Reliability optimization can be applied to find parameters that increase reliability and decrease costs, in the presence of uncertainty. Nowadays, with the increasing complexity of systems, it is important to find suitable optimization methods. In this regard, we can refer to gradient-based optimization methods. The power of stochastic gradient-based approaches in optimization under uncertainty resides in efficiency in using sampling information. These methods allow applying a small sample size in updating problem parameters. Using a small sample size also has its disadvantages, and it leads to oscillation around the minimum point when approaching the minimum. One of the ways to solve this problem is to use progressive batching. Here, to increase stability Progressive Batching L-BFGS (PB-LBFGS) and Progressive Batching LBFGS with momentum (PB-mLBFGS) are used for reliability optimization, and with an example, the effectiveness of these approaches is compared with some other optimization methods.

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