The Iterative Nature of the “Zig” and How to Define the “Hows”

The AD's design equation depicts the relationship between the functional requirements (FR) and the design parameters (DP) by the design matrix (DM), through a unique zigzag decomposition path. At the “zig part” of each level of the zigzag decomposition, the designer needs to find out the DPs that can fulfil the given FRs. This paper proposes that the designer has to perform three main actions in a zig process in order to define the design equation: to define the DPs at a nominal condition and its magnitude; to evaluate the interactions of the DP with the system at actual conditions; and to check back the set of FRs verifying if they fit inside the design range. The purpose of this paper is to illustrate the actions performed on a zig, emphasising the changes that may occur in the arrangement of the design during the synthesis of the DM at any level of the decomposition. At each level of decomposition, the estimation of the DPs that fulfil the FRs allows the designer to define a subset of the DM, making it possible to evaluate afterwards the DM with all the interactions of the system. Moreover, in what concerns to the information content, it is possible to evaluate the probability of success of the system taking into account the interactions of the system and the tolerances of the DPs. This paper presents an example regarding the evaluation of the DM using the equations of the design for a variable air volume (VAV) air conditioning system.