Robust tolerance analysis

Table 10 shows the three competing approaches to robust design. When the equation is known, a robust tolerance analysis should be performed. When the equation is not known, designed experiments must be used and all three... 

Designed experiments are a key tool for performing this specification translation process and helping to establish such controls. However, designed experiments are not the only tool required to accomplish this task. We will also explore other tools, such as tolerance analysis, robust design, capability studies, and Failure Modes and Effects Analysis (FMEA), to see how to combine these tools into an effective system for vahdation. 

Any analytical method should have favourable analysis efficiency, wide linear range, low cost and strong robustness. Kinetic analysis of reaction curve for Vm and So assay can have much better upper limit of linear response, but inevitably tolerates low analysis efficiency when wide linear range is required. Based on kinetic analysis of reaction curve, however, our group developed two integration strategies for enzyme initial rate and substrate assay, respectively, with both favourable analysis efficiency and ideal linear ranges. 

In Chap. 15 we reviewed a tittle matrix mathematics and notation. Now that the tools are available, we will apply them in this chapter to the analysis of multivariable processes. Our primary concern is with closedloop systems. Given a process with its matrix of openloop transfer functions, we want to be able to see the effects of using various feedback controllers. Therefore we must be able to find out if the entire closedloop multivariable system is stable. And if it is stable, we want to know how stable it is. The last question considers the robustness of the controller, i.e., the tolerance of the controller to changes in parameters. If the system becomes unstable for small changes in process gains, time constants, or deadtimes, the controller is not robust. 

The robustness and large size (diameter 1.2-1.3 mm) of the oocytes make them tolerant to repeated impalement of microelectrode and injection pipettes, permitting functional analysis by a number of electrophysiological techniques. 

I.N. Vuchkov and L.N. Boyadjieva, The robustness against tolerances of performance characteristics described by second order polynomials, paper presented at First international conference-work-shop on optimal design and analysis of experiments, Neuchatel, Switzerland, July 25-28, 1988. 

Now that you ve minimized the impact of variation on your design, the last step in robust design is the tolerance design phase. Here you establish detailed tolerances or specifications that your design needs to operate within to meet expectations. For example, through our analysis of the skin patch design, we determined that expected variation, including noise, is approximately 0.033 mg/hr. This is more than acceptable if the required performance is 1.0 mg/hr it 0.2. 

We all know that mathematics has scored brilliant successes in dealing with a wide variety of real-world problems. But what is also true is that there are many problems in economics, psychology, decision analysis, and other fields that do not lend themselves to precise analysis in the classical spirit. And, what is perhaps more important, there are many problems in which tolerance for imprecision can be exploited—through the use of fuzzy logic—to achieve tractability, robustness, low solution cost, and better rapport with reality. Today, most of the applications of fuzzy logic fall into this category. 

Robustness tests examine the effect operational parameters have on the analysis results. For the determination of a method s robustness, a number of chromatographic parameters (e.g., flow rate, column temperature, injection volume, detection wavelength, or mobile phase composition) are varied within a realistic range and the quantitative influence of the variables is determined. If the influence of the parameter is within a previously specified tolerance, the parameter is said to be within the method s robustness range. Obtaining data on these effects will allow one to judge whether a method needs to be revalidated when one or more of parameters are changed, for example, to compensate for column performance over time. 

It is commonly the case that a wide variety of properties can be included in a QSAR analysis and a decision must be made on whether to include all possibilities or limit the number of descriptors. This decision depends on the size of the data set and the correlation matrix between the properties. Farge sets of property data contain a lot of redundancy of information. For example, molecular weight, surface area and molar refraction are always highly correlated, therefore a decision to nse only molecular weight could be made. Some multivariate statistical analysis methods are tolerant of data sets which contain more properties than compounds, for example, PFS, while others are not, for example, linear discriminant analysis (FDA). Ideally, a set of uncorrelated properties is desirable as this is most likely to give a robust, interpretable model. 

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]. 

The virtues of ICP/MS include efficient production of positive atomic ions robustness of the plasma (tolerance of sample matrix material in the ion source) sample introduction at atmospheric pressure ability to handle solid, liquid or gaseous sample forms and speed of analysis. Sample preparation requires much less chemical purification than for TIMS, AMS or radiation detection by beta- or alpha-spectrometry. 

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