# Vol.5 No.1 2012 10/82

Research paper : Construction of a traceability matrix for high quality project management (A. Sakaedani et al.)−7−Synthesiology - English edition Vol.5 No.1 (2012) is most effective for reducing the complexity of the whole project is found in order to improve the project status. What follows is an explanation following the PDCA cycle.5.1 PLAN5.1.1 Uncovering the element and organizing the relationshipsThe analysis of the project status is conducted as shown in Fig. 4, the elements needed for the creation of system matrix are uncovered, and their relationships are organized. However, it can be expected that the system matrix cannot be created because the granularity of the elements may vary or the relationships are unknown. In that case, it can be assumed that there is some sort of problem in the project plan itself, and the solution is sought. 5.1.2 Organize the issues of the project planFor example, if there is a team where the organization is loose and capable of being described in large granularity only, it is necessary to reorganize such a team. In another example, when elements are uncovered in the upstream process, the component and function may not be clear in the downstream process. In such a case, it is necessary to check the basis of the estimate. There must have been some basis when making the estimate, and if the basis is unclear, it is necessary to review the plan quickly, as an issue in establishing the project plan.The above points are organized, and system matrix s and system matrix n are created. 5.1.3 Reduction of the interdependency and difficulty of individual matrices and the evaluation of complexityImprovements are done to diagonalize the individual matrices. However, there may be cases where the difficulty of an element increases as a result. Moreover, there may be cases where the difficulty of the elements of the non-diagonalized matrices may increase. Therefore, it is always necessary to check the degree of influence on the whole project by calculating the complexity, to maintain the overview of the project.As shown in Fig. 3, the system matrix that shows the project structure is calculated by the multiplication of seven matrices. Due to the properties of matrix multiplication, the solution of the calculation for the full matrix or one that contains a triangular matrix will always be the full matrix or the triangular matrix. To obtain the diagonal matrix as a solution, it is necessary to make each matrix into a diagonal matrix.In step 1, the relationships of each of the seven matrices that constitute system matrix s are organized, and the interdependency is reduced by approximating the diagonal matrix. In step 2, the difficulty of the matrix is reduced by reducing the relationship with highest component value among the relationships organized in the matrices that compose system matrix n, or the relationships with high degree of difficulty. The complexity (= interdependency × difficulty) of the whole system matrix is reduced by the above technique.However, in a real project, it is difficult to diagonalize all seven matrices of system matrix s. Therefore, the design of the project is improved (reduction of interdependency) by, for example, forming the triangular matrix for each matrix. The relationships among the elements are more simply by, for example, introducing some development tool, in order to reduce the component value of system matrix n (reduction of difficulty). There is also a plan to reduce the complexity of the whole project. As an alternative plan for effective improvement, the full matrix is concentrated into one or two matrices of the seven matrices of system matrix s, the remaining five or six matrices are diagonalized, and thereby the component value of system matrix n is made as low as possible. In this way of thinking, while some parts of the full matrix may have high complexity, by reducing the complexity of the diagonalized area, the complexity of the whole is reduced. However, since some cases may not necessarily be effective for decreasing the complexity, it is necessary to conduct a comparative review by simulation at the design stage of the project.For example, in planning scratch developmentTerm 10 where software is all made by hand, the case of using the tool to automatically generate the source code (hereinafter, called “generator”) or the case of using the package software (hereinafter, called “PKG”) are considered to reduce the complexity. The flow of this review will be explained (Fig. 5). The relationship of the whole elements when scratch development is done is shown in Reference Material 3. The elements that are considered particularly important are extracted in Fig. 6. The figure deals with only the screen Fig. 5 Evaluation flow of complexity considering the interdependency and difficultyCheck effect of complexity according to the change in difficultyComplexity is at minimum valueInterdependency is at minimum valueCheck effect of difficulty in simplifying the artifact-component-function relationshipsConsider use of generator or PKG as methods to simplify the artifact/component/function relationshipsSelect generator useEvaluation of complexity of PKG use and other optionsConsider selection of using generator or PKGEvaluation of difficulty when PKG is usedSelect PKG useReview reduction method for interdependency of scratch development project

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