Parameter analysis statistical

Failure analysis statistics have consistently shown that many machinery components failures can be directly attributed the equipment being operated outside of design parameters or unintended conditions. Most failure analysis and trouble-shooting activities are usually post-mortem and commence after installation and start-up of the equipment. The maintenance phase is now in motion, and failure analysis and trouble-shooting is now an integral part of that phase. 

A more detailed analysis using multivariable regression of the ibuprofen data demonstrated that a three-parameter model accurately fit the data (Table 7). The Bonding Index and the Heywood shape factor, a, alone explained 86% of the variation, while the best three-variable model, described in what follows, explained 97% of the variation and included the Bonding Index, the Heywood shape factor, and the powder bed density. All three parameters were statistically significant, as seen in Table 7. Furthermore, the coefficients are qualitatively as... 

For other parameters, though, statistical analysis is just one of several considerations that include historical control data and other relevant information about the test agent and related test agents. For example, statistical analysis of a low incidence of... 

Petrakis, P., Touris, I., Liouni, M., Zervou, M., Kyrikou, I., Kokkinofta, R., Theocharis, C. R., and Mavromoustakos, T. M. (2005). Authenticity of the traditional Cypriot spirit "Ziva-nia" on the basis of 1H NMR spectroscopy diagnostic parameters and statistical analysis.. Agric. Food Chem. 53, 5293-5303. 

In a simple sensitivity analysis, each parameter is varied individually, and the output is a qualitative understanding of which parameters have the most impact on project viability. In a more formal risk analysis, statistical methods are used to examine the effect of variation in all of the parameters simultaneously and hence quantitatively determine the range of variability in the economic criteria. This allows the design engineer to estimate the degree of confidence with which the chosen economic criterion can be said to exceed a given threshold. 

Statistical reliability is related to appropriateness of distributional assumptions, the stability of solutions to resampling, choice of dimensionality and confidence intervals of the model parameters. The statistical reliability is often difficult to quantify in practical data analysis, e.g., because of small sample sets or poor distributional knowledge of the system. 

Twenty-eight papers cover surface and borehole geophysics, direct push technology, well monitoring wall design, water level measurement and sampling, hydraulic parameters. and statistical analysis of data... 

The values in parentheses are the standard errors of the parameters. Since they are much smaller than the estimates of the regression coefficients, we conclude that aU three parameters are statistically significant. If a more rigorous analysis is necessary, we can perform a t test on each one. ... 

The catalyst layers evaluated in this model-based analysis are not intended to represent the best-in-class in terms of performance. Instead, the experimental studies were picked out from the literature because they provided porosimetry as well as performance data. Nevertheless, the low value of the CL effectiveness factor is a striking result of this analysis. The value of Fcl decreases from 4 % at jo < 0.4 A cm to 1 % aty o 1 A cm . This parameter incorporates statistical effects and transport phenomena across all scales in the CCL. The values found are consistent with an experimental evaluation of effectiveness factors by Lee et al. (2010) if the values found in that study are corrected with the atom utilization factor F p, the agreement is very good. The low value of Fcl suggests that tremendous improvements in fuel cell performance and Pt loading reduction could be achievable through advanced structural design of catalyst layers. 

The first subsection presents the electrostatics-based method of building sodium clusters and further the MTA-based method of optimization. Following sections furnishes a geometrical analysis on the best isomer with specific size through deformation parameter and statistical distance analyses. Further, the MESP-guided method is validated by comparing the resulting structures with those reported in the literature. 

Among the approaches proposed so far, we recall here single-parameter models [102-111, 115, 118-120, 122, 123, 125, 126, 129], and multi-parametric correlation equations (either based on the combination of two or more existing scales or on the use of specific parameters to account for distinct types of effects) [112, 113, 116, 117, 121, 124]. Additional popular models are the Abraham s scales of solute hydrogen-bond acidity and solute hydrogen-bond basicity [127, 128], and the Catalan et al. solvatochromic scales [130,132, 133]. Methods based on quantitative stmcture-property relationships (QSPR) with solvent descriptors derived from the molecular structure [131, 134], and on principal component analysis (PCA) [135, 136] have been also proposed. An exhaustive review concerning the quantification of the solvent polarity has been recently published [138-140], including a detailed list of solvent scales, interrelations between parameters and statistical approaches. 

Statistical functions are mathematically described in terms of statistical parameters. The following statistical parameters are the most commonly used parameters in statistical analysis population, sample, variate, variance, standard deviation, mean, median, and skewness. 

The degree of data spread around the mean value may be quantified using the concept of standard deviation. O. If the distribution of data points for a certain parameter has a Gaussian or normal distribution, the probabiUty of normally distributed data that is within Fa of the mean value becomes 0.6826 or 68.26%. There is a 68.26% probabiUty of getting a certain parameter within X F a, where X is the mean value. In other words, the standard deviation, O, represents a distance from the mean value, in both positive and negative directions, so that the number of data points between X — a and X -H <7 is 68.26% of the total data points. Detailed descriptions on the statistical analysis using the Gaussian distribution can be found in standard statistics reference books (11). 

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