Robustness

Robustness refers to the resistance versus deterioration of the performances when the active masses are run under abnormal conditions overcharge, overdischarge, extreme temperature, high 

Robustness testing is performed to examine the effect of operational parameters on the analysis results. Typical parameters to evaluate are mobile phase pH, mobile phase flow rate, percentage of organic modifier, and column temperature. To examine the effect of variation in pH when the mobile phase pH is, say, 5.5, analyses are carried out at, for example, pH 5.3 and 5.7. If no significant change in 

The robustness of a method is a measure of the method s ability to remain unaffected by small but deliberate changes to the method parameters (e.g., flow rate, detector wavelength, etc. see Table 8.6 for some further examples). 

The method must be evaluated against predefined acceptance criteria one parameter at a time or simultaneously as part of a design of experiment (DoE) approach (http //www.sigmaplus.fr). By identifying the parameters that are critical to the performance of the method, a range of values can be incorporated in the final version of the standard operating procedure or method  

Flow rate. The flow rate accuracy will be determined by the instrument used and will be documented in the supplier s operational qualification documentation. The impact of analyst error made during system setup should be validated and it would be appropriate to investigate the effect of small changes in the region of 10% of the target flow rate. The flow rate may be adjusted by as much as 50%, provided that there are no adverse effects on the chromatography (i.e., resolution, peak shape and retention time). Common causes of flow rate error will be discussed further in Chapter 10. 

Column temperature. This may be adjusted by as much as 20%, provided that there are no adverse effects on the chromatography (i.e., resolution, peak shape, and retention time). 

The robustness of a method is typically determined during the method development stage and is a measure of how consistently a method generates the same analytical result when small deliberate changes in operating parameters are made. Many times it is part of the intralaboratory development/validation process. For example, changeable parameters could include organic level in mobile phase, pH of mobile phase, concentration of mobile phase modifiers, and colutim. 

Within any meta-analysis some trials will be larger than others and because of the way the trials are combined, the larger trials, i.e. those that have higher precision, will tend to dominate. It is helpful therefore to assess the robustness of the overall conclusion by omitting maybe the largest study or studies to see if the result remains qualitatively the same. If it does then the result is robust. If it does not then the overall result is undermined as it is then giving a result that is driven by the largest trial or trials. 

A process that is not greatly affected by variations in process temperature, mixing, minor variations in rates of addition, and so on would be considered robust if these excursions did not adversely affect product quality. The main difference between robustness and controllability is that a capable or controlled process will stay within the desired parameters whereas a robust process may experience excursions outside the control parameters, but these excursions will not affect the critical quality attributes. 

A good understanding of key process inputs and parameters may be obtained through careful statistical design of experiment and will lead to a good understanding of how robust a process is. Factors that can adversely affect process robustness include non-selective chemistry or unwanted side reactions, physical and chemical stability of the reactants or reagents, and the complexity of the process separation train. 

Throughput is best understood as the time required to produce a quantity of average saleable product and cycle time is best understood as the average rate at which products are manufactured. Throughput will be affected by such things as the efficiency and rate of chemical conversion, the isolated process yield, plant capacity, the availability of equipment, process time, cycle time, the number of chemical steps, the number of unit operations, plant layout, warehouse processes, raw material availability, process bottlenecks, labor availability, and others. 

Several different approaches may be investigated to track throughput in a plant. These include such things as tracking the volume or mass of the product or intermediate manufactured over a given period of time, the number of products produced over a given period of time, and others. 

For the large integrated petrochemical and chemical manufacturing enterprise, process integration and modifications are continually pursued as a means of reducing the enormous amounts of energy consumed. However, the attention to energy efficiency is comparatively much less in the batch chemical environment. 

The design of a controller depends on a model of the process. If the controller is installed on a process whose parameters are not exactly the same as the model used to design the controller, what happens to its performance Is the system unstable Is it too underdamped or too slow These are very practical questions because the parameters of any industrial process always change somewhat due to nonlinearities, changes in operating conditions, etc. 

