The Integration of Axiomatic and Experimental Design to Achieve Optimization Unclassified- בלמ"ס

1. The Integration of Axiomatic and Experimental Design to Achieve Optimization Unclassified- בלמ"ס Elie Louzon Apr. 2012 סימוכין: 5557073v1

2. What is Six Sigma ? Six Sigma isn't but a method based on data and mathematical tools for analyzing them. It is as well a way of behavior leading to a specific organizational culture. The expression "Six Sigma" refers to the statistical safety margin of the products key characteristics in relation to their failure threshold (tolerance limits). Six Sigma stands for six standard deviations distance from that failure threshold, meaning a very high (good) safety margin and indicating a potential failure rate of 3.4 per million operations (or parts) as depicted in the following figure. 6σ Elie Louzon סימוכין5557073v1 :

3. DOE as one of the Main Tools One of the tools aimed at achieving this goal is called "DOE=Design of Experiments". Through the results of a predetermined set of experiments (real or simulated), the effect of each DP on the RV's is predicted, and a model is formulated. Among all the solutions sample space, the optimal one is selected- RV’s being on target and mainly robust against all relevant noise factors, including process tolerances. DP = Design Parameter RV = Response Variable Elie Louzon סימוכין5557073v1 :

4. AxD – Axiomatic Design (Sue) The Axiomatic Design method is aimed at simplifying products design by creating independence between parts which accomplish different functions. Total independence is called "uncoupled" while partial independence is "decoupled". Analogically, one can refer to DP's as “parts” (since they are indeed parts attributes) and RV's (the quality characteristics of the product) as the “functional requirements”. Assuming uncoupling or decoupling of DP's can be achieved, the optimization process of the DOE will be easier. Elie Louzon סימוכין5557073v1 :

5. Example 1– The Water Faucet Old Faucet Configuration New Faucet Configuration Elie Louzon סימוכין5557073v1 :

6. Analogically, we can look for the relation between DP's and RV's since these are derived from decomposition of the parts and the functional requirements into their ingredients. When the relation between the DP's and the RV's do not seem independent, one can sometimes, by changing order and location of the variables involved, achieve a structure similar to the uncoupled or decoupled case. Step Optimization means that the solution for each variable is set one at a time without affecting the previous variables dealt with. Elie Louzon סימוכין5557073v1 :

7. Example 2: Multitask Cannon Suppose we want to use a multitask cannon to launch shells to a maximum distance and maximum impact (to assure operation of a contact fuse which depends on the impact intensity). We decided to check the dependence of the impact and distance on four DP's (weight, velocity, height and angle). The following AxD table depicts the interdependencies and as seen it is totally coupled. Elie Louzon סימוכין5557073v1 :

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9. DOE Table With Results Elie Louzon סימוכין5557073v1 :

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12. Comparison Table Elie Louzon סימוכין5557073v1 :

13. Summary Optimal solutions to a multi response variables case in a DOE, can lead us to an exhausting process (finding the wise optimal trade-off, using complex mathematical functions, which do not always converge to an acceptable solution). It has been proved that, the AxD method can easily be adapted to describe the system of relations between RV's (the decomposition of functional requirements) and DP'S (the decomposition of components). If no creative thinking is used (to change the basic concept), then I find the "AxD+DOE" method most convincing and promising. However, it would be fair to mention, that sometimes, the uncoupling or decoupling process becomes very difficult or impossible, so that the whole approach could fail, (causing us to give-in and move to the other classical methods). Elie Louzon סימוכין5557073v1 :

14. Thanks טל: 04-8794473 סימוכין 14 סימוכין5557073v1 :