A methodology for probabilistic modeling of fatigue damage accumulation for single stress level and multistress level loading is proposed in this paper. The methodology uses linear damage accumulation model of Palmgren-Miner, a probabilistic - curve, and an approach for a one-to-one transformation of probability density functions to achieve the objective. The damage accumulation is modeled as a nonstationary process as both the expected damage accumulation and its variability change with time. The proposed methodology is then used for reliability prediction under single stress level and multistress level loading, utilizing dynamic statistical model of cumulative fatigue damage. The reliability prediction under both types of loading is demonstrated with examples. 1. Introduction Most of the mechanical components are subjected to fatigue due to random loading as well as constant amplitude loading during their usage. Fatigue is also recognized as one of the main reasons for failure of mechanical components [1]. This has led to a need for developing new approaches to predict the reliability and useful life of mechanical components, which are subjected to fatigue damage. This has been the primary focus of designers for many years, and the field still presents many challenges, even though extensive progress has been made in the past few decades [2]. Earlier models of fatigue damage accumulation reported in the literature focus on deterministic nature of the process whereas in practice, damage accumulation is of stochastic nature. This stochasticity results from the randomness in fatigue resistance of material as well as that of the loading process [3]. As a result of this, even under constant amplitude fatigue test at any given stress level, the fatigue life shows stochastic behavior with a specific distribution. The literature shows that fatigue life data follows either normal or log-normal distribution under constant amplitude or random loading [4–6]. Weibull distribution has also been reported to fit fatigue life data [7, 8], though there are no apparent physical or mathematical phenomenon explained for this [9]. Researchers have proposed different modeling approaches to the probabilistic damage accumulation paradigm. Shen et al. [3] developed a probabilistic distribution model of stochastic fatigue damage, wherein they have considered the randomness of loading process as well as the randomness of fatigue resistance of material by introducing a random variable of single cycle fatigue damage. Liu and Mahadevan [2] proposed a general methodology for
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