Decision contour

The Unbiased Decision Contour. A workplace which produces an unbiased decision is defined for purposes of this paper as one for which P(0K) = P(N0T OK). From Equation 4, (0 ) is represented by the area in the tail of pdjj(X) below the AL. From Equation 5, P(N0T OK) is represented by the area in the tail of... 

There are two important observations to be made concerning the contour of unbiased decisions. The first is that for workplaces lying to the left of the unbiased decision contour, P(0K)... 

P(N0T OK) while for workplaces lying to the right of the unbiased decision contour, P(N0T OK) > P(0K). The second is that since our decision criteria have been derived to provide high confidence in the decisions which are made, it frequently happens that the most likely outcome from a trial involving one sample taken from a workplace lying close to the unbiased decision contour is that a decision cannot be made with sufficient confidence. Because of this, it is important to define additional decision boundaries. 

The Single Decision Contours. A workplace which is more likely to produce a decision than to produce no decision and for which one decision is clearly predominant is defined for purposes of this paper as lying in a single decision region. There are two such regions ... 

Decisions Made by the NIOSH Action Level Criteria. Figure 3 shows the decision contours for the NIOSH Action Level Decision Criteria, and Table I summarizes the decision probabilities for each of the nine sample workplaces. Recall from Equation A-19 that the AL is computed from GSD to provide 95% confidence that no more than 5% of the daily exposures exceed the standard if one randomly collected sample is less than the AL. In terms of the variables used in this paper, (e > 0.05 with p > 0.05 if X > AL). 

Figure 3. Decision contours resulting from the NIOSH Action Level Criteria AL = f(GSD), and UAL = 1. Each marks the location of one of the charts from Figure 1. Note that the NO DECISION region includes nearly the whole area between the GSD axis and the NOT OK region.

Figure 6. Decision contours resulting from OSHA Compliance Criteria AL = 0.835, and UAL = 1.165, and assuming that the decision is based on six statistically independent samples. In comparison with Figure 5, many more environments are subject to a citation. This even includes some environments within the acceptable region bounded by the A EL contour in Figure 2.

Figure 6 shows the decision contours for a compliance officer who takes six statistically independent samples during an inspection. Table IV lists the decision probabilities for each of our nine sample workplaces. Clearly, collecting more samples increases the probability of demonstrating noncompliance and decreases the probability of demonstrating compliance. 

The principle is very easily generalized. By collecting enough samples, a compliance officer can move the single decision contour for a citation as far to the left as he chooses. Given enough samples, every workplace could be subjected to a citation For example, by collecting 14 samples, a compliance officer moves... 

Finally, any decision strategy can be compared to any other on the basis of the decision contours defined in this paper. It is recommended that every candidate decision criteria, whether it is based upon one or several samples, be evaluated to determine which workplaces are accepted and which are rejected before it is adopted. None of the decision criteria examined in this paper are able to fairly determine the quality of all workplaces. 

Decision Contours. Let AL = Xq in Equation A-11 and UAL = Xg in Equation A-12. Rearranging these equations ... 

To derive the unbiased decision contour, note that P( < AL)... 

The aim of this work which enter in a research project on NDT, is to conceive a system of aid for interpretation and taking decisions, on imperfections in metallic fusion welds, we have studied and tested several segmentation techniques based on the two approaches ( contour and regions ). A quantitative analysis will be applied to extract some relatives geometricals parameters. To the sight of these characteristics, a first classification will be possible. 

The F-N curve, the risk profile, and the risk contour are the three most commonly used methods of graphically presenting risk results. Normally, you will elect to use more than one of these methods when evaluating risk estimates for decision making. 

The availablility of an estimate of the conditional cdf F CzjCN)) at each nodal joint x allows an assessment of the risks a(x) or p(x) of making wrong decisions. Consider the contour map of a particular estimate p (x), x (see Figure 3a). Suppose that the threshold value 500 has been selected to declare any sub-area of A hazardous. The contour line 500 on Figure 3 delineates the zones which are candidates for cleaning. Within these zones, the probability that the concentration is actually under 500, i.e. the risk a(x) of cleaning unduly, can also be mapped ... 

Once the data are computed in this fashion, there are three numbers to associate with each point on the surface of Figure 2 the probability that the environment is OK the probability that it is NOT OK and the probability that no decision can be made on the basis of one exposure estimate. Therefore, a complete comparison between Figure 2 and the three decision criteria in this report requires careful consideration of ten 3-dimensional surfaces. This is not practical, so it is necessary to define contours of significance which can be used to provide a rapid, easily understood comparison of the different behavior of the three decision criteria. The first is the contour of unbiased decisions, and the other three are the contours marking the boundaries of the regions where one decision is the most likely outcome of evaluating the meaning of one representative exposure estimate. 

The boundaries of these regions may be computed from Equations A-23 and A-24. The region where the predominant decision is OK lies to the left of the contour defined by Equation A-23. The region where the predominant decision is NOT OK lies to the right of the contour defined by Equation A-24. The region between these two contours is the region where the decision rule makes most of its errors. Note that there are three types of error no decision when one should be made NOT OK when the decision should be OK and OK when the decision should be NOT OK. 

Ion radicals of conjugated acyclic or aromatic hydrocarbons (butadiene or naphthalene) are typical examples of the species with a released unpaired electron. They are named ir-elec-tron ion radicals and have a spin distribution along the whole molecular contour. An important feature of such species is that all the structural components are coplanar or almost coplanar. In this case, spin density appears to be uniformly or symmetrically distributed over the molecular framework. Spin-density distribution has a decisive effect on the thermodynamic stability of ion radicals. In general, the stability of ion radicals increases with an enhancement in delocalization and steric shielding of the reaction centers bearing the maximal spin density. 

It is also quite difficult to discern if a damage in a thermoplastic is a craze or already a crack. The interferometrical measurement of the contour of a particular structure may facilitate such a decision. Figure 3,3 shows interference fringe patterns in a specimen of PC broken in a tensile test at 77 K These optical interferences originating from crack-like structures below the fracture surface have been evaluated and the square of the local displacements were plotted as a function of the distance from the surface in Fig. 3.4. According to Eq. (4) this should be a linear function in the case of a crack in contrast to a curved one for a craze (Eq. (8 b)). Thus,... 

Data from the various parameters were contoured, and a final contour pattern was adopted after differences were resolved. The first parameter to be contoured was temperature, by taking XBTs into account. Subsequent contours were biased because the structure of the temperature field was known wherever subjective decisions on contouring were required, the patterns were biased toward similarity of features from one parameter to the next. The resulting contours for temperature, nitrate, and in vivo fluorescence are shown in Figure 5 electronic problems rendered salinity data invalid over this portion of the cruise. The control data fall along the dotted line in each figure. 

Indirect methods can also be applied to problems with two or more decision variables. In the steepest descent method (also known as the gradient method), the search direction is along the gradient at point (xi, xi), i.e., orthogonal to the contours of f xi, xi). A line search is then carried out to establish a new minimum point where the gradient is re-evaluated. This procedure is repeated until the convergence criterion is met, as shown in Figure 1.15b. 

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