Reliability analysis for uncertain competing failure degradation system with a change point

Modeling on dependent competing failure process (DCFP) with change points has been widely investigated in recent years. However, in actual engineering fields, the observed data of DCFP systems is often too limited to estimate the parameters and probability distributions by statistic methods, since the fundamental of probability theory will not satisfied, that is, the law of large numbers is no longer valid. Therefore, the reliability assessment for DCFP systems under small sample conditions is a challenge. This article proposes a modeling approach for DCFP systems with a change point that considers the uncertainty caused by small datasets. The system belief reliability is defined as the uncertain measure that the uncertain degradation does not exceed a threshold level (Formula presented.) and the uncertain external shocks do not cause the system failure. The system belief reliability is obtained by employing uncertainty theory under three different shock patterns. Finally, a numerical example is carried out to show the implementation of the proposed model.