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Variable traffic conditions cause travel time uncertainty and further lead to time-varying accessibility. Most current studies do not fully consider fluctuations in accessibility and use complicated methods that likely overestimate the level of accessibility and hinder the application of accessibility measures. To address this issue, we utilized large-scale open-source data and proposed an interpretation of the reliability of accessibility concept that incorporates reliability, travel time uncertainty, and a cumulative opportunity measure. We examined the reliability of accessibility to Shenzhen, a major city in China, focusing on transit accessibility and job opportunities. The results demonstrate that the reliability of accessibility displays a bimodal distribution along urban railway lines and can be used to calculate the impact of urban railways in terms of punctuality. The new approach illustrates time-varying characteristics in the form of probabilities and provides further guidance on accessibility for governments. [ABSTRACT FROM AUTHOR]