Engineering statistics characteristic parameters

The characteristic bell shape of many RTDs can be fit to well-known statistical distributions. Hahn and Shapiro (Statistical Models in Engineering, Wiley, 1967) discuss many of the standard distributions and conditions for their use. The most useful distributions are the gamma (or Erlang) and the gaussian together with its Gram-Charlier extension. These distributions are represented by only a few parameters that can be used to determine, for instance, the mean and the variance. 

Several related problems have been previously considered in the literature. In addition to the afore mentioned statistical approaches for structural change detection in data sets and their application for linear system identification [7], the joint problem of model structure determination and parameter estimation was addressed by [8-10]. A related approach was used by [11-13] in the context of data reconciliation. Additional aspects of model selection in chemical engineering are covered in [14]. Although the present problem shares common features with the all of the previous applications, it also presents unique characteristics that require a specific formulation. 

Engineering Tolerance" limits were chosen to apply the statistical techniques and begin control charts on these parameters, which had reasonable characteristics of a production process. 

During verification of adequacy of the mathematical models and the real gas sensors, statistical approaches have usually been employed, since both input and output parameters of the sensors in some respect are incidental quantities. Sometimes in practical engineering tasks, the average or maximum deviation of some characteristics, calculated by the model from the corresponding experimental values, can be used as an adequacy criterion. However, such a criterion is implemented at the practical measurement of partial gas pressures in different environments, assuming that both informative and noninformative parameters of the sensor are constant and strictly follow the scope and conditions of the laboratory experiments. This is not always the case. Furthermore, the allowed deviation between calculated and measured characteristics (10-15%) is subjective estimation. 

For dredging and reclamation projects, characteristic soil parameters can often not be defined based on a statistical analysis. A sufficient number of laboratory tests on samples from individual soil layers encountered at the project site is rarely available for such an analysis. Frequently, soil parameters have to be selected based on Engineering judgement . This is difficult to justify in view of the Eurocode design principle for important structures, which promotes very strongly the execution of an extensive soil investigation in order to arrive at a well-founded selection of parameters. 

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