Reliability analysis of a rangeland system: the application of Profust theory

Reliability is the ability of a system to perform its required functions under stated conditions for a specified period of time. A number of researchers from various research backgrounds have shown that the binary state assumption in the traditional reliability theory (e.g., defining a natural system as fully failed or functioning) is not extensively acceptable, and thus the fuzzy state assumption should be used to replace the binary state assumption. In the present paper, the concept of profust reliability theory is introduced and a conceptual model of profust reliability for reliability analysis of a rangeland system, on the basis of the fuzzy state and the probability assumptions, is developed. This model is consisted of two parts, the fuzzy part which considers the vagueness in the system failure and the probabilistic part that incorporates the failure randomness in the reliability analysis. The ability of this model in reliability analysis of a natural system is illustrated for a real case study of rangeland system. For this purpose, the failure is defined as the rangeland system's transition from its normal state. Generally, such transitions take place as a result of drought events. Furthermore, to determine the randomness in failure a conditional probability formulation is developed. This formulation determines the probability of the next drought duration, given the amount of severity in the present state. The result shows that the rangeland system reliability has been increased by 22% after constructing eight floodwater spreading systems.