Design model adequacy, test

With this book the reader can expect to learn how to formulate and solve parameter estimation problems, compute the statistical properties of the parameters, perform model adequacy tests, and design experiments for parameter estimation or model discrimination. 

Figure 30 portrays the grid of values of the independent variables over which values of D were calculated to choose experimental points after the initial nine. The additional five points chosen are also shown in Fig. 30. Note that points at high hydrogen and low propylene partial pressures are required. Figure 31 shows the posterior probabilities associated with each model. The acceptability of model 2 declines rapidly as data are taken according to the model-discrimination design. If, in addition, model 2 cannot pass standard lack-of-fit tests, residual plots, and other tests of model adequacy, then it should be rejected. Similarly, model 1 should be shown to remain adequate after these tests. Many more data points than these 14 have shown less conclusive results, when this procedure is not used for this experimental system.

Here, we want to emphasize that one is able to calculate the fraction of the experimental error only if replicate measurements (at least at one point x ) have been taken. It is then possible to compare model and experimental errors and to test the sources of residual errors. Then, in addition to the GOF test one can perform the test of lack of fit, LOF, and the test of adequacy, ADE, (commonly used in experimental design). In the lack of fit test the model error is tested against the experimental error and in the adequacy test the residual error is compared with the experimental error. 

The design allows checking the reliabihty of the model fitted to the data, typically by statistical tests about the model parameters and the model adequacy (lack-of-fit), and by cross validation. 

After the /zth experiment has been designed, the models are tested for their adequacy. In other words did the experiment provide sufficient information for discrimination between the rival models ... 

The estimation of purely experimental uncertainty is essential for testing the adequacy of a model. The material in Chapter 3 and especially in Figure 3.1 suggests one of the important principles of experimental design the purely experimental uncertainty can be obtained only by setting all of the controlled factors at fixed levels and replicating the experiment. 

If one wants to test the adequacy of the model and the effects or coefficients, replicates of the entire design or measurements at a central point of the design are necessary. The real position of the central point is easily obtained by the use of Eq. 3-8 which in our simple case immediately leads to x, = central value. 

In simple linear models (first order polynomials) the adequacy can be tested by another simple procedure. A /-test is performed between the mean result, y0, from the experiments on the central point and the mean, y, of response values from factorial design ... 

The various approaches to discriminate between models and to test a given model s adequacies have been treated above, and focus is given here on the design criterion A simple approach can be followed to determine the maximum divergence between model predictions Based on statistical considerations for two models, a simple expression was derived to measure the divergence D(x ) at the experimental settings x of the experimental grid... 

SRC compiled data from the literature as well as industry test data. Data were judged for adequacy and excluded if considered inadequate. Inadequate data could result from conflicting studies, poorly designed studies, or studies performed with poor laboratory practices. SRC supplemented test data with estimated results based on QSAR models for aquatic toxicity and certain physical properties. In addition, endpoints for the chemical products with little or no... 

The program ANSYS-14/CFX mathematical model of motion of polydispersed gas system. The character of the movement of dust particles under the influence of centrifugal force. This allowed choosing the desired hydrodynamic conditions and taking into account of the design under various conditions of scrubber. Experimental study of the hydrodynamic characteristics of the device to determine the empirical constants and test the adequacy of the hydrodynamic model. 

The adequacy of the design parameters of repositories cannot be tested in real operational conditions and as far as tests are carried out close to operational conditions they are timely limited. The verification analyses for checking the compliance are based on limited confirmation of the validity of calculation models as well as physical, chemical, geological, and other parameters. 

The predictability of a computer code and the adequacy of modeling of a plant used in the assessment of the anticipated transients and the accidents to assess the adequacy of the safety systems design must be validated through comparisons between predictions and the startup test data or system effect experiments. The adequacy of each model incorporated in a code to describe each of events included in the transients and the accidents must be validated based on information provided by separate effect experiments. Conservative assumptions may be made whenever those information to validate a code and modeling of a plant are not available. 

The purpose of a model test is to verify the methods of analysis and to provide a visible physical demonstration of the adequacy of the design requirements. As described earlier, model tests have been carried out to verify the service and ultimate state behaviour of vessels and to assess prestressing, reinforcement and liner requirements. The scale chosen for a specific model depends on the objective of the test and on the reduction in size of important vessel components. For a complete vessel a suitable scale varies from 1 25 to 1 10, and scales of 1 25 and 1 50 have been used for the investigation of the top slab behaviour. A large number of models for shear modes of failure have been tested with... 

A test conducted to verify the adequacy of the thermal model, the adequacy of the thermal design, and the capability of the thermal control system to maintain thermal conditions within established mission limits. 

The accumulation of some 200,000 hr of relatively trouble-free test operation in the temperature range of 1200 to 1500°E wdth molten salts and liquid metals as the ( irculated fluids has proved the adequacy of this basic-pump design with regard to the major problem of thermally induced dis-tortion.s. Four different sizes and eight models of pumps have been used to provide flows in the range of o to loOO gpm. Several individual pumps have operated for periods of GOOO to 8000 hr, consecutively, without maintenance. 

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