Modeling Failure Rate Time Series by a Fuzzy Arithmetic-based Inference System

In this study, a fuzzy arithmetic based inference system is introduced to model and forecast linear trends of empirical failure rate time series. Here, a simple heuristic is introduced to form the membership functions of the fuzzy rule antecedents, while each rule consequent is treated as a fuzzy number composed of a left hand side and a right hand side fuzzy set, each of which is given by a sigmoid membership function. The novelty of the proposed method lies in the application of pliant arithmetics to aggregate separately the left hand sides and the right hand sides of the individual fuzzy consequents, taking the activation levels of the corresponding antecedents into account. Here, Dombi's conjunction operator is applied to form the fuzzy output from the aggregates of the left hand side and right hand side sigmoid functions. The introduced defuzzification method does not require any numerical integration and its speed is independent of the number of fuzzy rules. The output of the pliant arithmetic based fuzzy inference system is used to predict linear trends of failure rate time series. Next, the modeling capability of the introduced methodology is compared to that of an Adaptive Neuro-Fuzzy Inference System. Based on the results, our method may be viewed as a viable alternative modeling and prediction technique.