Higher-order analysis of probabilistic long-term loss under nonstationary hazards

Yaohan Li, You Dong, Jing Qian

Research output: Journal article publicationJournal articleAcademic researchpeer-review

16 Citations (Scopus)


Quantification of hazard-induced losses plays a significant role in risk assessment and management of civil infrastructure subjected to hazards in a life-cycle context. A rational approach to assess long-term loss is of vital importance. The loss assessment associated with stationary hazard models and low-order moments (i.e., expectation and variance) has been widely investigated in previous studies. This paper proposes a novel approach for the higher-order analysis of long-term loss under both stationary and nonstationary hazards. An analytical approach based on the moment generating function is developed to assess the first four statistical moments of long-term loss under different stochastic models (e.g., homogeneous Poisson process, non-homogeneous Poisson process, renewal process). Based on the law of total expectation, the developed approach expands the application scope of the moment generating function to nonstationary models and higher-order moments (i.e., skewness and kurtosis). Furthermore, by employing the convolution technique, the proposed approach effectively addresses the difficulty of assessing higher-order moments in a renewal process. Besides the loss analysis, the mixed Poisson process, a relatively new stochastic model, is introduced to consider uncertainty springing from the stochastic occurrence rate. Two illustrative examples are presented to demonstrate practical implementations of the developed approach. Ultimately, the proposed framework could aid the decision-maker to select the optimal option by incorporating higher-order moments of long-term loss within the decision-making process.

Original languageEnglish
Article number107092
JournalReliability Engineering and System Safety
Publication statusPublished - Nov 2020


  • Discounted long-term loss
  • Life-cycle engineering
  • Moment generating function
  • Nonstationary stochastic process
  • Renewal process

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Industrial and Manufacturing Engineering


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