Expectation operator

This gives two choices ia interpreting calculated NRR values, ie, a direct comparison of NRR values for different options or a comparison of the NRR value of each option with a previously defined NRR cutoff level for acceptabiUty. The NPV, DTC, and NRR can be iaterpreted as discounted measures of the return, iavestment, and return rate, analogous to the parameters of the earher example. These three parameters characterize a venture over its entire life. Additional parameters can be developed to characterize the cash flow pattern duting the early venture years. Eor example, the net payout time (NPT) is the number of operating years for the cumulative discounted cash flow to sum to zero. This characterizes the early cash flow pattern it can be viewed as a discounted measure of the expected operating time that the investment is at risk. 

Another possibiUty is the net payout fraction (NPE), defined as the ratio of the NPT to the operating life of the venture. This is the fraction of the expected operating lifetime needed to recover the discounted investment. 

For this example, the tax-basis depreciation method in line-item 11 is a straight-line calculation based on the capitalized fixed capital, ie, fixed capital plus interest to the start of operation any salvage should be subtracted from the capitalized fixed capital and the result divided by the number of expected operating years to obtain the aimual tax-basis depreciation. 

To achieve the goal set above, measurements for reaction rates must be made in a RR at the flow conditions, i.e., Reynolds number of the large unit and at several well-defined partial pressures and temperatures around the expected operation. Measurements at even higher flow rates than customary in a commercial reactor are also possible and should be made to check for flow effect. Each measurement is to be made at point... 

Depreciation. This is a noncash cost that accumulates money to rebuild the facilities after the project life is over. There are usually two depreciation rates. One is the corporation s book depreciation, which reflects the expected operating life of the project. The other is the tax depreciation, which is usually the maximum rate allowed by tax laws. To be correct, the tax depreciation should now be called Accelerated Capital Cost Recovery System (ACRS). 

Linearity is the difference in the bias values through the expected operating range of the measuring device. 

Interstate pipelines also use computer simulation programs to calculate pipeline capacity, pressures, horsepower, fuel and other physical characteristics and properties of their systems. Using this information and incorporating variables such as ambient temperatures, facility outages, and changes in market patterns, transmission companies can run daily studies to determine how much natural gas their systems will deliver under expected operating conditions. 

The design velocity for selection of the holes also sets the minimum tower diameter. To take advantage of as much flexibility in operation as possible throughout the expected operating range, the following points should be considered in setting this velocity. 

Physical properties at expected operating temperatures. See Figure 10-112 for temperature-pressure effects in vertical thermosiphon reboilers. 

Allowing for pressure drop through piping, equipment, and control valves, establish the expected operating temperatures and pressures. 

Refer to Figure 11-51A for a diagram of the system. The selected conditions are also presented as a summary of expected operations. Figure 11-51B. 

This is too hot an installation for V-belt drives. However, they may be used if ventilation is good and perhaps an insulated hot wall is interposed between the sheaves and fan housing. Allowance must be made for belt losses from manufacturers tables and also any other mechanical losses of the driver. If a motor is used, the shaft output should be 5 hp to cover losses and allow for nonoverload. The 0.2 overload at peak conditions does not justify a 7.5 hp motor because expected operations will be at 3.0, and a 5 hp motor can usually be overloaded 10% without difficulty. 

Performance testing is long term (months to years). Once a potentially attractive formulation has been determined it is used to produce detailed data on its performance and behaviour as an anode material under the anticipated exposure conditions. For this reason the test should mirror as closely as possible the expected operating conditions, or where practicable be conducted in the field. Large specimens (tens or hundreds of kilograms) may be used for these tests. 

Conditioning Equilibrating a column with a flow of carrier gas (mobile phase) at the maximum expected operating temperature of the column. 

Pop = Normal expected or maximum expected operating pressure, psia... 

A plant having a shelf area of = 30 m2 has been loaded with 300 kg of water in trays and frozen on the shelves. Water vapor transport and condenser temperatures have been measured in this case between 0.4 and 0.6 mbar, which is approx, two to three times higher than the normally expected operation pressure of the plant (to get an measurable quantity of ice sublimed in a reasonable test time). The data of the test are shown in Fig. 2.19. Three Pt 100 (resistance thermometers) have been frozen in the ice. One CA each have been... 

The requirements on the measure-, control- and safety installations are described in Sections 2.2.8 and 2.4. The degree of automation of pilot plants will depend on the expected operation conditions. However it is recommended to automate the BTM and DR measurements, this being far more accurate and less tedious than hand operation and visual reading. 

Application of the expectation operation on both sides of equation (8.9) and substitution into Eq. (8.6) yields... 

The correlation coefficient measures the linear dependence between the two variables X and Y. Let us assume that they are perfectly correlated, i.e., Y = aX + b with a and b constant. The linearity of the expectation operator amounts to... 

This is typically tested for at least two flow rates. Typical flow rates that are chosen are within a range from 0.2 to 3.0mL/min. The specific flow rates tested will depend on the operating range of the pump and may be influenced by the user s expected operating range. 

Note The purchaser should consider an appropriate NPSH margin in addition to the NPSHR specified in 2.1.8 above. An NPSH margin is the NPSH that exists in excess of the pump s NPSHR (see 1.4.30). It is usually desirable to have an operating NPSH margin that is sufficient at all flows (from minimum continuous stable flow to maximum expected operating flow) to protect the pump from damage caused by flow recirculation, separation, and cavitation. The vendor should be consulted about recommended NPSH margins for the specific pump type and intended service. 

It is noteworthy that from a modeling perspective, 0j is also a scaling factor, since the expectation operator and the variance are of different dimensions. If it is desirable to obtain a term that is dimensionally consistent with the expected value term, then the standard deviation of z0 may be considered, instead of the variance, as the risk measure (in which standard deviation is simply the square root of variance). Moreover, 0i represents the weight or weighting factor for the variance term in a multiobjective optimization setting that consists of the components mean and variance. 

Some other sources have definitions that are different from the one given above [7,14]. The US Pharmacopeia [7] defines ruggedness as The ruggedness of an analytical method is the degree of reproducibility of test results obtained by the analysis of the same sample under a variety of normal test conditions, such as different laboratories, different analysts, different instruments, different lots of reagents, different elapsed assay times, different assay temperatures, different days, etc. Ruggedness is normally expressed as the lack of influence on test results of operational and environmental variables of the analytical method. Ruggedness is a measure of reproducibility of test results under normal, expected operational conditions from laboratory to laboratory and from analyst to analyst . In fact this is nearly the definition of reproducibility. This definition is also followed by other authors [15]. 

A well-designed QMS and the processes that comprise it require competent ownership with defined roles and responsibilities for program success. This combination ensures that the system and processes are established, maintained, improved, and remain current with industry practices and business expectations. Operational execution of the QMS and the processes comprising it will engage stakeholders, management, and leadership, provide business results, and support and ensure comphance. 

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