Inverse reliability measures and reliability-based design optimisation

Several inverse reliability measures (e.g. Probabilistic Performance Measure (PPM) and Probabilistic Sufficiency Factor (PSF)) that are essentially equivalent have been introduced in recent years as measures of safety. The different names for essentially the same measure reflect the fact that different researchers focused on different advantages of inverse measures. These advantages include improved computational efficiency of Reliability-Based Design Optimisation (RBDO), accuracy in Response Surface Approximations (RSAs) and easy estimates of resources needed for achieving target safety levels. This paper surveys these inverse measures and describes their advantages compared with the direct measures of safety such as probability of failure and reliability index. Methods to compute the inverse measures are also described. RBDO with inverse measure is demonstrated with a beam design example.