Statistical technique

The statistical approach has been something of a latecomer to G2P conversion, perhaps because of the success of other data-driven techniques such as pronunciation by analogy or owing to the impression that context-sensitive rewrite rules are adequate so long as they can be automatically trained, e.g. by a decision tree. In recent years, however, various approaches that give a properly statistical approach have been developed. 

Fragrance profiles are often presented as a series of complex tables or graphs from which patterns, order or exceptions need to be found. Looking at individual profiles it is possible to determine the main odour 

However, this sort of comparison becomes extremely complex when large numbers of perfumes are involved. Multivariate Analysis methods are descriptive procedures that help in this process. These methods are used to model or describe data, such that they can be more easily understood by the researcher and thus simplify data comparison. Sophisticated software now exists that makes this kind of analysis possible without it being necessary to understand fully the mathematical modelling involved in the analysis. However, to interpret and understand the results a basic understanding of the technique is necessary. 

Multidimensional scaling is just one of the multivariate techniques available. To be asked to take a map of England and measure with a ruler the distance between 20 towns is a fairly straightforward project. Multidimensional scaling does the opposite to this it takes a set of distances and recreates the map. The distances in this case are derived 

In addition to depicting the associations among the original variables, PCA can be used to describe the relative locations of the measured samples. A plot of principal component scores for a set of products reveals groupings of the samples that may not have been readily apparent from the original data. 

The samples are grouped so that those that are most similar in odour character are closest together on the map (e.g. Lilial and Bourgeo-nal ), and those that are most different are furthest apart (e.g. cyclamen aldehyde and Lyral ). The arrows indicate the direction of increasing perception of the odour characteristics shown. Only the odour characteristics that significantly correlate with the distribution of the samples across the map are shown these are the characteristics that are responsible for the systematic differences between the samples. 

General References Shinskey, Process Control Systems, 4th ed., McGraw-Hill, New York, 1996. Luyben, Practical Distillation Control, Van Nostrand Reinhold, New York, 1992. Luyben, Tyreus, and Luyben, Plantwide Process Control, McGraw-Hill, New York, 1998. 

The piping and instrumentation (P I) diagram provides a graphical representation of the control configuration of the process. P I diagrams illustrate the measuring devices that provide inputs to the con- 

The symbol for the control valve in Fig. 8-49 is for a pneumatic modulating valve without a valve positioner. 

Electronic (4- to 20-mA) signals are represented by dashed lines. In Fig. 8-49, these include the signal from the transmitter to the controller and the signal from the controller to the I/P transducer. Pneumatic signals are represented by solid lines with double crosshatching at regular intervals. The signal from the I/P transducer to the valve actuator is pneumatic. 

The ISA symbology provides different symbols for different types of actuators. Furthermore, variations for the controller symbol distinguish control algorithms implemented in distributed control systems from those in panel-mounted single-loop controllers. 

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The range of uncertainty in the UR may be too large to commit to a particular development plan, and field appraisal may be required to reduce the uncertainty and allow a more suitable development plan to be formed. Unless the range of uncertainty is quantified using statistical techniques and representations, the need for appraisal cannot be determined. Statistical methods are used to express ranges of values of STOMP, GIIP, UR, and reserves. 

The parametric method is an established statistical technique used for combining variables containing uncertainties, and has been advocated for use within the oil and gas industry as an alternative to Monte Carlo simulation. The main advantages of the method are its simplicity and its ability to identify the sensitivity of the result to the input variables. This allows a ranking of the variables in terms of their impact on the uncertainty of the result, and hence indicates where effort should be directed to better understand or manage the key variables in order to intervene to mitigate downside and/or take advantage of upside in the outcome. 

One therefore needs a smooth density estimation techniques that is more reliable than the histogram estimates. The automatic estimation poses additional problems in that the traditional statistical techniques for estimating densities usually require the interactive selection of some smoothing parameter (such as the bin size). Some publicly available density estimators are available, but these tended to oversmooth the densities. So we tried a number of ideas based on numerical differentiation of the empirical cdf to devise a better density estimator. 

Graham R C 1993. Data Analysis for the Chemical Sciences. A Guide to Statistical Techniques. New York, VCH Publishers. 

Each observation in any branch of scientific investigation is inaccurate to some degree. Often the accurate value for the concentration of some particular constituent in the analyte cannot be determined. However, it is reasonable to assume the accurate value exists, and it is important to estimate the limits between which this value lies. It must be understood that the statistical approach is concerned with the appraisal of experimental design and data. Statistical techniques can neither detect nor evaluate constant errors (bias) the detection and elimination of inaccuracy are analytical problems. Nevertheless, statistical techniques can assist considerably in determining whether or not inaccuracies exist and in indicating when procedural modifications have reduced them. 

Moore, D. S., Statistics Concepts and Controversies, W. H. Freeman, New York, 1985. MuUiolland, H., and C. R. Jones, Fundamentals of Statistics, Plenum Press, New York, 1968. Taylor, J. K., Statistical Techniques for Data Analysis, Lewis, Boca Raton, FL, 1990. 

Youden, W. J. Statistical Techniques for Collaborative Tests in Statistical Manual of the Association ofOjficial Analytical Chemists. Association of Official Analytical Chemists Washington, D.C., 1975. 

Statistical Process Control. A properly miming production process is characterized by the random variation of the process parameters for a series of lots or measurements. The SPG approach is a statistical technique used to monitor variation in a process. If the variation is not random, action is taken to locate and eliminate the cause of the lack of randomness, returning the process or measurement to a state of statistical control, ie, of exhibiting only random variation. 

