Aging stochastic theories

It may be noted that in this case the life expectancy of a surviving unit is at any time independent of N and t. This is equivalent to the assumption that the residual strength is equal to the initial strength, i.e., that no aging or deterioration has taken place in the stressed sample. The rate K of failure occurrence can be determined experimentally from the scatter of tb [4]. Using this assumption Kawabata and Blatz [5] developed a simple stochastic theory of creep failure. They argued that the first moments of tb for an ensemble of ruptured specimens should reveal whether or not K is independent of time. If K depends only on initial load and is independent of N the equation... 

Robertson et al. [1984] developed a stochastic model for predicting the kinetics of physical aging of polymer glasses. The equilibrium volume at a given temperature, the hole fraction, and the fluctuations in free volume were derived from the S-S cell-hole theory. The rate of volume changes was assumed to be related to the local free volume content thus, it varied from one region to the next according to a probability function. The model predictions compared favorably with the results from Kovacs laboratory. Its evolution and recent advances are discussed by Simha and Robertson in Chapter 4. 

The theory of stochastic processes and its apph-cations to reliability analysis have been discussed in several monographs (Aven and Jensen 1999, Tijms 2003). The cumulative damage models are popularly applied to the optimization of maintenance policies using the condition or age based criteria. Nakagawa (1976) formulated a preventive maintenance pohcy. 

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