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Axiomatic Design Theory (Axiom 2)

Axiomatic Design Theory (Axiom 2). Axiom 2. Motivation for Axiom 2: There may be more than one design that satisfies with Axiom 1. The problem is to select one of them. Such a selection process demands criterion or criteria. Is there any generic criterion or criteria?

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Axiomatic Design Theory (Axiom 2)

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  1. Axiomatic Design Theory (Axiom 2)

  2. Axiom 2 Motivation for Axiom 2: There may be more than one design that satisfies with Axiom 1. The problem is to select one of them. Such a selection process demands criterion or criteria. Is there any generic criterion or criteria? Complexity of making or manufacturing designs. What is complexity? Uncertainty and vagueness of information that is presented in a design specification for a system. How can we measure complexity? – difficulty to do There are two aspects: (a) design or plan and (b) manufacturing and implementation, because difficulty to do depends on different techniques or tools used just the same as for a same problem, one human may feel difficult while another may feel not difficult.

  3. Axiom 2 The result of detailed design Example 1: A design specification for a shaft is as follows: length of the shaft is 10 with a tolerance being ±0.10 mm. Tool 1: measurement ability: 0.01 mm Tool 2: measurement ability: 0.05 mm Tool 3: measurement ability: 0.20 mm Comment: From the above, we can see that tool 1 can achieve the design specification with the highest successful rate. Yet, tool 3 may never be able to make the shaft to satisfy the requirement. Need to define a quantity to represent the easy or difficult state to fulfill this task.

  4. Axiom 2 • Probability to succeed in make a product based on the design result or design specification. In this case: make = measure. • Probability of a variation on DP (in the process of fulfilling FR). For instance, in travel, one flight A to connect flight B. The connection time is the concept of DP. It depends on what airline and country you take the flight. • Probability of a variation of a system to make it happens. In the case of travel, the probability of delay of a particular airline company makes sense. • For the travel example, if the connection time is 40 minutes, and if A flies from Saskatoon to Calgary, and A and B are connecting in Calgary, then I would say it is possible or not quite difficult, as air Canada (assume it is) is quite on time in their operation. • It is clear that two aspects need to be considered: desire and realization.

  5. Black-area where the measurement tool cannot reach Axiom 2 Probability density 10 10 + 0.1 10 - 0.1 Assume uniform probability density 3 2 1 H Length 10±0.10 means that the true length will be within 10-0.10 and 10+0.10. Design area Remark: by assuming a total area is 1 (probability theory), we can determine the height H in the above figure.

  6. Axiom 2 Probability density Design area Assume uniform probability density 10 + 0.1 10 10 - 0.1 2 3 1 Length 1: the maximum common area with design range. 3: the minimum (or no) common area with design range. 2: the common area with design range is less than that for tool 1. System area: an area that represents the manufacturing capability: 1, 2, 3 System area / common area -> H. The smaller H, the easier to do.

  7. Axiom 2 Probability density 10 10 + 0.1 10 - 0.1 Design area Length System range for 1. Notice that we need to make the area be 1 according to the concept of probability density function (PDF). As well, we can see: range replaces area.

  8. Axiom 2 Probability density 10 10+0.1 10-0.1 Design area Length System range for 3. Notice that we need to make the area be 1 according to the concept of probability density function (PDF). As well, range replaces area.

  9. Axiom 2 Probability density 10 10+0.1 10-0.1 Design area Length System range for 2. Notice that we need to make the area be 1 according to the concept of probability density function (PDF). As well, range replaces area.

  10. Axiom 2 • Design range is the range of values of the DP that will satisfy the FR; • System range is the range of values of the DP which can be made by a manufacturing system or system; • The common range is the intersection of the system range and the design range.

  11. Axiom 2 • Information content, I, is defined by • The overall information content can be calculated by

  12. Axiom 2: Information Content • Information content of designs should be minimized. Among designs that satisfy function requirements, the design with the minimum information content has the highest probability of success. • The information axiom provides a quantitative way to select the optimum from design solutions

  13. Summary • Given n designs, which one is the best? • The best design should have the minimum information content • Information content is a measure of the complexity of a design in the context of means or systems that are available to make the design • In application, the key is to define design range and system range assuming that the probability density is uniform N.P. Suh, The principle of design, Oxford University Press, 1990 Pages: beginning to 46-51; 147-153; 307-311.

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