Statistical Control. Statistical quahty control (SQC) is the apphcation of statistical techniques to analytical data. Statistical process control (SPC) is the real-time apphcation of statistics to process or equipment performance. Apphed to QC lab instmmentation or methods, SPC can demonstrate the stabihty and precision of the measurement technique. The SQC of lot data can be used to show the stabihty of the production process. Without such evidence of statistical control, the quahty of the lab data is unknown and can result in production challenging adverse test results. Also, without control, measurement bias cannot be determined and the results derived from different labs cannot be compared (27). 

When the data are already in the computer, tracking lab performance using statistical techniques can be done with Htde effort. By having the data archived, historical trends can be charted and past process capabiUty compared to current capabiUty. This can be useful in responding to challenges to test results (30). The avadabihty of production data makes periodic comparison of process capabiUty to specification limits easy. 

What statistical techniques are required for the analysis of the resulting data, and can these tools be rapidly brought to bear after the experiment has been conducted ... 

Neural nets can also be used for modeling physical systems whose behavior is poorly understood, as an alternative to nonlinear statistical techniques, eg, to develop empirical relationships between independent and dependent variables using large amounts of raw data. 

Joback, K. G., A Unified Appr oach to Physical Pr operiy Estimation Using Multivariate Statistical Techniques, M.S. Thesis, Massachusetts Institute of Technology, Cambridge, MA, 1984. 

Design of experiments. When conclusions are to be drawn or decisions made on the basis of experimental evidence, statistical techniques are most useful when experimental data are subject to errors. The design of experiments may then often be carried out in such a fashion as to avoid some of the sources of experimental error and make the necessary allowances for that portion which is unavoidable. Second, the results can be presented in terms of probability statements which express the reliabihty of the results. Third, a statistical approach frequently forces a more thorough evaluation of the experimental aims and leads to a more definitive experiment than would otherwise have been performed. 

Statistical Process Control (SPC) The use of statistical techniques (such as control charts) to analyze a process and take appropriate action to maintain statistical control and improve process capability. 

W.E. Duckworth. Statistical Techniques in Technological Research. Methuen, London (1968). 

The use of various statistical techniques has been discussed (46) for two situations. For standard air quality networks with an extensive period of record, analysis of residuals, visual inspection of scatter diagrams, and comparison of cumulative frequency distributions are quite useful techniques for assessing model performance. For tracer studies the spatial coverage is better, so that identification of meiximum measured concentrations during each test is more feasible. However, temporal coverage is more limited with a specific number of tests not continuous in time. 

The information obtained during the background search and from the source inspection will enable selection of the test procedure to be used. The choice will be based on the answers to several questions (1) What are the legal requirements For specific sources there may be only one acceptable method. (2) What range of accuracy is desirable Should the sample be collected by a procedure that is 5% accurate, or should a statistical technique be used on data from eight tests at 10% accuracy Costs of different test methods will certainly be a consideration here. (3) Which sampling and analytical methods are available that will give the required accuracy for the estimated concentration An Orsat gas analyzer with a sensitivity limit of 0.02% would not be chosen to sample carbon monoxide... 

With the exception of coupling agent technology, primers for structural adhesive bonding have received little theoretical treatment in the literature beyond a discussion of mechanisms of corrosion inhibition by primer additives and limited discussion about statistical techniques for primer formulation. Perhaps because of the much more widespread use and greater economic importance of corrosion-protective coatings, the design and function of primers for these systems have... 

Are statistical techniques used to determine process and product variation and are the results used to consistently reduce variation ... 

Are mechanisms in place to identify the need for statistical techniques required for verifying the acceptability of process capability and product characteristics ... 

Is the application of statistical techniques controlled in accordance with documented procedures ... 

If you can t predict the course of action or sequence of steps you need to take, you can t write a procedure. You can t plan for unforeseen events and as the unexpected will happen sooner or later, it would be wasteful of resources to produce procedures for such hypothetical situations. If you do not use statistical techniques, for instance, it is a waste of time writing a procedure that will not be used even though the standard requires one. 

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. 

The only statistical techniques which need control are those used to determine the acceptability of a product or service or the capability of a process that produces the product or service. Any activity where you rely on statistical evidence rather than physical measurement is an activity which should be governed by these requirements. The use of recognized techniques is important to the confidence one has in the result. It is similar to the use of measuring equipment that has been calibrated against known standards of accuracy. Unless you actually check every product, measure every attribute or variable you cannot be 100% certain. But that is costly and you can be 99.99% certain by using statistical techniques 99.99% may be sufficiently accurate for your needs. 

Figure 20.1 Clause relationships with the statistical techniques element...

The standard does not require you to use statistical techniques but identify the need for them. Within your procedures you will therefore need a means of determining when statistical techniques will be needed to determine product characteristics and process capability. One way of doing this is to use checklists when preparing customer specifications, design specifications, and verification specifications and procedures. These checklists need to prompt the user to state whether the product characteristics or process capability will be determined using statistical techniques and if so which techniques are to be used. 

There are many uses for statistical techniques in establishing and controlling product characteristics. 

Reliability prediction - a technique for establishing product characteristics where the reliability targets cannot be measured without testing many hundreds of products over many thousands of hours. (On long production runs of low value items, reliability testing is possible but with one-off systems of high value it is not cost effective hence reliability has to be predicted using statistical techniques.)... 

Market analysis - a technique for establishing product characteristics where the customer requirements are revealed by market survey and determined by statistical techniques for inclusion in specifications. 

The standard requires that the supplier establish and maintain documented procedures to implement and control the application of statistical techniques. 

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