Reliability assessment for systems suffering competing degradation and random shocks under fuzzy environment

Reliability assessment of multi-component systems under competing degradation and random shocks has been intensively investigated in recent years. In most cases, the parameters associated with competing degradation and random shocks are represented by crisp values. However, due to insufficient data and vague judgments from experts, it may produce epistemic uncertainty with those parameters and they are befitting to be described as fuzzy numbers. In this article, the internal degradation is treated as a continuous monotonically increasing random process with respect to operating time, whereas the amount of cumulative damage produced by each external random shock is modeled by a geometric process. As components in a system suffer the same environmental condition, an external random shock will produce different amounts of cumulative damage to each component simultaneously. Each component fails when either the internal degradation or cumulative damage from the random shocks, whichever comes first, exceeds its corresponding random thresholds. Moreover, the parameters associated with the internal degradation and the random shocks are represented by triangular fuzzy numbers. The fuzzy reliability functions of components and the entire system are evaluated by a set of optimization models. A multi-component system, together with some comparative results, is presented to illustrate the implementation of the proposed method.