In multivariable systems the question of robustness is very important. One method developed by Doyle and Stein (IEEE Trans., 1981, Vol. AC-26, p. 4) is quite usefiil and easy to use. It has the added advantage that it is quite similar to the maximuni closedloop log modulus criterion used in SISO systems. 

Another proeedure, recommended by Skogestad and Morari (Chemical Engineering Science, Vol. 24, 1987, p. 1765), involves designing the controller so that the closedloop resonant peak occurs at a frequency region where the uncertainty is not too large. 

Before we discuss these two methods of robustness analysis, let us consider the general relationship between performance and robustness. 

A method is linear if there is a linear relationship between the analytical response and concentration of analyte in the sample solution over a specified range of concentrations of the analyte. The plot of analytical response versus analyte concentration should have negligible intercept. 

With respect to an HPLC method, the analytical response is almost always based on peak area. Peak heights may be used when working close to the limit of detection but are otherwise not used since if there is any peak asymmetry present a plot of peak height versus concentration will deviate from a straight line. 

For a controller to be robust it must perform well over the normal variation of process dynamics. Dynamics are rarely constant and it is important to assess how much they might vary before finalising controller design. 

A common oversight is not taking account of the fact that process dynamics vary with feed rate. Consider our example of a fired heater. If it is in a nonvaporising service we can write the heat balance 

On the feed side Ff ed is the flow rate to the heater, Cp is the specific heat, T is the outlet temperature and Ti iet is the inlet temperature. On the fuel side F is the flow of fuel, NHV the net heating value (calorific value) and rj the heater efficiency. Rearranging we get 

This effect is not unique to fired heaters almost all process gains on aplant will vary with feed rate. Given that we tolerate 20 % variation in process gain, we can therefore tolerate 20 % variation in feed rate. Assuming a reference feed rate of 100, oiu controller will work reasonably well for feed rates between 80 and 120. The turndown ratio of a process is defined as the maximum feed rate divided by the minimum. We can see that if this value exceeds 1.5 (120/80) then the performance of almost all the controllers on the process will degrade noticeably as the minimum or maximum feed rate is approached. Fortunately most processes have turndown ratios less than 1.5, so providing the controllers are tuned for the average feed rate their performance should be acceptable. The technique used, if this is not the case, is covered in Chapter 6. 

Feed flow rate may also affect process deadtime. If the prime cause of deadtime is transport delay than an increase in feed will cause the residence time to fall and a reduction in deadtime. At worst, deadtime may be inversely proportional to feed rate. If so then the maximum turndown limit of 1.5 will apply. In fact controllers are more sensitive to increases in deadtime than decreases. Rather than design for the average deadtime, a value should be chosen so that it varies between —30 % and 10 %. Techniques for accommodating excessive variation in deadtime are covered in Chapter 7. 

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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. 

Another useful profitability indicator is the internal rate of return (IRR), already introduced in the last section. This shows what discount rate would be required to reduce the NPV to zero. The higher the IRR, the more robust the project is, i.e. the more risk it can withstand before the IRR is reduced to the screening value of discount rate. Screening values are discussed below. 

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. 

Our first instrument had to be robust tmd very easy to operate this has been an objective for every instrument made by this company and we would be happy to be remembered for it. 

Thanks to this technology,films with a high quality,very robust and environmentally friendly have been designed. 

Neuronal networks are nowadays predominantly applied in classification tasks. Here, three kind of networks are tested First the backpropagation network is used, due to the fact that it is the most robust and common network. The other two networks which are considered within this study have special adapted architectures for classification tasks. The Learning Vector Quantization (LVQ) Network consists of a neuronal structure that represents the LVQ learning strategy. The Fuzzy Adaptive Resonance Theory (Fuzzy-ART) network is a sophisticated network with a very complex structure but a high performance on classification tasks. Overviews on this extensive subject are given in [2] and [6]. 

