Reliability parameter sensitivity based on failure probability integration and Markov chain simulation

Reliability Sensitivity (RS) is usually defined as partial derivatives of failure probability with respect to distribution parameter of basic random variable. Based on the definition of failure probability, the integration of joint Probability Density Function (PDF) of the basic random vector in failure region, an efficient RS analysis method is presented by use of Markov chain simulation, which possesses high efficiency to draw samples from the interested region. The presented method is suitable for a system with single failure mode or with multiple faiure modes. The RS can be expressed as an expectation of a function related to PDF in failure region. The expectation is evaluated by means of samples in failure region, and the samples in failure region are drawn by Markov chain simulation. Since Markov chain simulation can efficiently draw sample from the interested region, the presented method has higher efficiency than the method based on Monte-Carlo simulation, especially for the small failure probability cases. After explaining the basic concept and the detailed implementation, a few examples are given to illustrate the rationality and the feasibility of the presented method.