Information axiom

Two axioms underlie axiomatic design—the independence axiom and the information axiom. 

The information axiom is based on information theory, which essentially says that the best design is the one with the least information content—while also satisfying the independence axiom. Information content is defined in terms of probability the more likely the design is to reduce the influence of variation from process parameter changes, different customer-usage conditions and repeated use, the better it meets the information axiom. 

A design that meets the information axiom is called a robust design (see Technique 38) because it maximizes the probability that it will meet its specihcations (process variables, or PVs) on an ongoing basis. For example, a process variable like tensile strength or data-entry errors can function as intended along a spectrum from zero to absolute perfection but in reality it always functions somewhere in between the two extremes. 

Your first objective with axiomatic design is to make your design as independent as possible with reference to functionai requirements. After this you wouid make it as robust as possible, as per the information axiom, using such techniques as Robust Design (Technique 38), Design FMEA (Technique 40), and Mistake Proofing (Technique 49). 

While zigging and zagging, the designer ensures that each set of lower-order FRs, DPs, and PVs retains as much independence as possible and also fulfills the information axiom. 

The second axiom, the Information Axiom, makes it possible to benchmark different design alternatives by comparing their information content. The design, which offers the lowest information content, that is the design with the highest probability of success, will be selected. Information content, 7, can be expressed by the following logarithmic function ... 

Kim (2004) illustrated the four causalities of complexity with respect to the design axioms (Fig. 2). Type 1 complexity is a result of heavy coupling of the functional requirements, which is a violation of the independence axiom. Time-independent complexity is a type II complexity and is a result of the information axiom violation. 

Axiomatic design (AD) is a systems design methodology using matrix methods to systematically analyze the transformation of customer needs into functional requirements, design parameters, and process variables [25]. Hereby, the attempt is made to build on the development of new products based on a system of axioms, which are based on mathematics or physics sciences. The formalization is supposed to lead to the design of technical systems. Starting from two axioms (the independence axiom and the information axiom) a system of theorems is set up. 

We have already seen hints of the kinds of theories that are possible using the first axiom see Kantor s Information Mechanics (section 12.4.5), Stonier s Information Physics (section 12.4.6) and Frieden s Extreme Physics Information Principle (section 12.4.7). Minsky, Zuse and Fredkiii, among many others, have speculated on a CA-like dynamics of primitive information (see section 12.6). 

Evidence theory also known as the Dempster-Shafer theory, has been first introduced by Dempster [5], then formalized by [25] and finally axiomized later into the framework of the Transferable Belief Model (Evidence theory) by Smets [28]. The Evidence theory can be understood as an alternative to probability theory for the representation of uncertainty It allows one to manipulate non-necessarily exclusive events and thus to represent explicitly information uncertainty... 

In this chapter, we examine the environmental chemistry associated with both global and local issues. One goal of this chapter is to provide a balanced perspective on the subject. This in turn should help the reader use chemistry to make informed decisions about environmental issues. An axiom of the environmental movement is to think globally and act locally. While both global and local issues will be treated separately, the nature of having an enviromnen-tal perspective means knowing that local decisions made by many individuals cumulatively have global consequences. 

The operator serves to extract information from the state vectors and may correspond to any physical observable such as position, momentum, angular momentum (spin or orbital) or energy. The state vector itself is not observable. In most systems the number of eigenfunctions is infinite and it is an axiom of quantum mechanics that the set of all eigenfunctions of a Hermitian operator forms a complete set. These eigenfunctions define a Hilbert space on which the operator acts. 

The MEP is now well known to set an axiom of modem statistical mechanics [12-14]. The Shannon information entropy... 

My purpose here is to join these two lines of thought in a single comprehensive theory. The theory is not a formal one of the type most frequently encountered in textbooks, with attendant definitions, axioms, postulates, and laws. Rather it is an informal theory of the sort that most often guides psychological research. At its heart is the premise that a schema consists of several different kinds of knowledge, as described later. A second and equally essential premise is that schema functioning involves both parallel and sequential processing. Both of these ideas have been noticeably absent from previous theories. 

This information comes from the National Safety Council, inter alia, and is by no means complete. To the axiom,... 

C[ and Cj are the concepts of nodes i and j in the two schemas, as generated in the first step and C is the conjunction of all the relations that hold between concepts of labels mentioned in C, and Cj (this includes all nodes on the path to nodes i and j). This is done by using a SAT solver to test unsatisfiability. It is worth noting that the unsatisfiability problem is known to be CO-NP, yet modern SAT solvers have shown very good performance in solving such problems. To reason about relations between concepts of nodes, a set of premises (axioms) is built as a conjunction of the concepts of labels computed in the third step. For example, R. Card Info, type will be defined to be subsumed by S. Card Information while an equivalence semantic relationship is defined between R. Card Info, type and S.Cardlnformation.type. 

This introductory chapter describes the scope of the book and gives a brief summary of the history, advantages, limitations, and some common-sense axioms of HPLC. Major separation modes are discussed and illustrated with examples. Information resources on HPLC are also listed. 

Sometimes there are some situations that the knowledge of an event B does not give us any more information about A than what we already had. Like this situation the event A is called independent of the event B if P(A B) = P A). In this case, we have the following axiom ... 

Local information systems, 68, 107 Locality, axiom of, 1734 Local optima, 2590... 

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