Crows

This sum, when divided by the number of data points minus the number of degrees of freedom, approximates the overall variance of errors. It is a measure of the overall fit of the equation to the data. Thus, two different models with the same number of adjustable parameters yield different values for this variance when fit to the same data with the same estimated standard errors in the measured variables. Similarly, the same model, fit to different sets of data, yields different values for the overall variance. The differences in these variances are the basis for many standard statistical tests for model and data comparison. Such statistical tests are discussed in detail by Crow et al. (1960) and Brownlee (1965). 

Sci. 1989, 29(3), 227-228. p5] O. Ivanciuc, Coding the constitution -Graph Theory in chemistry, in Handbook of Chemoinfbrmatics, J. Gasteiger (Ed.), Wiley-VCH, Weinheim, 2003, Chapter II, Section 4. pq L. Euler, Soluho Problematis ad Geo-metriam Situs Pertinentis, Commen-tarii Academiae Sdentiarum Imperia-lis Petropolitanae 8,1736, pp. 128-140. p7] A. Beck, M. Bleicher, D. Crowe, Excursion into Mathematics, Worth, 1969. 

M. Crow and co-workers. Synthetic FuelTechnology Development in the United States—-A. Retrospective Assessment, Praeger Pubhshing, New York, 1988. 

A-1 Refuse Service, Crow and Sons Sanitary Landfill and Pit, Estes Service Co., and West Side Sanitary Landfill, Fort Worth, Tex., personal communications. Sept. 3, 1986. 

Crowe, C.M., Recursive Identification of Gross Errors in Linear Data Reconciliation, AJChE Journal, 34(4), 1988,541-550. (Global chi square test, measurement test)... 

Crowe, C.M., Reconciliation of Process Flow Rates by Matrix Projection, part 2, The Nonlinear Case," AlChE Journal, 32(4), 1986, 616-62.3. 

References A variety of mathematical methods are proposed to cope with hnear (e.g., material balances based on flows) and nonhnear (e.g., energy balances and equilibrium relations) constraints. Methods have been developed to cope with unknown measurement uncertainties and missing measurements. The reference list provides ample insight into these methods. See, in particular, the works by Mah, Crowe, and Madron. However, the methods all require more information than is tvpicaUy known in a plant setting. Therefore, even when automated methods are available, plant-performance analysts are well advised to perform initial adjustments by hand. 

Glasser, D., Hildebrandt, D., and Crowe, C. (1987). A geometric approach to steady flow reactors The attainable region and optimization in concentration space. Ind. Eng. Chem. Res., 26, 1803-1810. 

Roberson, j. A., and C. T. Crow. E.ngineering Fluid Mechanics. Boston Houghton Mifflin (1980). 

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