Cumulative average

Y Cumulative average cost, production /unit, hour/... 

The particular learning curve is usually characterized by the percentage reduction in the cumulative average value Y when the number of units X is doubled. From this definition it follows that... 

If the batch units are capable of continuous subdivision, we proceed as follows. We substitute the given values of the cumulative-average cost Y and cumulative production X for the first batch into Eq. (9-63) to give, by taking logarithms of each side,... 

The cost of the first batch is 120 X 21 = 2520, and that of the second batch is 75.81 X 80 = 6065. The total cost of the first 101 units is therefore 8585, with a cumulative-average unit cost of 85. We substitute as before to give... 

Values calculated in this way are plotted in Fig. 9-16 and also in Fig. 9-18. It will he noted that after about 10 units this latter curve becomes parallel to the cumulative-average-cost curve and that the Y values are (N + 1) times those obtained from the latter curve. 

Since the cumulative-average cost Y9 of the first 101 units was 85, it follows from Eq. (9-67) that the average cost of the third hatch of 50 units, bringing the cumulative total to 151, is given by... 

Electronic Flow Calibrators These units are high accuracy electronic bubble flowmeters that provide instantaneous air flow readings and a cumulative averaging of multiple samples. These calibrators measure the flow rate of gases and report volume per unit of time. The timer is capable of detecting a soap film at 80... 

The WAPT values are summed to obtain the cumulative average of phase toxicity (CAPT), which is finally expressed on a logarithmic scale, to generate the SED-TOX score ... 

Figure 5 The instantaneous (top) and cumulative average (bottom) of the quantity A = E(t) - (0)l/l (0)l for the canonical harmonic oscillator of Figure 4 integrated with the Martyna-Tuckerman-Klein (MTK) thermostat using the integration techniques of Ref. 28.

Cumulative average metal releases for all four samples showed that 50% of the arsenite and 20% of the cadmium had not been leached during the extractions. For the less soluble heavy metals, 85% of the chromium and 75% of the lead remained in the silica rich solids. Of the metals naturally in cement, 90% of the aluminum, 98% of the iron, and 80% of the silicon remained after the extractions. Only 8.0% of the calcium remained after the acetic acid extractions. 

JTiOj other than rutile or anatase cip/iep average 5 66, median 5 0 cumulative average 5 6, median 5 8... 

ZrOj monoclinic cip/iep average 7 01, median 7 cumulative average 6 9, median 7... 

Problem 7.5 A monomer pair with rj = 0.2 and T2 = 5.0 is copolymerized beginning with a molar monomer ratio [Mi]/[M2] = 60/40. Assuming that the copolymer composition within a 10 mol% conversion interval is constant, calculate instantaneous monomer and copolymer compositions and cumulative average copolymer compositions at 10 mol% conversion intervals up to 100% total conversion. Show the results graphically as change in composition of the copolymer and the monomer mixture during copolymerization. 

With r = 0.52 and T2 = 0.46, calculate from Eq. (7.24) the changes in instantaneous monomer and copolymer compositions as a function of conversion and compare the results graphically with the above experimental data. Also calculate the cumulative average copolymer composition at different conversions. 

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... 

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