Tolerance regions

The ALARP or tolerability region (risk Is undertaken only if a benefit is desired)... 

Figure 6.6. Illustration of the PLS methodology to relate two co-ordinate systems (X and YJ via score vectors (t and u, respectively). The upper left co-ordinate system contains the measurements X and the upper right co-ordinate system contains the external information, Y. The points in the two co-ordinate systems represent the same set of subjects. By fitting a line in each co-ordinate system to the points and then increasing the correlation between the t-scores and the u-score (lower middle plot) by tilting both lines, the PLS solution is obtained. The Y values of a new subject inside the tolerance region in X can be predicted by following the path indicated by the dotted line.

Figure 6.12. Scatter plot of the t-scores of the first two PCs calculated from the BHT920 data. Black circles are controls, black triangles are rats given BHT920 0.05 mg/kg and open circles are rats given BHT 920 0.1 mg/kg. The outlier in the lower right quadrant has largely influenced the second PC. The subject in the lower left quadrant pointed at by an arrow is an outlier in a direction at an angle with PC, and PC2. The tolerance region is roughly bounded in the direction of PC, by 2 sd(tu).

Fig. 4.7 Inverted file for retrieval of infrared spectra generated from pealc tables for fast searching by peak positions (in the tolerance region +10 cm"1).

Methods of Deriving Tolerance Regions from Combined Visual and Instrumental Data... 

The CMC equation has grown to be very complex in its form. As can be seen in the equations below, there are many terms that adjust the size of the tolerance region. Initially, these terms were felt to be due to industrial biases between the just perceptible level of color difference and the just acceptable level of color difference. More recent work has shown this not to be the case. In fact, there now appears to be quite good perceptual and physiological reasons for the inclusion of the various terms. 

Human error is defined as an act outside the tolerance bounds. These are determined by the technical boundary conditions and may therefore be influenced— within limits— by the designer in the sense that the tolerance region becomes large (fault-tolerant design). This reduces the probability of human error. 

Subjects LCSH Chemical reactors-Design and construction. I Statistical tolerance regions. 

Several methods of imcertainty propagation based in the theory of tolerance regions have been proposed in the literature depending on the particular characteristics of the variables in the output and their relations. 

Ensuring the multinormality of the output vector allows us to apply parametric versions of uncertainty propagation. The simplest case, the univariate, is equivalent to the multivariate case when all variables in the output are independent repeating, as pointed out earlier, the same procedure for all variables. When output vector compromises more than one dependent variables obtaining the tolerance region presents more complexity. 

The problem to obtain tolerance regions for random vectors with normal multivariate distributions is easy to establish. Generalizing Eq. (1), it will consists in finding the tolerance region R which verifies the equation... 

Let the random vector y Np (fi, ) and, since /I and are unknown, let M and S their respective estimations from a random sample of size n. Then M Np (/i, /n) independent of S Wp (n — 1, ) and the problem to construct a tolerance region satisfying coverage and confidence levels y and fi, will consist in finding the tolerance factor K which fulfils Eq. (5). Firstly we define the following auxiliary random variables... 

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