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

Abstract

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.

Drought Frequency Analysis Using Hidden Markov Chain Model and Bivariate Copula Function

“…특히 가뭄해석 연구에서는 지속시간, 심도, 강도 등 가뭄 특성 인자의 발생분포 특성을 다변량으로 해석하는 연구가 활발히 이루어지고 있다 (Bonaccorso et al, 2003;Kim et al, 2003;Salas et al, 2005;Mirakbari and Ganji, 2010). 가뭄 특성인자들의 다변량 의존구조를 고려한 빈도해석을 수행 시 최근에는 코플라를 이용한 해석이 다수 이루어지 고 있다 (Zhang and Singh, 2006;Govindaraju, 2007, 2010).…”

Multiyear Discrete Stochastic Programming with a Fuzzy Semi-Markov Process

“…As the difference between irrigation water demanded and supplied increases, severity of drought intensifies along a continuous gradient. While the characterization of drought varies across studies, the following definition of drought provided by Yevjevich [14] has been widely used [6] [15] [16]:…”

“…When economic models represent drought in binary terms (i.e., a water allocation either qualifies or does not qualify as drought), this overly-simplified or deceivingly-crisp (as opposed to fuzzy) measurement of drought severity can cause inefficient resource allocation. Unlike this crisp set (in which an element is either a member of the set or not), fuzzy sets allow elements to be included through a degree of membership, as expressed by a membership function, thus relaxing the binary state assumption [6] [17]. Introduced by Zadeh [18], fuzzy logic and fuzzy set theory have since been widely adopted to deal with linguistic vagueness in various mathematical optimization models, including fuzzy dynamic programming [19] [20], and optimal fuzzy control [21].…”

“…They left more sophisticated approaches to these three modeling issues-linguistic vagueness, assumption of independence of yearly water allocation, and more complex assumptions about uncertainty of drought duration-for future research. Uncertainty caused by linguistic vagueness has been dealt with more recently using fuzzy logics [6]. A principal difference between discrete-stochastic and fuzzy optimization approaches is in the way uncertainty is modeled: discrete stochastic programming represents random parameters through discrete or continuous probability functions, whereas fuzzy programming treats random parameters as fuzzy numbers and hence constraints as fuzzy sets [7].…”

Fuzzy availability modeling and analysis of biscuit manufacturing plant: a case study

“…In fact, if the system fails due to the failure of a key component, it is rational and practical to repair a key component so that the system will soon function again after repair. Mirakbari and Ganji (2010) developed a new profust model of reliability evaluation as an appropriate tool to evaluate possibility of improvement in rangeland condition where the water management of the system has been changed. Profust reliability theory is based on the fuzzy state assumption and the probability assumption.…”