Error analog

The light source. In many cases a rather primitive light source, such as a long automobile lamp is used, but by chance this happens to compensate partially for the uneven distribution of protein on paper (Fig. 30), as the central and darker zone is better illuminated than the lateral zones (P17, S9 Fig. 31). If even illumination of the slit is obtained, this may cause an error analogous to that of a too wide slit whenever there is irregular protein distribution on the strip. 

All the catalysts had limited lifetimes (minutes) under the exothermic conditions of these polymerizations. Complete details of chain termination proceeses are not known. Within experimental error analogous lutetium and ytterbium complexes had very similar activities and lifetimes. It can be estimated from the data that the intrinsic ethylene propagation rate is faster than that for propene by a factor of >10. ... 

Triosmium dodecacarbonyl (Os 3(00)12)/ yellow crystalline solid/ was first prepared by decon osition of the Os(CO)5 obtained by carbonylation of osmiton tetrox-ide at elevated temperatures and pressures (196). Initially Os 3(CO)12 was incorrectly identified as 0s2(C0)g, in an error analogous to that associated with the identification of Ru3(C0)i2 discussed previously. In this case this error was corrected not only by a crystal structure of 033(00)12 by x-ray diffraction (87, 88) but also by the recent (304) preparation of authentic Os2(CO)g as a yellow, thermally unstable ( 75 C) solid by the photolysis of Os(CO)5 at -40°C. The x-ray-diffraction study of 033(00)12 demonstrated structure 11 (M = Os) with no bridging... 

Analogous methods are used to calculated the measuring error related to inexact measuring of voltage Ur and/or Up. It is counted that the value of U is determined with measuring error 5%. The measuring error 5hu-, Shut at too low and high value of U are separately analyzed. 

The other necessary instrumental component for controlled-current coulometry is an accurate clock for measuring the electrolysis time, fe, and a switch for starting and stopping the electrolysis. Analog clocks can read time to the nearest +0.01 s, but the need to frequently stop and start the electrolysis near the end point leads to a net uncertainty of +0.1 s. Digital clocks provide a more accurate measurement of time, with errors of+1 ms being possible. The switch must control the flow of current and the clock, so that an accurate determination of the electrolysis time is possible. 

Vector and Matrix Norms To carry out error analysis for approximate and iterative methods for the solutions of linear systems, one needs notions for vec tors in iT and for matrices that are analogous to the notion of length of a geometric vector. Let R denote the set of all vec tors with n components, x = x, . . . , x ). In dealing with matrices it is convenient to treat vectors in R as columns, and so x = (x, , xj however, we shall here write them simply as row vectors. 

The resolution of the analog I/O channels of the controller vaiy somewhat, with 12-bit and 14-bit conversions quite common. Sample rates for the majority of the constant sample rate controllers range from I to 10 samples/second. Hard-wired single-pole, low-pass filters are installed on the analog inputs to the controller to protect the sampler from aliasing errors. 

Sample times for the microprocessor-based SLCs vaiy from O.I to 0.4 seconds. Low-pass analog electronic filters are installed on the process inputs to stop abasing errors caused by fast changes in the process signal. Input filter time constants are typically in the range From O.I to I s. Microprocessor-based SLCs may be made part of a DCS by using the communication port (RS-488 is common) on the controller or may be operated in a standalone mode independent of the DCS. 

The first set of case studies illustrates errors due to the inadequate design of the human-machine interface (HMI). The HMI is the boundary across which information is transmitted between the process and the plant worker. In the context of process control, the HMI may consist of analog displays such as chart records and dials, or modem video display unit (VDU) based control systems. Besides display elements, the HMI also includes controls such as buttons and switches, or devices such as trackballs in the case of computer controlled systems. The concept of the HMI can also be extended to include all means of conveying information to the worker, including the labeling of control equipment components and chemical containers. Further discussion regarding the HMI is provided in Chapter 2. This section contains examples of deficiencies in the display of process information, in various forms of labeling, and the use of inappropriate instrumentation scales. 

From a reliability engineering perspective, error can be defined by analogy with hardware reliability as "The likelihood that the human fails to provide a required system function when called upon to provide that fimction, within a required time period" (Meister, 1966). This definition does not contain any references to why the error occurred, but instead focuses on the consequences of the error for the system (loss or unavailability of a required function). The disadvantage of such a definition is that it fails to consider the wide range of other actions that the human might make, which may have other safety implications for the system, as well as not achieving the required function. 

It is important, however, not to take this analogy too far. In general, the performance of a piece of hardware, such as a valve, will be much more predictable as a function of its operating conditions than will human performance as a function of the PIFs in a situation. This is partly because human performance is dependent on a considerably larger number of parameters than hardware, and only a subset of these will be accessible to an analyst. In some ways the job of the human reliability specialist can be seen as identifying which PIFs are the major determinants of human reliability in the situation of interest, and which can be manipulated in the most cost-effective manner to minimize error. 

The specific heat of a substance must always be defined relatively to a particular set of conditions under which heat is imparted, and it is here that the fluid analogy is very liable to lead to error. The number of heat units required to produce unit rise of temperature in a body depends in fact on the manner in which the heat is communicated. In particular, it is different according as the volume or the pressure is kept constant during the rise of temperature, and we have to distinguish between specific heats (and also heat capacities) at constant volume and those at constant pressure, as well as other kinds to be considered later. 

Thus the rather easily obtained atomic sizes are the best indicator of what the f-electrons are doing. It has been noted that for all metallic compounds in the literature where an f-band is believed not to occur, that the lanthanide and actinide lattice parameters appear to be identical within experimental error (12). This actually raises the question as to why the lanthanide and actinide contractions (no f-bands) for the pure elements are different. Analogies to the compounds and to the identical sizes of the 4d- and 5d- electron metals would suggest otherwise. The useful point here is that since the 4f- and 5f-compounds have the same lattice parameters when f-bands are not present, it simplifies following the systematics and clearly demonstrates that actinides are worthy of that name. 

When the fluid behaviour can be described by a power-law, the apparent viscosity for a shear-thinning fluid will be a minimum at the wall where the shear stress is a maximum, and will rise to a theoretical value of infinity at the pipe axis where the shear stress is zero. On the other hand, for a shear-thickening fluid the apparent viscosity will fall to zero at the pipe axis. It is apparent, therefore, that there will be some error in applying the power-law near the pipe axis since all real fluids have a limiting viscosity po at zero shear stress. The procedure is exactly analogous to that used for the Newtonian fluid, except that the power-law relation is used to relate shear stress to shear rate, as opposed to the simple Newtonian equation. 

Remark By analogy with the preceding section it is possible to evaluate the errors of approximation for either of the equations (48) such as... 

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