Resilience is a system’s ability to withstand a disruption and return to a normal state quickly. It is a random variable due to the randomness of both the disruption and resilience behavior of a system. The distribution characteristics of resilience are the basis for resilience design and analysis, such as test sample size determination and assessment model selection. In this paper, we propose a systematic resilience distribution identification and analysis (RDIA) method based on a system’s performance processes after disruptions. Typical performance degradation/recovery processes have linear, exponential, and trigonometric functions, and they have three key parameters: the maximum performance degradation, the degradation duration, and the recovery duration. Using the Monte Carlo method, these three key parameters are first sampled according to their corresponding probability density functions. Combining the sample results with the given performance function type, the system performance curves after disruptions can be obtained. Then the sample resilience is computed using a deterministic resilience measure and the resilience distribution can be determined through candidate distribution identification, parameter estimation, and a goodness-of-fit test. Finally, we apply our RDIA method to systems with typical performance processes, and both the orthogonal experiment method and the control variable method are used to investigate the resilience distribution laws. The results show that the resilience of these systems follows the Weibull distribution. An end-to-end communication system is also used to explain how to apply this method with simulation or test data in practice.

Considering the random characteristics of the disturbances that may occur on the engineering system, this paper proposes a test-based probabilistic resilience assessment methodology. It is a sampling-based test method, including five main steps: (1) the bottom-up disturbance identification; (2) the sample size determination according to the law of large numbers and the central limit theorem; (3) the sample stratification and selection based on proportion stratified sampling method; (4) resilience test and performance data collection; and (5) probabilistic resilience assessment, consisting of point estimates and confidence intervals. Besides, two probabilistic resilience measures are defined to reflect the average and the percentile characteristics of the system resilience under random disturbances, and the traditional performance normalization method is extended to adapt to different types of parameters. A wireless DC servo motor is used to verify the effectiveness of our methodology, and this generic methodology can be further applied in other engineering systems.