Run-out error

The run-out error could also be avoided by going to a S/R approach and limiting mask size to a few centimeters. This would also alleviate problems due to mask and/or wafer distortions but exposure times with presently available resists and conventional sources are too long for this to be economical. Exposure times of a few seconds would be needed for a source to wafer distance of about 50 cm which infers similar sensitivity to that required for the full-wafer case. 

Figure 4. Run-out error encountered with conventional point source x-ray...

Two students are assigned two pure compounds to investigate. They observe that compound A boils at 37°C and compound B at 126°C. However, they run out of time to make any additional measurements, so make the following guesses about the two compounds. In each case indicate whether the guess can be justified by the data, is in error, or could be either true or false. Justify your answers, (a) Compound B has the higher molar mass, (b) Compound A is the more viscous. 

There is a tendency among control and statistics theorists to refer to trial and error as one-variable-at-a-time (OVAT). The results are often treated as if only one variable were controlled at a time. The usual trial, however, involves variation in more than one controlled variable and almost always includes uncontrolled variations. The trial-and-error method is fortunately seldom a random process. The starting cycle is usually based on manufacturers specifications or experience with a similar process and/or material. Trial variations on the starting cycle are then made, sequentially or in parallel, until an acceptable cycle is found or until funds and/or time run out. The best cycle found, in terms of one or a combination of product qualities, is then selected. Because no process can be repeated exactly in all cases, good cure cycles include some flexibility, called a process window, based on equipment limitations and/or experience. 

When you use a pipette, do you really fill it exactly to the same mark each time A series of 10 experiments of filling a pipette with distilled water and weighing what runs out, gives a range of values from 9.95 to 10.04mL. The analyst s contribution to the error is definitely random. 

The possible results Z3 may return are (1) a proof for the validity of the formulas. (2) a counter-example. (3) Z3 runs out of resources (time or space). In Case (1) above, the program verification was successful. In Cases (2) and (3), the verification engineer has to analyze the problem and correct the error. In Case (3), he/she may also find that the program indeed satisfies the annotations. Then new aimotations (stronger invariants, helpful lemmas, etc.) have to be added. This process is repeated imtil Z3 finds a proof. 

Knowledge-based errors are concerned with performance in novel or new situations. Actions have to be planned on-line and the process is intellectually demanding. The problem solver will only resort to this type of activity when he has run out of rule-based solutions. An example of knowledge-based performance is that of first learning to operate a piece of machinery. The hydraulic controls of a winch provide a good example. Experimentation will help the operator to build a mental model of how the controls can be co-ordinated to achieve the desired movements. Eventually, the operator will adopt a set of rules derived from that mental model. With practice, the task will become skill-based. Training offers the opportunity to miss out the experimentation phase by guiding the trainee to a correct model of situations, based on the experiences of others. 

To determine if a process unit is at steady state, a program monitors key plant measurements (e.g., compositions, product rates, feed rates, and so on) and determines if the plant is steady enough to start the sequence. Only when all of the key measurements are within the allowable tolerances is the plant considered steady and the optimization sequence started. Tolerances for each measurement can be tuned separately. Measured data are then collec ted by the optimization computer. The optimization system runs a program to screen the measurements for unreasonable data (gross error detection). This validity checkiug automatically modifies tne model updating calculation to reflec t any bad data or when equipment is taken out of service. Data vahdation and reconciliation (on-line or off-line) is an extremely critical part of any optimization system. 

Apart from their pedagogical value, reversible rules may be used to explore possible relationships between discrete dynamical systems and the dynamics of real mechanical systems, for which the microscopic laws are known to be time-reversal invariant. What sets such systems apart from continuous idealizations is their exact reversibility, discreteness assures us that computer simulations run for arbitrarily long times will never suffer from roundoff or truncation errors. As Toffoli points out, ...the results that one obtains have thus the force of theorems [toff84a]. ... 

It is clear that, in the long run, we cannot rely on a more or less fortuitous cancellation of errors, the nature of which we do not know about in detail. The theory may be in a dilemma, but the only way out is probably to overcome our desire to get quick results and to start investigating the correlation effects in full detail. 

An examination of some laboratory runs with diluted C150-1-02 catalyst can illustrate this problem. In one run with 304°C at inlet, 314 °C at exit, and 97,297 outlet dry gas space velocity, the following results were obtained after minor corrections for analytical errors. Of the CO present (out of an inlet 2.04 mole % ), 99.9885% disappeared in reaction while the C02 present (from an initial 1.96%) increased by over 30%. Equilibrium carbon oxides for both methanation reactions were essentially zero whereas the equilibrium CO based on the water-gas shift reaction at the exit composition was about one-third the actual CO exit of 0.03 mole %. From these data, activities for the various reactions may be estimated on the basis of various assumptions (see Table XIX for the effect of two different assumptions). 

ASSAYl.dat As part of a cross-validation of a modification of a given analytical method, 20 samples were run on either method. There is at least one result that is out of trend (OOT), and another two to three are indicative of laboratory errors. 

The catalyst reuse is carried out without treating Pd/ ACF between the runs. Negligible leaching (<10% within the experimental error) was observed after catalyst reuse. Figure 8 shows the initial reaction rate and the selectivity for several runs. After activity drops in the first run, it stabilizes at 0.085 0.008 kmolHj/kgp /s, while selectivity to 1-hexene is 94+1%. Kinetic curves are identical from the second to the sixth runs. 

There are several sources of irreproducibility in kinetics experimentation, but two of the most common are individual error and unsuspected contamination of the materials or reaction vessel used in the experiments. An individual may use the wrong reagent, record an instrument reading improperly, make a manipulative error in the use of the apparatus, or plot a point incorrectly on a graph. Any of these mistakes can lead to an erroneous rate constant. The probability of an individual s repeating the same error in two successive independent experiments is small. Consequently, every effort should be made to make sure that the runs are truly independent, by starting with fresh samples, weighing these out individually, etc. Since trace impurity effects also have a tendency to be time-variable, it is wise to check for reproducibility, not only between runs over short time spans, but also between runs performed weeks or months apart. 

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