not worse than +1.5%, which is considerably smaller than the range of the variation in the response value. 

For smaller hydro power systems, such a solution is considered to be complex and additionally a danger exists of rapid control valve movement introducing damaging surge pressure waves in the pipelines or instability in the overall control system (Roberts, 2002). A preferable solution to maintain frequency close to its nominal value is the utilisation of load control. For the implementation of this scheme, secondary or even dump controllable loads are switched on and off, according to frequency-deviation measurements. 

An isotopically unmodified compound is one whose isotopic nuclides are present in the proportions that occur in nature. An isotopically modified compound has a nuclide composition that deviates measurably from that occurring in nature. 

Ficken and Kendall " discuss the relative basicities of the pyridine and pyrrolenine nitrogen atoms in the azaindolenines (Scheme 7) based on Brooker deviation measurements from light-absorption data of their cyanine dyes. These indicate that N(7 in the 7-azaindolenine (31) is considerably more basic than N(d in the sense that the 7-quaternary salt (117) displays less tendency to be stabilized by a isomerization than does the 1-quaternary salt (120). They relate this to the formation of an unstable o-quinonoid resonance form. In the case of the 4-azaindolenine (32), it was suggested that the pyridine N(4) is expected to be more basic than N(X), although reaction 12 J. Clark and D. D. Perrin, Quart. Rev. London) 18, 295 (1964). 

The detection limit is the lowest concentration level for which it is possible to say that the concentration differs significantly from the blank. It is generally defined, for each element, as the concentration level corresponding to six times the standard deviation measured in the case of the blank test. 

Limit of Detection. Make seven blank readings. Calculate the (absolute) standard deviation. Measure a standard seven times that should give a response 5 to 10 times the standard deviation above the blank signal. Calculate the detection Unfit as the concentration that gives a net response of 3 standard deviations above the blank. 

In Hz estimated precision of three experiments mean deviation) Measured at 32°C... 

The standard deviation measures the variability of concrete strength and thus defines its quality in fact, the variability increases if poor quaHty control is carried out on raw materials, moisture content of aggregates, mixing, and transport... 

---