Statistics statistical problem solving

If a process is not operating at permissible control levels or appears unstable, and when we need to improve the process output, then our first step should be to pay closer attention to the process inputs. We should begin by correlating each of the input variables relationship to each of the key output variables through statistical problem-solving techniques to answer the question Is the process predictable, and therefore subject to being modeled satisfactorily, or is it unpredictable ... 

Opportunities to model a process based on defined inputs and then predict an output generally begins with statistical problem solving (SPS) techniques detailed... 

Allwood C, Montgomery H (1982) Detection errors in statistical problem solving. Scand J Psychol 23 131-143... 

Allwood CM (1984) Error detection processes in statistical problem solving. Cognitive Sci 8 413-437... 

Developing design skills (4.4.2), problem solving skills (4.14.1), statistical skills (4.20.2)... 

Statistical techniques can be used for a variety of reasons, from sampling product on receipt to market analysis. Any technique that uses statistical theory to reveal information is a statistical technique, but not all applications of statistics are governed by the requirements of this part of the standard. Techniques such as Pareto Analysis and cause and effect diagrams are regarded as statistical techniques in ISO 9000-2 and although numerical data is used, there is no probability theory involved. These techniques are used for problem solving, not for making product acceptance decisions. 

Statistical Approaches in Machinery Problem Solving Table 62.2 Primary machinery component failure... 

An interesting problem solved by operations research methods is that of the flow of traffic through the New York tunnels. The presence of toll booths causes congestion of traffic at the entrances and exits of tunnels. Economical operation of the toll booths necessitates that not all booths be open at all times. By studying the statistics of the traffic, a schedule was developed indicating the number of booths to be operated at different times of the day. In this manner congestion was alleviated, and the frequency of traffic jams was reduced considerably.8... 

Monomer concentrations Ma a=, ...,m) in a reaction system have no time to alter during the period of formation of every macromolecule so that the propagation of any copolymer chain occurs under fixed external conditions. This permits one to calculate the statistical characteristics of the products of copolymerization under specified values Ma and then to average all these instantaneous characteristics with allowance for the drift of monomer concentrations during the synthesis. Such a two-stage procedure of calculation, where first statistical problems are solved before dealing with dynamic ones, is exclusively predetermined by the very specificity of free-radical copolymerization and does not depend on the kinetic model chosen. The latter gives the explicit dependencies of the instantaneous statistical characteristics on monomers concentrations and the rate constants of the elementary reactions. 

KBSs can be viewed with increasing levels of commitment to problem solving. At the level described in the previous section, a KBS accomplishes symbolic-symbolic mappings between input and output variables analogous to the numeric-symbolic mappings of approaches such as neural networks and multivariate statistical interpreters. For each problem-solving task, the particular numeric-symbolic or symbolic-symbolic approach is based on the task and the knowledge and data available. 

These considerations raise a question how can we determine the optimal value of n and the coefficients i < n in (2.54) and (2.56) Clearly, if the expansion is truncated too early, some terms that contribute importantly to Po(AU) will be lost. On the other hand, terms above some threshold carry no information, and, instead, only add statistical noise to the probability distribution. One solution to this problem is to use physical intuition [40]. Perhaps a better approach is that based on the maximum likelihood (ML) method, in which we determine the maximum number of terms supported by the provided information. For the expansion in (2.54), calculating the number of Gaussian functions, their mean values and variances using ML is a standard problem solved in many textbooks on Bayesian inference [43]. For the expansion in (2.56), the ML solution for n and o, also exists, lust like in the case of the multistate Gaussian model, this equation appears to improve the free energy estimates considerably when P0(AU) is a broad function. 

Hunter, J.S. (1987), Applying Statistics to Solving Chemical Problems , CHEMTECH, 17, 167-169. 

As analysts become more aware of the fact that automation offers a variety of tools, such as robotics, computing, and statistics, to solve analytical problems, then future progress will be far quicker, allowing the installation of more successful and reliable automatic systems. 

Frieden, B. R. (1983). Probability, Statistical Optics, and Data Testing A Problem Solving Approach. Springer-Verlag, New York. 

Belloto, R.J., Jr., Dean, A.M., Moustafa, M.A., Molokhia, A.M., Gouda, M.W, and Sokoloski, T.D. Statistical techniques applied to solubility predictions and pharmaceutical formulations an approach to problem solving using mixture response surface methodology). Pharm., 23, 195, 1985. 

Middlebrooks, E. J. Statistical Calculations How to Solve Statistical Problems. Ann Arbor, MI Ann Arbor Science Publishers, 1977. (No theory but a lot of practical exercises) Snedecor, G. W., and W. G. Cochran. 1996 and Numerous editions. Statistical Methods. Ames Iowa State University Press. (One of the classical textbooks on theory and use of statistics) Steele, R. G. D., and J. H. Torre. 1992 and Numerous editions. Principles and Procedures of Statistics. New York McGraw-Hill. (Another classical textbook)... 

Naive approaches avoid theoretical assumptions and instead focus on statistics about solved RNA structures, using these to probabilistically align new sequences with solved structures. One elegant approach to this problem has used an rRNA database to generate a novel RNA-specific substitution matrix. The advantage of this approach is that it makes the whole spectrum of primary-structure sequence-analysis tools available for secondary-structure prediction (27). 

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