The output variability is the variability of a performance measure induced by the input variability, or randomness of the input variable. The analytical form of the output variability is difficult to obtain, while the input variability can be represented analytically using the input joint probability density function (PDF). The absence of the analytical output variability impedes the accurate evaluation of probability of failure (PoF), the effect of output variability on a product design. For this reason, reliability analysis methods have been researched to effectively approximate PoF. The first-order reliability method (FORM) and the second-order reliability method (SORM) calculate the PoF using first- and second-order Taylor series expansion, respectively [1–7]. In addition, the dimension reduction method (DRM) uses higher-order approximation with additional function evaluations [8,9]. The most probable failure point (MPFP), where the PoF is approximated, is necessary in the reliability analysis methods, and the sensitivity (gradient) of the performance measure is required to find the MPFP. Hence, the aforementioned methods can be categorized as sensitivity-based reliability methods. Based on the sensitivity-based methods, RBDO has been developed to obtain a reliable and cost-effective design under the output variability. For the sensitivity-based RBDO, the performance measure approach (PMA) [2] has been developed using concept of MPTP and probabilistic constraint from the aforementioned methods in Refs. [1–8]. PMA method finds RBDO optimum design showing a more stable and robust nature in the RBDO process [2]. To find MPTP in PMA efficiently, the advanced mean value (AMV) [10,11] method is used first. Recently, more advanced methods, such as hybrid mean value (HMV) [12], enriched HMV (HMV+) [13,14], hybrid chaos control (HCC) [15], adaptive chaos control (ACC) [16,17], self-adaptive modified chaos control (SMCC) [18], adjusted advanced mean value (AAMV) [19], and relaxed mean value (RMV) [20] methods, have been developed to improve convergence of MPTP search in PMA for highly nonlinear performance measure.