The specific advanced properties of the ceramic insulator eliminate the need for oil or resin insulation. The metal vacuum envelope of the tube provides higher beam stability, more robust design, and even X-ray shielding up to certain levels. Furthermore, even difScult mechanical problems (e.g. mounting, coohng, or beam emission) can be solved by an appropriate customised tube design. 

The tubes of the new MCB series are a highly integrated and reliable ready-to-use component for radiation applications, which until now were not feasible due to the lack of robustness, size, or stability requirements. 

Our company is dedicated solely to metal-ceramic X-ray tubes since 25 years over this time, we have made lots of different tube models especially for tyre inspection systems. The major reasons for the use of metal-ceramic tubes in this inspection technology are robustness, their small and individual shapes, and the frequent need for modifications of their design due to custom designed systems. 

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. 

One remarkably simple yet seemingly robust outcome of Turnbull s experiments was his empirical finding that the solid-liquid interfacial free energy was... 

Li and Neumann sought an equation of state of interfacial tensions of the form 7 l = /(Tlv. TSv). Based on a series of measurements of contact angles on polymeric surfaces, they revised an older empirical law (see Refs. 216, 217) to produce a numerically robust expression [129, 218]... 

While a number of proteins have been crystallized in this manner, the majority of studies have focused on a robust system comprising the tetrameric protein streptavidin and the vitamin biotin. The choice of this system is primcirily motivated by the strong bond between biotin and streptavidin (having an association equilibrium constant, Ka Tbe binding properties were recently... 

The third alternative is a more robust, sensitive and specialized fonn of the first, in that only hydrogen nuclei indirectly spin-spin coupled to in a specific molecular configuration are imaged. In achieving selectivity, the technique exploits the much wider chemical shift dispersion of compared to H. The metliod involves cyclic transfer from selected H nuclei to indirectly spin-spin coupled C nuclei and back according to the sequence... 

Bain A D and Duns G J 1994 Simultaneous determination of spin-lattioe (T1) and spin-spin (T2) relaxation times in NMR a robust and faoile method for measuring T2. Optimization and data analysis of the offset-saturation experiment J. Magn. Reson. A 109 56-64... 

For a recent critical evaluation of situations where current DFT approaches experience difficulties, see Davidson E R 1998 How robust is present-day DFT ... 

The mean field teclmique is one of the most robust and simple methods used to handle larger molecules in gas and liquid enviromnents [M, 134. 135 and 136]. The basic premise of all mean-field methods is that the fiill wavefiinction represents N very weakly coupled modes (2 ) and can be approximated as... 

Altliough an MOT functions as a versatile and robust reaction cell for studying cold collisions, light frequencies must tune close to atomic transitions and an appreciable steady-state fraction of tire atoms remain excited. Excited-state trap-loss collisions and photon-induced repulsion limit achievable densities. 

The Fresnel equations predict that reflexion changes the polarization of light, measurement of which fonns the basis of ellipsometry [128]. Although more sensitive than SAR, it is not possible to solve the equations linking the measured parameters with n and d. in closed fonn, and hence they cannot be solved unambiguously, although their product yielding v (equation C2.14.48) appears to be robust. 

Schaaff T G efa/1997 Isolation of smaller nanocrystal Au molecules robust quantum effects in the optical spectra J. Phys. Chem. B 101 7885... 

The long term behavior of any system (3) is described by so-called invariant measures a probability measure /r is invariant, iff fi f B)) = ft(B) for all measurable subsets B C F. The associated invariant sets are defined by the property that B = f B). Throughout the paper we will restrict our attention to so-called SBR-measures (cf [16]), which are robust with respect to stochastic perturbations. Such measures are the only ones of physical interest. In view of the above considerations about modelling in terms of probabilities, the following interpretation will be crucial given an invariant measure n and a measurable set B C F, the value /r(B) may be understood as the probability of finding the system within B. 

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