Application of Statistical Processes on a Set Theory Model for Anomaly Handling in System Requirements Analysis
James A. Sanchez · INCOSE International Symposium · 1996
Abstract In 1995 Ronald Carson developed a mathematical model for system requirements analysis (SRA) utilizing set theory to explicitly treat unwanted or unexpected conditions that may be experienced by the system being analyzed. He showed that the SRA model can be used to derive completeness criteria. He claimed that the highest utility of the model would be found in the area of software requirements because of the focus on system states. A simple example using a Power Distribution Unit (PDU) was made in order to clarify the salient points. This simple example had only three states and six transitions, which were identified as nine antecedents (conditions which precede). Eight requirements were generated for the PDU. In this paper, the author assumes that the requirements for this simple example are stochastic, rather than deterministic, in nature. The arguments in support of this assumption are compelling. One is that many processes which are defined by a set of requirements are themselves stochastic in nature. Another is that a near deterministic model can be developed from a stochastic model in many applications. One can also argue that a stochastic process is more robust and better suited to a set of requirements subject to change due to ambiguities in syntax or lexicon or in how a system is thought to behave. The entire set of requirements constitutes the probabilistic universe of the system. Each requirement has a probability associated with it that the requirement is satisfied. Furthermore, the requirements may have dependencies. The methodology is developed from simple Bayesian relationships that have been used in a number of computer automated tools. What may seem different is that the probability is a characteristic of the antecedent rather than the requirement itself. This model, though not desirable for all classes of requirements, may fit a number of situations where the outcome of the requirement is not certain. In conclusion, the SRA model utilizing elementary set theory is expanded from a deterministic system to a stochastic system. The method is rigorous, and can account for 1) ambiguities in language, 2) unforeseen conditions, 3) undefined initial conditions, and 4) probability density function of primitives. It can also make the system defined by a set of requirements more robust.