Trumpet curve

A paper published by Hall and Selinger [3] points out that an empirical formula relating the concentration (c) to the coefficient of variation (CV) is also known as the precision (cr). They derive the origin of the trumpet curve using a binomial distribution explanation. Their final derived relationship becomes equation 72-2 ... 

FIGURE 25.2 Trumpet curve for several representative large-volume infusion pumps operated at 5 mL/h. Note that peristaltic pumps were designed for low-risk patients. 

FIGURE 25.4 Effect of syringe type on trumpet curve of a syringe pump at 1 mL/h. 

Bhatt et al. (1994) describe the results of intercomparison of CaS04 Dy teflon discs as personal monitoring TLDs. The work was conducted independently in Japan and Australia. The irradiations were performed free in the air and on the surface of water and PMMA-equivalent composite phantoms. The performance of the analysis was according to the ANSI-Nl 3-1983 criteria. Results were also analyzed according to the trumpet curve analysis with the requirements of ICRP-35 and ICRP-60. The results showed satisfactory performance of the TLDs which fell within the limits of the requirements. 

Option (Valid) presents a graph of relative standard deviation (c.o.v.) versus concentration, with the relative residuals superimposed. This gives a clear overview of the performance to be expected from a linear calibration Signal = A + B Concentration, both in terms of (relative) precision and of accuracy, because only a well-behaved analytical method will show most of the residuals to be inside a narrow trumpet -like curve this trumpet is wide at low concentrations and should narrow down to c.o.v. = 5% and rel. CL = 10%, or thereabouts, at medium to high concentrations. Residuals that are not randomly distributed about the horizontal axis point either to the presence of outliers, nonlinearity, or errors in the preparation of standards. 

Figure 71-1 Relationship of Laboratory CV (as %) with analyte concentration as powers of 1C)—exp. (For example, 6 on the abscissa represents a concentration of 10-6 or 1 ppm.) Note the shape of the curves has been referred to as Florwitz s trumpet.

Fig. 7. Sketch of a large catalytic disc set in a trumpet-shaped former. The dotted curves indicate the lines of flow below the disc.

Figure 4.32. Graphical summary of validation indicators for file VALIDl.dat. In this depiction, the typical trumpet form (A, E) of the c.o.v./CL curves is seen the fact that there is a spread toward the right-hand edge (C) suggests that the measurement errors grow in a slightly over-proportional fashion with the concentration. The narrowing down of the "trumpet at the lowest concentration (D) is a sign that due to the proximity to the LOD, the measurement distribution is not truly Gaussian but has the low side clipped. The data points for the lowest concentration (10 ng/ml) are off scale (-r31.2 -r65.9), while the fourth-smallest con-...

FIGURE 7.4 Fourier analysis of trumpet playing single note of frequency Vo 523 Hz, one octave above middle C. Upper curve represents the signal in the time domain and lower curve in the.frequency domain. 

This equation leads to the trumpet-shaped curve shown in Figure 4.10, which can be used to derive target values of o for any analysis. Such target values can also be estimated from prior knowledge of the standard deviations usually achieved in the analysis in question. Another approach uses fitness for purpose criteria if the results of the analysis, used routinely, require a certain precision for the data to be interpreted properly and usefully or to fulfil a legislative requirement, that precision provides the... 

The geometric figure known as Gabriel s horn or Toricelli s trumpet is found by revolving the curve y about the x-axis, beginning at x = 1. Calculus shows that this olject, an infinitely long horn shape, has an infinite surface area but only finite volume. 

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