Axiomatic Design Theory (Axiom 2)

Axiom 2 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. Note that uncertainty and vagueness both contributes to incompleteness or imprecision in information or data. How can we measure complexity? – difficulty to do or successful rate 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.

Axiom 2 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. The result of detailed design

Axiom 2  Probability to succeed in making 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, flight A is 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 is the probability of delay a particular airline company may make.  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 for Japanese airline company (assume it is), as it is quite on time in its operation. It would be more worrisome for Chinese airline company.  It is clear that two aspects need to be considered in determining the success of making a thing: desire to have a thing and means to make the thing.

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

Axiom 2 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 Design area System area / common area -> H. The smaller H, the easier to do. Probability density Length Assume uniform probability density System area: an area that represents the manufacturing capability: 1, 2, 3

Axiom Design area 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. Length Probability density

Axiom Design area 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. Length Probability density

Axiom Design area 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. Length Probability density

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. 10 Axiom 2

Information content, I, is defined by The overall information content can be calculated by 11

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 12

Summary 1.Given n designs, which one is the best? 2.The best design should have the minimum information content 3.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 4.In application, the key is to define design range and system range assuming that the probability density is uniform 13 N.P. Suh, The principle of design, Oxford University Press, 1990 Pages: beginning to 46-51; ;