Probability box as a tool to model and control the effect of epistemic uncertainty in multiple dependent competing failure processes

Engineering components and systems are often subject to multiple dependent competing failure processes (MDCFPs). MDCFPs have been well studied in literature and various models have been developed to predict the reliability of MDCFPs. In practice, however, due to the limited resource, it is often hard to estimate the precise values of the parameters in the MDCFP model. Hence, the predicted reliability is affected by epistemic uncertainty. Probability box (P-box) is applied in this paper to describe the effect of epistemic uncertainty on MDCFP models. A dimension-reduced sequential quadratic programming (DRSQP) method is developed for the construction of P-box. A comparison to the conventional construction method shows that DRSQP method reduces the computational costs required for P-box constructions. Since epistemic uncertainty reflects the unsureness in the predicted reliability, a decision maker might want to reduce it by investing resource to more accurately estimate the value of each model parameter. A two-stage optimization framework is developed to allocate the resource among the parameters and ensure that epistemic uncertainty is reduced in a most efficient way. Finally, the developed methods are applied on a real case study, a spool valve, to demonstrate their validity.