# Secure Business Secure Proprietary of RAFAEL - Advanced Defense Systems LTD. סימוכין: 5557073v1 1 The Integration of Axiomatic and Experimental Design.

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Secure Business Secure Proprietary of RAFAEL - Advanced Defense Systems LTD. סימוכין: 5557073v1 1 The Integration of Axiomatic and Experimental Design to Achieve Optimization Unclassified- בלמ"ס Elie Louzon Apr. 2012

Secure Business Secure Proprietary of RAFAEL - Advanced Defense Systems LTD. סימוכין5557073v1 : 2 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. What is Six Sigma ? 6σ6σ Elie Louzon

Secure Business Secure Proprietary of RAFAEL - Advanced Defense Systems LTD. סימוכין5557073v1 : 3 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 ParameterRV = Response Variable DOE as one of the Main Tools Elie Louzon

Secure Business Secure Proprietary of RAFAEL - Advanced Defense Systems LTD. סימוכין5557073v1 : 4 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. AxD – Axiomatic Design (Sue) Elie Louzon

Secure Business Secure Proprietary of RAFAEL - Advanced Defense Systems LTD. סימוכין5557073v1 : 5 Example 1– The Water Faucet Old Faucet Configuration New Faucet Configuration Elie Louzon

Secure Business Secure Proprietary of RAFAEL - Advanced Defense Systems LTD. 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

Secure Business Secure Proprietary of RAFAEL - Advanced Defense Systems LTD. סימוכין5557073v1 : 7 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. Example 2: Multitask Cannon Elie Louzon

Secure Business Secure Proprietary of RAFAEL - Advanced Defense Systems LTD. סימוכין5557073v1 : 8 Elie Louzon

Secure Business Secure Proprietary of RAFAEL - Advanced Defense Systems LTD. סימוכין5557073v1 : 9 DOE Table With Results Elie Louzon

Secure Business Secure Proprietary of RAFAEL - Advanced Defense Systems LTD. סימוכין5557073v1 : 10 Elie Louzon

Secure Business Secure Proprietary of RAFAEL - Advanced Defense Systems LTD. סימוכין5557073v1 : 11 Elie Louzon

Secure Business Secure Proprietary of RAFAEL - Advanced Defense Systems LTD. סימוכין5557073v1 : 12 MethodAnglei-speedHeightMassRH Max R, H2074714 AD+DOE0.852001041910608 Taguchi0.852001541884589 Desire fct10.85200123.71880561 Desire fct20.952001241867649 Comparison Table Elie Louzon

Secure Business Secure Proprietary of RAFAEL - Advanced Defense Systems LTD. 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

Secure Business Secure Proprietary of RAFAEL - Advanced Defense Systems LTD. סימוכין5557073v1 : 14 24.12.2002 סימוכין 14 טל: 04-8794473 Thanks

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