Examples robustness

In the following example, robustness and ruggedness of a procedure used in two laboratories, LI and L2, will be considered. It is supposed that they use the same procedure to determine the analyte A in the presence of the interferents B and C under the influence of the factors a, b, and c. The input data for the computation are given in the following table. 

To prevent material loss due to excursions such as the previous example, robust process control systems are required throughout the supply chain from the raw materials manufacturer to the pad manufacturer and the CMP module. Invariably, incident reviews of such excursions reveal that the excursion could have been prevented or limited to only a small amount of material lost if the proper statistical process control systems had been in place. Invariably, the excursion could have been detected by careful scrutiny of an in-process parameter that was either monitored or should have been monitored by the subsupplier, pad manufacturer, and/or the CMP operation. 

During the prestudy evaluation phase, an attempt should be made to evaluate the variety of conditions that may reflect the execution and performance of the method during the in-study phase. The final conditions should be clearly documented in the analytical procedures prior to in-study sample analysis. As an example, robustness assessment could include incubation time tolerances, while ruggedness assessment could include changes in analysts and batch size (Table 4.7). Most robustness and ruggedness evaluations are empirical in nature however, more formal evaluations can also be used [29]. 

It is expected that nature developed a limited number of tricks and principles independent of specific implementations to ensure, for example, robustness of the biological function in a noisy environment. Mathematics will be helpful in discovering these general design principles. 

A different emphasis may be required for pharmacopoeial as opposed to registration purposes. For example, robustness is a critical characteristic for pharmacopoeial methodology but may be less significant for a manufacturer s release specification. 

Key elements of a validation should be documented by raw data, for example, robustness, with respect to pH of the mobile phase, the mobile phase composition, the shelf life of reference samples, and the column temperature. 

With numerous worked examples, robust review support, a wealth of end-of-chapter problems and a solutions manual written by the text s author, students have everything they need to master the basics of physical chemistry. 

Environmental vulnerability varies considerably from area to area. For example the North Sea, which is displaced into the Atlantic over a two year period,-is a much more robust area than the Caspian Sea which is enclosed. Regional standards should reflect those differences. 

Once the production potential of the producing wells is insufficient to maintain the plateau rate, the decline periodbegins. For an individual well in depletion drive, this commences as soon as production starts, and a plateau for the field can only be maintained by drilling more wells. Well performance during the decline period can be estimated by decline curve analysis which assumes that the decline can be described by a mathematical formula. Examples of this would be to assume an exponential decline with 10% decline per annum, or a straight line relationship between the cumulative oil production and the logarithm of the water cut. These assumptions become more robust when based on a fit to measured production data. 

In order to test the economic performance of the project to variations in the base case estimates for the input data, sensitivity analysis is performed. This shows how robust the project is to variations in one or more parameters, and also highlights which of the inputs the project economics is more sensitive to. These inputs can then be addressed more specifically. For example if the project economics is highly sensitive to a delay in first production, then the scheduling should be more critically reviewed. 

Taking into account that size and weight can change tremendously fi-om one object to the next, it is obvious that the CT- system had to be build in a very versatile but robust manner. For example heavy objects have to be moved very carefully, whereas small objects have to be measured as fast as possible and as accurate as possible. For that reason the turntable is equipped with an instrument, which limits the velocity, if the weight of the object is above a preselectable threshold. 

The AIM scheme is popular due to its reliability with large basis sets for which some other schemes fail. Unfortunately, the numerical surface finding and integration involved in this scheme are not completely robust. For example, nonnuclear attractor compounds like Li2 and Na clusters have maxima in the middle... 

The TINKER documentation provides a description of the input, but not a tutorial. Documentation is available as html. Acrobat, or postscript. A set of example input files is provided. The researcher can expect to invest some time in learning to use this system of programs. Most of the executables seem to be fairly robust and as tolerant as possible of variations in the input format. When... 

The mean is the most common estimator of central tendency. It is not considered a robust estimator, however, because extreme measurements, those much larger or smaller than the remainder of the data, strongly influence the mean s value. For example, mistakenly recording the mass of the fourth penny as 31.07 g instead of 3.107 g, changes the mean from 3.117 g to 7.112 g ... 

As shown by Examples 4.1 and 4.2, the mean and median provide similar estimates of central tendency when all data are similar in magnitude. The median, however, provides a more robust estimate of central tendency since it is less sensitive to measurements with extreme values. For example, introducing the transcription error discussed earlier for the mean only changes the median s value from 3.107eto3.112e. 

The choice of the solvent also has a profound influence on the observed sonochemistry. The effect of vapor pressure has already been mentioned. Other Hquid properties, such as surface tension and viscosity, wiU alter the threshold of cavitation, but this is generaUy a minor concern. The chemical reactivity of the solvent is often much more important. No solvent is inert under the high temperature conditions of cavitation (50). One may minimize this problem, however, by using robust solvents that have low vapor pressures so as to minimize their concentration in the vapor phase of the cavitation event. Alternatively, one may wish to take advantage of such secondary reactions, for example, by using halocarbons for sonochemical halogenations. With ultrasonic irradiations in water, the observed aqueous sonochemistry is dominated by secondary reactions of OH- and H- formed from the sonolysis of water vapor in the cavitation zone (51—53). 

C. Daniel, App/ications of Statistics to lndustria/Experimentation, ]oE Wiley Sons, Inc., New York, 1976. This book is based on the personal experiences and insights of the author, an eminent practitioner of industrial appHcations of experimental design. It provides extensive discussions and concepts, especially in the areas of factorial and fractional factorial designs. "The book should be of use to experimenters who have some knowledge of elementary statistics and to statisticians who want simple explanations, detailed examples, and a documentation of the variety of outcomes that may be encountered." Some of the unusual features are chapters on "Sequences of fractional repHcates" and "Trend-robust plans," and sections entided, "What is the answer (what is the question )," and "Conclusions and apologies."... 

The properties of the least squares (LS) method (5 = 0, the non-robust procedure) and the least modules (LM) one (5 = 100%, the robust procedure) are comprehensively compared with the use of several examples of data treatment in the QSAR problems. 

The main problem of determination of molecular weight distribution (MWD) of dextrans (polysachaiides which ai e used as active substances for infusion medicines) is low robustness of the existing method. It means that obtained results are strongly dependent on controlled and uncontrolled pai ameters of chromatographic system standai d substances for calibration loading on columns etc. It has been shoved on practical examples. 

On a different note, after some 50 years of intensive research on high-pressure shock compression, there are still many outstanding problems that cannot be solved. For example, it is not possible to predict ab initio the time scales of the shock-transition process or the thermophysical and mechanical properties of condensed media under shock compression. For the most part, these properties must presently be evaluated experimentally for incorporation into semiempirical theories. To realize the potential of truly predictive capabilities, it will be necessary to develop first-principles theories that have robust predictive capability. This will require critical examination of the fundamental postulates and assumptions used to interpret shock-compression processes. For example, it is usually assumed that a steady state is achieved immediately after the shock-transition process. However, due to the fact that... 

Designing for robustness has also been associated with the DFM guidelines (Russell and Taylor, 1995). Robust design has different meanings to different engineering communities. For example, the three descriptions below focus on three different but connected aspects of product design ... 

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