A System Engineering Approach to Mathematical Properties of System Readiness Level Open Access
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System engineers use qualitative and quantitative measurements in their work. The use of quantitative measurements is growing but the mathematical rigor behind these measurements is not always done and presented in the literature. Without the mathematical rigor misleading results can occur. System readiness level (SRL), is a new quantitative measurement being developed as a decision-making aid for system engineers and program managers. The SRL was first developed by Sauser et al  and is continuing to be developed and refined, by Sauser and others. The SRL is defined as a function of technology readiness level (TRL) and integration readiness level (IRL), both of which are ordinal ranking numbers. Currently matrix algebra, with and without graph theory, is being used to define this function. Concern has been voiced in the system engineering community about the continuous development of the SRL without the proper mathematical rigor being conducted. This dissertation examines the development of the SRL, the intended use of the SRL, the mathematical operations that have been proposed for calculating SRL and the inherent mathematical properties of these operations. This dissertation develops and defines desired mathematical properties that a quantitative measurement used to define the readiness level of a system should possess. These mathematical properties are introduced to increase the validity and rigor of SRL calculations, increasing the confidence system engineers and program managers will have in the calculated SRL for their system and the decisions made based on these calculations. Through the development of the mathematical properties a new method for calculating SRL was formulated. This new method uses tropical algebra as the mathematical operation for calculating SRL. Tropical algebra, an area of mathematics, combines ordinal numbers using addition, versus multiplication like matrix algebra. Addition of ordinal numbers is more meaningful than the multiplication of ordinal numbers; therefore the resulting SRL will be more meaningful to the system engineer and program manager when making resource allocation decisions and technology selections.