Stochastic and fuzzy analyses in reliability design

Abstract

The risk analysis process involving information acquisition, modeling, analysis, and decision steps results in the product design improvement. To perform product risk assessment, this study addresses stochastic and fuzzy analyses in reliability design. Using decision-making techniques and the flow-graph concept, the main objective of this study is to develop analytical models with time varying input data, and/or fuzzy input data for reliability techniques. The models (i.e., Graph-based failure effects analysis, Group-based failure effects analysis, Imprecise-chance Markov chains, Fuzzy and stochastic fault tree analysis, Binary k-out-of-n system with self-loop units, Reversible multi-state k-out-of-n:G/F/Load sharing system, and Imprecise-chance reliability estimation) incorporate the stochastic self-healing mechanisms represented by self-loop graph, and/or conflict resolution approach. Stochastic models developed in this study compute Time-To-Event/State data made up of probability of the system failure, and mean and standard deviation of time to an event/state. To identify, prioritize and eliminate potential failures in the system, the fuzzy models presented in this study introduce aggregated/compensated approaches for mitigating conflict of input data. The applications of the stochastic and fuzzy models are demonstrated through practical examples. Using typical, practical, and extreme values of the basic parameters of the models and performing sensitivity analysis, the end results demonstrate the robustness of and conflict resolution capability of the models.