Cumulative drifts

Figure 6. Computed drift curves for instantaneous and cumulative DPs (S)...

This shde gives an example of the use of a Cusum Chart. The upper chart is a conventional X-chart, the lower one a Cusum Chart. Starting from the 11th value, all values are below the target value originating from slow between-batch-drift in the analyses. This can be seen in the Cusum Chart by a descending cumulative sum. 

Apart from the standard Shewart charts, the analyst can also apply X-charts, on which the mean of several replicate measurements is plotted, or R-charts, where the difference between two replicate measurements is plotted. X- and R-charts give an indication of the reproducibility of the method. Drift in analytical procedure, for example, slows changes in the system caused by the aging of parts of instruments, decalibration in wavelength, or the aging of calibration stock solutions, can be detected early when a Cusum chart (cumulative sum) is applied. In Cusum charts, the analyst reports the cumulative sum of the differences between delivered and reference values. If this reference value is certified (CRM), the Cusum chart allows the accuracy of the determination to be monitored. 

The derivation of the basic relation (4.147) reveals the conditions under which the proportionality between drift velocity (or flux) and electric field breaks down. It is essential to the derivation that in a collision, an ion does not preserve any part of its extra velocity component arising from the force field. If it did, then the actual drift velocity would be greater than that calculated by Eq. (4.147) because there would be a cumulative carryover of the extra velocity from collision to collision. In other words, every collision must wipe out all traces of the force-derived extra velocity, and the ion must start afresh to acquire the additional velocity. This condition can be satisfied only if the drift velocity, and therefore the field, is small (see the autocorrelation function. Section 4.2.19). 

Brown and Skrebowski [37] first suggested the use of x-rays for particle size analysis and this resulted in the ICl x-ray sedimentometer [38,39]. In this instrument, a system is used in which the difference in intensity of an x-ray beam that has passed through the suspension in one half of a twin sedimentation tank, and the intensity of a reference beam which has passed through an equal thickness of clear liquid in the other half, produces an inbalance in the current produced in a differential ionization chamber. This eliminates errors due to the instability of the total output of the source, but assumes a good stability in the beam direction. Since this is not the case, the instrument suffers from zero drift that affects the results. The 18 keV radiation is produced by a water-cooled x-ray tube and monitored by the ionization chamber. This chamber measures the difference in x-ray intensity in the form of an electric current that is amplified and displayed on a pen recorder. The intensity is taken as directly proportional to the powder concentration in the beam. The sedimentation curve is converted to a cumulative percentage frequency using this proportionality and Stokes equation. 

The essential procedure for calculating the composition drift with conversion is that fi is decreased or increased in suitable increments from (/i), to 0 or to 1.0. For each value of f, the corresponding degree of conversion is obtained from Eq. (7.24) and the corresponding instantaneous copolymer composition from Eq. (7.18). With the monomer mixture composition, fi, and the degree of conversion p = 1 — N/No thus known, it is then easy to also calculate cumulative average copolymer composition Fi from Eq. (P7.6.2). For the given monomer system and feed composition, Eq. (7.18) shows that < /i, i.e., the... 

The cumulated effect of the radiation (with a constant heat flow released by the waste containers equal to 86400 W) and of the natural air convection can be approximated by a constant temperature gradient along the well, with a temperature T, =45°C at the base and Th=95°C at the top. This boundary condition is established from the assumption that the heat flow penetrating in the rock mass by conduction is negligible in front of the heat flow convected by the drifts. 

Hint 2. One can also appreciate the composition drift picture by plotting the cumulative mole fraction of Mj in the copolymer chains, F, versus conversion. 

The V-mask can now be placed over the graph with P-0 parallel to the x-axis and the point P over the current data point. If any part of the cumulative function protrudes the boundaries prescribed by the V-mask, we would conclude that the current mean of the process has deviated from the target. The CUSUM chart, in general, is more effective than the Shewhart Control Chart when used to monitor continuous processes that tend to drift over time. The CUSUM Chart, however, is quite vulnerable to the impact of process interruptions. Another drawback of the CUSUM Chart is that its direct relationship to the actual time variation of the process is not always clear, making it rather difficult for us to analyze and to improve the process. Refer to Stepwise SPC Chart. 

Other charts that are also used are the cusum (cumulative sum) charts, in which the sum of the differences between the values found experimentally and the reference value (of the RM) are plotted in time. This latter type of chart allows for a more rapid detection of drifts. 

This time control mechanism allows the control of the overall reaction time of an architecture. These reaction times are generally cumulative as a result of all processing and communication stages, considering worst-case values. The accumulation of worst-case values is associated with a clock drift scenario within the hmits of tolerance. Usually, we assume a maximum theoretical drift of 10% of the cycle time. 

The fragility curve is defined by a median value of the engineering demand parameter (EDP), which is, for example, spectral displacement in HAZUS and maximum interstory drift ratio (IDR) in Jayaram et al. 2012, and by the variability associated with the estimation of that damage state for that EDP. The median EDP corresponds to the threshold of the damage state. The curve is assumed to follow the cumulative lognormal distribution function as shown below ... 

In Fig. 9 the cumulative distribution for drift at the structural damage state threshold is compared with the curve obtained assuming a confidence factor of 1.25 in agreement with EC8 knowledge level and with the confidence boundaries computed by FaMIVE according to the procedure outlined above. 

Fig. 9 Cumulative distribution for drift at structural damage threshold comparison with curve obtained for an ECS confidence factor of 1.25 and with FaMIVE confidence boundary...

The composition of the copolymers produced in batch reactors wiU be dictated by the reactivity ratios of the monomers, r see Equation 4.6, as well as by the mole fractions of the monomers, in the polymer particles, see Equation 4.7. The instantaneous composition can then be predicted by the terminal model, see Equation 4.5. Most of the common monomers employed in emulsion polymerisation recipes present different reactivities, and a consequence of this is the compositional drift (non-constant copolymer composition) produced in batch operation. The compositional drift can be easily calculated by computing the instantaneous, see Equation 4.2, and cumulative copolymer compositions. 

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