Factorial coding

J. P. Nadal and N. Parga, Nonlinear neurons in the low noise limit a factorial code maximized information transfer, Alenvorl 5 565-581 (1994). 

The factory code in the manual of the device shows the correlation of the charger to the battery. Later in the plant during operation, if necessary, an adjustment can be performed, but only by educated staff. 

The linear regression calculations for a 2 factorial design are straightforward and can be done without the aid of a sophisticated statistical software package. To simplify the computations, factor levels are coded as +1 for the high level, and -1 for the low level. The relationship between a factor s coded level, Xf, and its actual value, Xf, is given as... 

A 2 factorial design with two factors requires four runs, or sets of experimental conditions, for which the uncoded levels, coded levels, and responses are shown in Table 14.4. The terms Po> Po> Pfc> and Pafc in equation 14.4 account for, respectively, the mean effect (which is the average response), first-order effects due to factors A and B, and the interaction between the two factors. Estimates for these parameters are given by the following equations... 

Example of Uncoded and Coded Factor Levels and Responses for a 2 Factorial Design... 

Table 14.5 lists the uncoded factor levels, coded factor levels, and responses for a 2 factorial design. Determine the coded and uncoded empirical model for the response surface based on equation 14.10. 

A 2 factorial design was used to determine the equation for the response surface in problem lb. The uncoded levels, coded levels, and the responses are shown in the following table. 

Labelling die variables as T, S and M, widi reference symbols, a, b, c respectively in trials involving a low (1) and high (h) levels of each variable, each trial having die result jc, die factorial procedure would produce die design code as follows ... 

Factory tests establish the pressure head, power, efficiency and NPSH over the complete flow range the pump can deliver running at design speed. British Standard, DIN standard or ANSI standard codes or national variations from such main codes lay down the manner of test procedure, and a minimum requirement is quite often defined by industry codes such as API 610. This is not the place to discuss instrument accuracy, as the codes lay down the limits possible from conventional instruments. There are two main classes of test the commercial requirements normally possible in the maker s test plant and high-accuracy tests that are only possible by using substandard instruments and very sophisticated techniques. 

Ensure that the application of a protective coating (applied in situ or in a factory) is adequately supervised and inspected in accordance with the specification or code of practice. 

Several industry standards, codes, and company internal standards were used in developing the information in Table 1.2. These include internal company standards NFPA 30, Flammable and Combustible Liquids Code (Ref. 22) NFPA 59A. Liquefied Natural Gas (Ref. 23) API 2510, Design and Construction of Liquefied Petroleum Gas(LPG) Installations (Ref. 24) iRlnformation IM.2.5.2, Plant Layout and Spacing for Oil and Chemical Plants (Ref. 25), and Factory Mutual 7-44, Spacing of Facilities In Outdoor Chemical Plants (Ref. 26). 

Types that define the behavior expected at the interfaces to classes. Classes implement types. In some design styles, all parameters and variables are declared with types classes are referred to in the code only to instantiate new objects, and even that is encapsulated within factory objects. 

But there is one case in which this does not work well When you want to create an object, you must say which class you want it to belong to. However, there are a number of patterns, such as Factory, that help localize the dependencies, so that adding a new Shape to the drawing editor (for example) causes only one or two alterations to be necessary to the existing code. 

Calculations for factorial designs are often greatly simplified if coding of factor levels is employed (see Section 8.5). For the present example, setting c,i = c = 5... 

Inspection of the coded experimental design matrix shows that the first four experiments belong to the two-level two-factor factorial part of the design, the next four experiments are the extreme points of the star design, and the last four experiments are replicates of the center point. The corresponding matrix for the six-parameter model of Equation 12.54 is... 

Factorial designs are usually discussed in terms of coded factor spaces. Table 14.1 shows some of the common coding systems for two- and three-level designs. Our emphasis in this chapter will be on the two-level designs. 

Common coding systems for two- and three-level factorial designs. 

Notice that this is an orthogonal design in coded factor space (-1 and +1) any one column multiplied by any other column will give a vector product of zero. Other saturated fractional factorial designs may be found in the literature [Box and Hunter (1961a, 1961b), Anderson and McLean (1974), Barker (1985), Bayne and Rubin (1986), Wheeler (1989), Diamond (1989)]. 

Calculate the grand average (MEAN), the two classical main effects (A and B), and the single two-factor interaction (AB) for the two-factor two-level full factorial design shown in the square plot in Section 14.1. (Assume coded factor levels of -1 and +1). 

---